Network Meta-Analysis

Author

Caio Vallio

Published

August 7, 2025

Abstract
A network meta-analysis of fibromyalgia treatments
Code 
# Install packages
# install.packages("netmeta")
# install.packages("readxl")
library(netmeta)
library(readxl)
library(dplyr)
library(tidyr)

1 NMA for continuous outcomes

Note

Please: Select an outcome to proceed.

Code 
# Read data
data_pim <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "P | Im") |>
    mutate(
        Mean1 = as.numeric(Mean1),
        Mean2 = as.numeric(Mean2),
        SD1 = as.numeric(SD1),
        SD2 = as.numeric(SD2)
    )


# Transform to contrast-based
pw <- pairwise(
    treat = list(Treat1, Treat2),
    n = list(N1, N2),
    mean = list(Mean1, Mean2),
    sd = list(SD1, SD2),
    studlab = StudyID,
    data = data_pim
)

# Check network connections
net_con <- netconnection(pw)
net_con
Number of studies: k = 33
Number of pairwise comparisons: m = 33
Number of treatments: n = 12
Number of designs: d = 11
Number of networks: 2

Details on subnetworks: 
 subnetwork  k  m n
          1  5  5 4
          2 28 28 8


There are two sub-networks:

Subnet 1:
- 5 studies
- 5 comparisons
- 4 treatments

Subnet 2:
- 28 studies
- 28 comparisons
- 8 treatments

Tip

There are two treatment sub-networks that do not connect.



Note

Please: Select the treatment sub-networks before proceeding.

Select the procedures performed

Important

The first subnet contains 5 studies, 5 comparisons and 4 treatments.

Code 
# Filter data for subnet 1
sr1 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 1)

# Display comparison table
sr1



Code 
# Unique treatments in subnet 1
unique_treat1 <- sr1$treat1 |> unique()
unique_treat2 <- sr1$treat2 |> unique()

# Combination of all unique treatments
trat_sr1 <- unique(c(unique_treat1, unique_treat2))
print(trat_sr1)
[1] "MnT"  "Bal"  "Cry"  "WlNi"
Code 
# Total number of treatments
length(trat_sr1)
[1] 4



Code 
# Filter pairwise object only for comparisons within subnet 1
pw_pim_sr1 <- pw %>%
    filter(treat1 %in% trat_sr1 & treat2 %in% trat_sr1)

# Number of comparisons in subnet 1
nrow(pw_pim_sr1)
[1] 5



Code 
# Fit NMA model for subnet 1
nma_sr1 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_pim_sr1,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    sm = "MD", # can be "MD" or "SMD"
    ref = "WlNi" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr1)
Number of studies: k = 5
Number of pairwise comparisons: m = 5
Number of observations: o = 232
Number of treatments: n = 4
Number of designs: d = 3

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
          MD             95%-CI     z  p-value
Bal  -1.2500 [-2.2645; -0.2355] -2.41   0.0157
Cry  -6.5000 [-8.0223; -4.9777] -8.37 < 0.0001
MnT   0.0100 [-1.6642;  1.6842]  0.01   0.9907
WlNi       .                  .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.4690; tau = 0.6849; I^2 = 58.5% [0.0%; 88.2%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           4.82    2  0.0898
Within designs  4.82    2  0.0898
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(
    nma_sr1,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 1 (P | Im)



Code 
# Detailed model summary
summary(nma_sr1)
Original data:

            treat1 treat2      TE   seTE
Albers2018     MnT   WlNi  0.0100 0.5105
Buskila2001    Bal   WlNi -1.7000 0.4818
Neumann2001    Bal   WlNi -0.2100 0.5836
Ozkurt2011     Bal   WlNi -1.8500 0.6816
Kiyak2022      Cry   WlNi -6.5000 0.3664

Number of treatment arms (by study):
            narms
Albers2018      2
Buskila2001     2
Neumann2001     2
Ozkurt2011      2
Kiyak2022       2

Results (random effects model):

            treat1 treat2      MD             95%-CI
Albers2018     MnT   WlNi  0.0100 [-1.6642;  1.6842]
Buskila2001    Bal   WlNi -1.2500 [-2.2645; -0.2355]
Neumann2001    Bal   WlNi -1.2500 [-2.2645; -0.2355]
Ozkurt2011     Bal   WlNi -1.2500 [-2.2645; -0.2355]
Kiyak2022      Cry   WlNi -6.5000 [-8.0223; -4.9777]

Number of studies: k = 5
Number of pairwise comparisons: m = 5
Number of observations: o = 232
Number of treatments: n = 4
Number of designs: d = 3

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
          MD             95%-CI     z  p-value
Bal  -1.2500 [-2.2645; -0.2355] -2.41   0.0157
Cry  -6.5000 [-8.0223; -4.9777] -8.37 < 0.0001
MnT   0.0100 [-1.6642;  1.6842]  0.01   0.9907
WlNi       .                  .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.4690; tau = 0.6849; I^2 = 58.5% [0.0%; 88.2%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           4.82    2  0.0898
Within designs  4.82    2  0.0898
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr1)

Forest plot of treatment effects for Subnet 1



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr1, ci = TRUE)
League table (random effects model):
                                                      
                        Bal                          .
  5.2500 [ 3.4206;  7.0794]                        Cry
 -1.2600 [-3.2176;  0.6976] -6.5100 [-8.7728; -4.2472]
 -1.2500 [-2.2645; -0.2355] -6.5000 [-8.0223; -4.9777]
                                                     
                         . -1.2500 [-2.2645; -0.2355]
                         . -6.5000 [-8.0223; -4.9777]
                       MnT  0.0100 [-1.6642;  1.6842]
 0.0100 [-1.6642;  1.6842]                       WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr1 <- netrank(nma_sr1, small.values = "good")
print(ranking_sr1)
     P-score
Cry   1.0000
Bal   0.6295
MnT   0.1996
WlNi  0.1708



Code 
# Rankogram
ran_sr1 <- rankogram(nma_sr1)
plot(ran_sr1)

Rankogram of treatments for Subnet 1



Code 
# Design decomposition
decomp_sr1 <- decomp.design(nma_sr1)
print(decomp_sr1)
Q statistics to assess homogeneity / consistency

                   Q df p-value
Total           4.82  2  0.0898
Within designs  4.82  2  0.0898
Between designs 0.00  0      --

Design-specific decomposition of within-designs Q statistic

   Design    Q df p-value
 WlNi:Bal 4.82  2  0.0898

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 0.00  0      --     0.6849      0.4690



Code 
# Node-splitting analysis to detect inconsistency
split_sr1 <- netsplit(nma_sr1, show = "all")
print(split_sr1)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop     nma  direct  indir. Diff z p-value
    Bal:Cry 0    0  5.2500       .  5.2500    . .       .
    Bal:MnT 0    0 -1.2600       . -1.2600    . .       .
   Bal:WlNi 3 1.00 -1.2500 -1.2500       .    . .       .
    Cry:MnT 0    0 -6.5100       . -6.5100    . .       .
   Cry:WlNi 1 1.00 -6.5000 -6.5000       .    . .       .
   MnT:WlNi 1 1.00  0.0100  0.0100       .    . .       .

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr1)

Forest plot of node-splitting for Subnet 1



Code 
# Heatmap
netheat(nma_sr1)



Code 
# Funnel plot
funnel(nma_sr1,
    order = "WlNi",
)

Funnel plot for Subnet 1 (P | Im)





Select the procedures performed

Important

The second subnet is more robust, containing 28 studies, 28 comparisons and 8 treatments. This is the main analysis network.

Code 
# Filter data for subnet 2
sr2 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 2)

# Display first rows of comparison table
sr2 |> head()



Code 
# Unique treatments in subnet 2
unique_treat1_sr2 <- sr2$treat1 |> unique()
print(unique_treat1_sr2)
[1] "Acu"  "CBT"  "rTMS" "tDCS" "PbT"  "Elec" "MfT"
Code 
unique_treat2_sr2 <- sr2$treat2 |> unique()
print(unique_treat2_sr2)
[1] "PlaSh" "tDCS"
Code 
# Combination of all unique treatments
trat_sr2 <- unique(c(unique_treat1_sr2, unique_treat2_sr2))
print(trat_sr2)
[1] "Acu"   "CBT"   "rTMS"  "tDCS"  "PbT"   "Elec"  "MfT"   "PlaSh"
Code 
# Total number of treatments
length(trat_sr2)
[1] 8



Code 
# Filter pairwise object only for comparisons within subnet 2
pw_pim_sr2 <- pw %>%
    filter(treat1 %in% trat_sr2 & treat2 %in% trat_sr2)

# Number of comparisons in subnet 2
nrow(pw_pim_sr2)
[1] 28
Code 
# Number of unique studies
length(unique(pw_pim_sr2$studlab))
[1] 28



Code 
# Fit NMA model for subnet 2
nma_sr2 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_pim_sr2,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "PlaSh" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr2)
Number of studies: k = 28
Number of pairwise comparisons: m = 28
Number of observations: o = 1074
Number of treatments: n = 8
Number of designs: d = 8

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'PlaSh'):
           MD             95%-CI     z  p-value
Acu   -0.0541 [-1.3868;  1.2787] -0.08   0.9366
CBT   -1.3351 [-2.8528;  0.1826] -1.72   0.0847
Elec  -2.8500 [-4.8458; -0.8542] -2.80   0.0051
MfT   -0.4900 [-2.2447;  1.2647] -0.55   0.5842
PbT   -2.3053 [-3.5414; -1.0691] -3.66   0.0003
PlaSh       .                  .     .        .
rTMS  -1.2459 [-1.8859; -0.6059] -3.82   0.0001
tDCS  -1.3183 [-1.8843; -0.7523] -4.57 < 0.0001

Quantifying heterogeneity / inconsistency:
tau^2 = 0.5164; tau = 0.7186; I^2 = 65.7% [46.3%; 78.1%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f.  p-value
Total           61.3   21 < 0.0001
Within designs  60.6   20 < 0.0001
Between designs  0.7    1   0.4031

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(nma_sr2,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 2 (P | Im)



Code 
# Detailed model summary
summary(nma_sr2)
Original data:

              treat1 treat2      TE   seTE
Assefi2005       Acu  PlaSh  0.6200 0.4939
Babu2007         CBT  PlaSh -1.7000 1.0070
Boyer2014      PlaSh   rTMS -0.3000 0.7445
Brietzke2019   PlaSh   tDCS  1.7900 0.3988
Cheng2019      PlaSh   rTMS  0.9000 1.3742
Curatolo2017   PlaSh   tDCS  3.2000 0.8829
Fagerlund2015  PlaSh   tDCS  0.9600 0.5231
Fregni2006     PlaSh   tDCS -0.2800 0.8557
Gur2002a         PbT  PlaSh -2.0900 0.4526
Gur2002b         PbT  PlaSh -2.5700 0.6087
Khedr2017      PlaSh   tDCS  2.0000 0.3598
Lauretti2013    Elec  PlaSh -2.8500 0.7215
Lee2012        PlaSh   rTMS  0.5600 1.3631
Maestu2013     PlaSh   rTMS -0.4400 0.5614
Mendonça2011   PlaSh   tDCS  2.1800 1.1082
Mhalla2011     PlaSh   rTMS  1.8300 0.3834
Oka2019          MfT  PlaSh -0.4900 0.5340
Passard2007    PlaSh   rTMS  1.4400 0.5723
Short2011      PlaSh   rTMS  1.0800 0.8475
Stival2013       Acu  PlaSh -1.1000 0.8145
Tekin2014      PlaSh   rTMS  2.6300 0.4230
Valle2009      PlaSh   tDCS  1.2200 0.7126
Yagci2014      PlaSh   rTMS  1.1700 1.0040
deMelo2020     PlaSh   tDCS -0.3000 1.1882
Forogh2021      rTMS   tDCS -1.0600 0.7943
Caumo2023      PlaSh   tDCS  0.8100 0.1056
Gungomus2023     CBT  PlaSh -1.1000 0.6852
Loreti2023     PlaSh   tDCS  1.9900 0.4623

Number of treatment arms (by study):
              narms
Assefi2005        2
Babu2007          2
Boyer2014         2
Brietzke2019      2
Cheng2019         2
Curatolo2017      2
Fagerlund2015     2
Fregni2006        2
Gur2002a          2
Gur2002b          2
Khedr2017         2
Lauretti2013      2
Lee2012           2
Maestu2013        2
Mendonça2011      2
Mhalla2011        2
Oka2019           2
Passard2007       2
Short2011         2
Stival2013        2
Tekin2014         2
Valle2009         2
Yagci2014         2
deMelo2020        2
Forogh2021        2
Caumo2023         2
Gungomus2023      2
Loreti2023        2

Results (random effects model):

              treat1 treat2      MD             95%-CI
Assefi2005       Acu  PlaSh -0.0541 [-1.3868;  1.2787]
Babu2007         CBT  PlaSh -1.3351 [-2.8528;  0.1826]
Boyer2014      PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Brietzke2019   PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Cheng2019      PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Curatolo2017   PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Fagerlund2015  PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Fregni2006     PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Gur2002a         PbT  PlaSh -2.3053 [-3.5414; -1.0691]
Gur2002b         PbT  PlaSh -2.3053 [-3.5414; -1.0691]
Khedr2017      PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Lauretti2013    Elec  PlaSh -2.8500 [-4.8458; -0.8542]
Lee2012        PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Maestu2013     PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Mendonça2011   PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Mhalla2011     PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Oka2019          MfT  PlaSh -0.4900 [-2.2447;  1.2647]
Passard2007    PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Short2011      PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Stival2013       Acu  PlaSh -0.0541 [-1.3868;  1.2787]
Tekin2014      PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
Valle2009      PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Yagci2014      PlaSh   rTMS  1.2459 [ 0.6059;  1.8859]
deMelo2020     PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Forogh2021      rTMS   tDCS  0.0724 [-0.7466;  0.8914]
Caumo2023      PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]
Gungomus2023     CBT  PlaSh -1.3351 [-2.8528;  0.1826]
Loreti2023     PlaSh   tDCS  1.3183 [ 0.7523;  1.8843]

Number of studies: k = 28
Number of pairwise comparisons: m = 28
Number of observations: o = 1074
Number of treatments: n = 8
Number of designs: d = 8

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'PlaSh'):
           MD             95%-CI     z  p-value
Acu   -0.0541 [-1.3868;  1.2787] -0.08   0.9366
CBT   -1.3351 [-2.8528;  0.1826] -1.72   0.0847
Elec  -2.8500 [-4.8458; -0.8542] -2.80   0.0051
MfT   -0.4900 [-2.2447;  1.2647] -0.55   0.5842
PbT   -2.3053 [-3.5414; -1.0691] -3.66   0.0003
PlaSh       .                  .     .        .
rTMS  -1.2459 [-1.8859; -0.6059] -3.82   0.0001
tDCS  -1.3183 [-1.8843; -0.7523] -4.57 < 0.0001

Quantifying heterogeneity / inconsistency:
tau^2 = 0.5164; tau = 0.7186; I^2 = 65.7% [46.3%; 78.1%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f.  p-value
Total           61.3   21 < 0.0001
Within designs  60.6   20 < 0.0001
Between designs  0.7    1   0.4031

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr2)

Forest plot of treatment effects for Subnet 2



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr2, ci = TRUE)
League table (random effects model):
                                                      
                        Acu                          .
  1.2810 [-0.7388;  3.3008]                        CBT
  2.7959 [ 0.3961;  5.1958]  1.5149 [-0.9924;  4.0222]
  0.4359 [-1.7675;  2.6394] -0.8451 [-3.1651;  1.4749]
  2.2512 [ 0.4335;  4.0689]  0.9702 [-0.9872;  2.9276]
 -0.0541 [-1.3868;  1.2787] -1.3351 [-2.8528;  0.1826]
  1.1918 [-0.2866;  2.6703] -0.0892 [-1.7363;  1.5579]
  1.2643 [-0.1836;  2.7122] -0.0168 [-1.6366;  1.6031]
                                                      
                          .                          .
                          .                          .
                       Elec                          .
 -2.3600 [-5.0175;  0.2975]                        MfT
 -0.5447 [-2.8923;  1.8029]  1.8153 [-0.3312;  3.9617]
 -2.8500 [-4.8458; -0.8542] -0.4900 [-2.2447;  1.2647]
 -1.6041 [-3.7000;  0.4918]  0.7559 [-1.1119;  2.6237]
 -1.5317 [-3.6062;  0.5428]  0.8283 [-1.0154;  2.6721]
                                                      
                          . -0.0541 [-1.3868;  1.2787]
                          . -1.3351 [-2.8528;  0.1826]
                          . -2.8500 [-4.8458; -0.8542]
                          . -0.4900 [-2.2447;  1.2647]
                        PbT -2.3053 [-3.5414; -1.0691]
 -2.3053 [-3.5414; -1.0691]                      PlaSh
 -1.0594 [-2.4514;  0.3326]  1.2459 [ 0.6059;  1.8859]
 -0.9869 [-2.3465;  0.3726]  1.3183 [ 0.7523;  1.8843]
                                                     
                         .                          .
                         .                          .
                         .                          .
                         .                          .
                         .                          .
 1.1307 [ 0.4612;  1.8002]  1.4065 [ 0.8208;  1.9921]
                      rTMS -1.0600 [-3.1593;  1.0393]
 0.0724 [-0.7466;  0.8914]                       tDCS

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr2 <- netrank(nma_sr2, small.values = "good")
print(ranking_sr2)
      P-score
Elec   0.9088
PbT    0.8510
tDCS   0.5685
CBT    0.5639
rTMS   0.5361
MfT    0.2985
Acu    0.1582
PlaSh  0.1151



Code 
# Rankogram
ran_sr2 <- rankogram(nma_sr2)
plot(ran_sr2)

Rankogram of treatments for Subnet 2



Code 
# Design decomposition
decomp_sr2 <- decomp.design(nma_sr2)
print(decomp_sr2)
Q statistics to assess homogeneity / consistency

                    Q df  p-value
Total           61.30 21 < 0.0001
Within designs  60.60 20 < 0.0001
Between designs  0.70  1   0.4031

Design-specific decomposition of within-designs Q statistic

     Design     Q df p-value
 PlaSh:tDCS 30.32  9  0.0004
 PlaSh:rTMS 26.38  8  0.0009
  PlaSh:Acu  3.26  1  0.0710
  PlaSh:PbT  0.40  1  0.5269
  PlaSh:CBT  0.24  1  0.6223

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from 0.4031)

 Detached design    Q df p-value
      PlaSh:rTMS 0.00  0      --
      PlaSh:tDCS 0.00  0      --
       rTMS:tDCS 0.00  0      --

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 1.30  1  0.2544     0.7336      0.5382



Code 
# Node-splitting analysis to detect inconsistency
split_sr2 <- netsplit(nma_sr2)
print(split_sr2)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison  k prop     nma  direct  indir.    Diff     z p-value
 rTMS:PlaSh  9 0.91 -1.2459 -1.1307 -2.4665  1.3357  1.15  0.2509
 tDCS:PlaSh 10 0.93 -1.3183 -1.4065 -0.0707 -1.3357 -1.15  0.2509
  rTMS:tDCS  1 0.15  0.0724 -1.0600  0.2757 -1.3357 -1.15  0.2509

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr2)

Forest plot of node-splitting for Subnet 2



Code 
# Heatmap
netheat(nma_sr2)

Heatmap of contribution matrix for Subnet 2



Code 
# Funnel plot
funnel(nma_sr2,
    order = "PlaSh",
)

Funnel plot for Subnet 2 (P | Im)





Code 
# Read data
data_psh <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "P | Sh") |>
    mutate(
        Mean1 = as.numeric(Mean1),
        Mean2 = as.numeric(Mean2),
        Mean3 = as.numeric(Mean3),
        SD1 = as.numeric(SD1),
        SD2 = as.numeric(SD2),
        SD3 = as.numeric(SD3),
    )


# Transform to contrast-based
pw <- pairwise(
    treat = list(Treat1, Treat2, Treat3),
    n = list(N1, N2, N3),
    mean = list(Mean1, Mean2, Mean3),
    sd = list(SD1, SD2, SD3),
    studlab = StudyID,
    data = data_psh,
    sm      = "MD"
)

# Check network connections
net_con <- netconnection(pw)
net_con
Number of studies: k = 106
Number of pairwise comparisons: m = 120
Number of treatments: n = 27
Number of designs: d = 53
Number of networks: 1


There are network:

Network:
- 106 studies
- 120 comparisons
- 27 treatments



Tip

The network is fully connected.

1.0.1 Network

Select the procedures performed

Important

The network contain 106 studies, 120 comparisons and 28 treatments.

Code 
# Filter data for network
sr <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
)


# Display comparison table
sr



Code 
# Unique treatments in network
unique_treat_sr1 <- sr$treat1 |> unique()
print(unique_treat_sr1)
 [1] "MnT"    "McT"    "WBV"    "MfT"    "ManTh"  "AqET"   "CBT"    "ReET"  
 [9] "Bal"    "Acu"    "AeET"   "FlET"   "MiET"   "MasTh"  "PbTh"   "rTMS"  
[17] "tDCS"   "DryN"   "Elec"   "MasT"   "HtT"    "Cry"    "PbT"    "FlexEx"
Code 
unique_treat_sr2 <- sr$treat2 |> unique()
print(unique_treat_sr2)
 [1] "WlNi"   "WBV"    "PlaSh"  "Bal"    "FlET"   "AqET"   "ReET"   "ManTh" 
 [9] "CBT"    "McT"    "MasT"   "Elec"   "MiET"   "Plt"    "HtT"    "FlexEx"
Code 
# Combination of all unique treatments
trat_sr <- unique(c(unique_treat_sr1, unique_treat_sr2))
print(trat_sr)
 [1] "MnT"    "McT"    "WBV"    "MfT"    "ManTh"  "AqET"   "CBT"    "ReET"  
 [9] "Bal"    "Acu"    "AeET"   "FlET"   "MiET"   "MasTh"  "PbTh"   "rTMS"  
[17] "tDCS"   "DryN"   "Elec"   "MasT"   "HtT"    "Cry"    "PbT"    "FlexEx"
[25] "WlNi"   "PlaSh"  "Plt"
Code 
# Total number of treatments
length(trat_sr)
[1] 27



Code 
# Filter pairwise object only for comparisons within network
pw_psh <- pw %>%
    filter(treat1 %in% trat_sr & treat2 %in% trat_sr)

# Number of comparisons in network
nrow(pw_psh)
[1] 120



Code 
# Fit NMA model for network
nma_sr <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_psh,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "WlNi" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr)
Number of studies: k = 106
Number of pairwise comparisons: m = 120
Number of observations: o = 6143
Number of treatments: n = 27
Number of designs: d = 53

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD             95%-CI     z  p-value
Acu    -1.3839 [-2.5896; -0.1783] -2.25   0.0245
AeET   -1.2086 [-2.0827; -0.3346] -2.71   0.0067
AqET   -1.8413 [-2.7839; -0.8986] -3.83   0.0001
Bal    -2.8847 [-4.3709; -1.3984] -3.80   0.0001
CBT    -0.7147 [-1.2553; -0.1740] -2.59   0.0096
Cry    -1.9000 [-4.2920;  0.4920] -1.56   0.1195
DryN   -3.3305 [-4.8468; -1.8142] -4.31 < 0.0001
Elec   -1.6758 [-3.0833; -0.2683] -2.33   0.0196
FlET   -0.5039 [-1.6815;  0.6738] -0.84   0.4017
FlexEx -0.5589 [-2.6868;  1.5689] -0.51   0.6067
HtT    -1.2291 [-3.5457;  1.0874] -1.04   0.2984
ManTh  -2.5304 [-4.5731; -0.4877] -2.43   0.0152
MasT   -1.3100 [-2.6708;  0.0508] -1.89   0.0592
MasTh  -3.3378 [-5.2250; -1.4506] -3.47   0.0005
McT    -1.2167 [-1.8929; -0.5406] -3.53   0.0004
MfT    -1.8893 [-3.4052; -0.3733] -2.44   0.0146
MiET   -0.8110 [-1.5615; -0.0606] -2.12   0.0342
MnT    -1.6825 [-3.1520; -0.2131] -2.24   0.0248
PbT    -2.4965 [-5.0988;  0.1058] -1.88   0.0601
PbTh   -4.7147 [-7.9324; -1.4970] -2.87   0.0041
PlaSh  -0.1965 [-1.2575;  0.8645] -0.36   0.7166
Plt    -1.7711 [-3.2552; -0.2870] -2.34   0.0193
ReET   -1.2674 [-2.3388; -0.1960] -2.32   0.0204
rTMS   -1.4710 [-2.9354; -0.0066] -1.97   0.0490
tDCS   -1.5891 [-3.0801; -0.0980] -2.09   0.0367
WBV    -1.7159 [-3.2907; -0.1411] -2.14   0.0327
WlNi         .                  .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 1.1798; tau = 1.0862; I^2 = 83.6% [80.3%; 86.4%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           531.18   87 < 0.0001
Within designs  285.41   53 < 0.0001
Between designs 245.77   34 < 0.0001

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(nma_sr,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Network (P | Sh)



Code 
# Detailed model summary
summary(nma_sr)
Original data (with adjusted standard errors for multi-arm studies):

                        treat1 treat2      TE   seTE seTE.adj narms multiarm
Albers2018                 MnT   WlNi -2.0900 0.6365   1.2589     2         
Alentorn-Geli2008          McT    WBV  1.8100 0.7468   1.5867     3        *
Alentorn-Geli2008          McT   WlNi -1.2900 0.7892   1.6431     3        *
Alentorn-Geli2008          WBV   WlNi -3.1000 0.8292   1.7054     3        *
Alfano2001                 MfT  PlaSh -0.6200 0.5434   1.2145     2         
Alptug2023               ManTh   WlNi -3.4000 0.6919   1.2878     2         
Altan2004                 AqET    Bal  0.1800 0.6504   1.2660     2         
Ang2010                    CBT   WlNi  0.1000 0.6426   1.2620     2         
Arakaki2021               FlET   ReET  2.1800 0.8189   1.3603     2         
Ardic2007                  Bal   WlNi -4.2500 0.6931   1.2885     2         
Assefi2005                 Acu  PlaSh  0.6100 0.5069   1.1986     2         
Assis2006                 AeET   AqET  0.5000 0.5320   1.2095     2         
Assumpçao2018             FlET   ReET  0.2000 1.0224   1.8271     3        *
Assumpçao2018             FlET   WlNi -1.8000 1.0018   1.7937     3        *
Assumpçao2018             ReET   WlNi -2.0000 1.0408   1.8591     3        *
Atan2020                  MiET   WlNi -3.6000 0.4812   1.1880     2         
Audoux2023               ManTh  MasTh  1.8000 0.8445   1.3759     2         
Baelz2022                  Acu  PlaSh -0.7000 0.8905   1.4046     2         
Barranengoa-Cuadra2021     CBT   WlNi -2.6000 0.3939   1.1554     2         
Bircan2008                AeET   ReET -0.4600 0.6518   1.2667     2         
Boggiss2022                CBT   PbTh  4.0000 1.1997   1.6184     2         
Bongi2010                  CBT   WlNi -2.8300 0.5312   1.2091     2         
Bongi2012                  CBT    McT  0.6500 0.3294   1.1351     2         
Bourgault2015              McT   WlNi -0.1300 0.5563   1.2204     2         
Boyer2014                PlaSh   rTMS -1.2000 0.8003   1.3492     2         
Bressan2008               AeET   FlET  0.4700 1.1193   1.5597     2         
Brietzke2019             PlaSh   tDCS  2.4800 0.3776   1.1500     2         
Calandre2009              AqET   WlNi  0.0000 0.5134   1.2014     2         
Cao2020                    Acu   MasT -0.2200 0.3452   1.1397     2         
Carretero2009            PlaSh   rTMS -1.2000 0.8010   1.3496     2         
Carson2010                 McT   WlNi -1.0200 0.5934   1.2377     2         
Casanueva2014             DryN   WlNi -1.5000 0.3493   1.1410     2         
Castro-Sanchez2019        DryN   MasT -2.9300 0.4500   1.1757     2         
Castro-Sanchez2020        DryN   Elec -2.6800 0.4366   1.1707     2         
Caumo2023                PlaSh   tDCS  1.6600 0.1140   1.0922     2         
Ceballos-Laita2020         McT   MiET -2.1600 0.8359   1.3706     2         
Colbert1999                MfT  PlaSh -1.8100 0.8309   1.3676     2         
Collado-Mateo2017         MiET   WlNi -1.3300 0.4507   1.1760     2         
Coste2021                  MnT  PlaSh -0.2900 0.6548   1.2683     2         
Da Costa2005              MiET   WlNi -0.9400 0.6066   1.2441     2         
Dailey2019                Elec  PlaSh -1.3000 0.3488   1.1408     2         
daSilva2008               AqET   Elec  3.2000 1.1908   1.6118     2         
deMedeiros2020            AqET    Plt -0.6000 0.6063   1.2440     2         
Ekici2008                 MasT    Plt  0.4200 0.4772   1.1864     2         
Ekici2017                 MasT    Plt  0.3800 0.5255   1.2067     2         
Espi-Lopes2016            MiET   WlNi -0.2800 0.9255   1.4270     2         
Evcik2002                  Bal   WlNi -3.4000 1.7701   2.0768     2         
Fernandes2016             AeET   AqET  0.5000 0.6362   1.2588     2         
Fitzgibbon2018           PlaSh   rTMS  0.4800 0.8369   1.3712     2         
Franco2023                AeET    Plt  1.2000 0.5585   1.2214     2         
Friedberg2019              CBT   WlNi -0.5500 0.3803   1.1509     2         
Giannotti2014              McT   WlNi -0.2500 0.8210   1.3616     2         
Goldway2019                CBT  PlaSh  0.8200 0.7901   1.3432     2         
Gomez-Hernandez2019       AeET   MiET  1.0100 0.1025   1.0910     2         
Gowans1999                 McT   WlNi -0.3000 0.6841   1.2837     2         
Gunther1994                Bal    CBT -1.1200 1.1934   1.6137     2         
Hargrove2012             PlaSh   tDCS  1.4000 0.6895   1.2865     2         
Harris2005                 Acu  PlaSh -0.3100 0.6954   1.2897     2         
Harte2013                  Acu  PlaSh  0.5800 0.5773   1.2301     2         
Hsu2010                    CBT   WlNi -0.5800 0.6751   1.2789     2         
Izquierdo-Alventosa2020   MiET   WlNi -0.1200 0.7797   1.3371     2         
Jamison2021               Elec  PlaSh -0.6200 0.2762   1.1208     2         
Jensen2012                 CBT   WlNi -1.0900 0.8702   1.3918     2         
Jones2002                  McT   ReET  0.5300 0.5654   1.2246     2         
Jones2012                  CBT    McT  1.1000 0.5460   1.2157     2         
Karatay2018                Acu  PlaSh -2.5200 0.5807   1.2317     2         
Kayo2012                  AeET   ReET -0.9700 0.7347   1.6206     3        *
Kayo2012                  AeET   WlNi -1.6000 0.7111   1.5877     3        *
Kayo2012                  ReET   WlNi -0.6300 0.6963   1.5685     3        *
Lami2018                   CBT   WlNi -0.0800 0.3222   1.1330     2         
Lauche2016                MasT  PlaSh -0.9200 0.4103   1.1611     2         
Lee2024                    CBT    McT -0.5000 0.3579   1.1436     2         
Lopes-Rodrigues2012       AqET   FlET -2.5300 0.5685   1.2260     2         
Lopes-Rodrigues2013       AqET   FlET -2.1600 0.4565   1.1782     2         
Luciano2014                CBT   WlNi -1.7700 0.2840   1.1227     2         
Lynch2012                  McT   WlNi -1.5700 0.3863   1.1528     2         
Maestu2013               PlaSh   rTMS  2.0000 0.6998   1.2921     2         
McCrae2019                 CBT   WlNi -0.4900 0.6214   1.2514     2         
Menzies2014                CBT   WlNi -0.5000 0.5384   1.2123     2         
Mhalla2011               PlaSh   rTMS  2.1200 0.3835   1.1519     2         
Mingorance2021.2           WBV   WlNi -0.5100 0.1736   1.1000     2         
Mist2018                   Acu    CBT -1.6000 0.1918   1.1030     2         
Nadal-Nicolas2020         MasT  PlaSh -2.9000 0.9876   1.4681     2         
Norrengaard1997           AeET    HtT  1.0000 1.1510   2.0716     3        *
Norrengaard1997           AeET   MiET  1.0000 1.1426   2.0454     3        *
Norrengaard1997            HtT   MiET  0.0000 0.5714   1.3535     3        *
Oka2019                    MfT  PlaSh -0.5500 0.6779   1.2804     2         
Paolucci2016               MfT  PlaSh -2.5000 0.4369   1.1708     2         
Paolucci2022               CBT   MiET -1.5000 0.9648   1.4528     2         
Park2021                  FlET   ReET -0.0400 0.6996   1.2920     2         
Parra-Delgado2013          CBT   WlNi -0.0600 0.1291   1.0939     2         
Redondo2004                CBT   MiET  0.4000 0.8083   1.3540     2         
Rivera2018                 Cry   WlNi -1.9000 0.5565   1.2204     2         
Rodriguez-Mansilla2021     McT   MiET -0.6300 0.5229   1.4766     3        *
Rodriguez-Mansilla2021    MiET   WlNi -0.5200 0.4364   1.3981     3        *
Rodriguez-Mansilla2021     McT   WlNi -1.1500 0.5830   1.5501     3        *
Ruaro2014                  PbT  PlaSh -2.3000 0.5385   1.2124     2         
Samartin-Veiga2022       PlaSh   tDCS  0.3100 0.7259   1.3064     2         
Sarmento2020               McT  PlaSh -3.7000 0.8544   1.3820     2         
Schachter2003             AeET   WlNi -1.2600 0.5078   1.1990     2         
Schulze2023             FlexEx  MasTh  2.4500 0.2841   1.3761     3        *
Schulze2023              MasTh   WlNi -2.6800 0.2735   1.3697     3        *
Schulze2023             FlexEx   WlNi -0.2300 0.2841   1.3761     3        *
Sencan2004                AeET  PlaSh -2.1500 0.4530   1.1769     2         
Sevimli2015               AeET   AqET  0.0200 0.2773   1.3607     3        *
Sevimli2015               AeET   MiET -2.4200 0.3318   1.3960     3        *
Sevimli2015               AqET   MiET -2.4400 0.3388   1.4013     3        *
Silva2019                  CBT   ReET  1.0400 0.5562   1.2203     2         
Sutbeyaz2009               MfT  PlaSh -2.7600 0.4486   1.1752     2         
Tanwar2020               PlaSh   rTMS  3.9000 0.2989   1.1266     2         
To2017                   PlaSh   tDCS  0.8100 0.4671   1.1824     2         
Tomas-Carus2007b&c        AqET   WlNi -2.0000 0.7472   1.3184     2         
Torres2015                 CBT    MnT  1.6700 0.5133   1.2014     2         
Udina-Cortés2020          Elec  PlaSh -1.9000 0.5940   1.2380     2         
Ugurlu2017                 Acu  PlaSh -2.8900 0.4682   1.1828     2         
Valim2003                 AeET   FlET  0.3000 0.6728   1.2777     2         
Vas2016                    Acu  PlaSh -1.4800 0.3803   1.1509     2         
Verkaik2013                CBT   WlNi  0.0400 0.5154   1.2023     2         
Wicksell2013               CBT   WlNi -0.4000 0.3706   1.1477     2         
Wong2018                   McT   WlNi -1.7000 0.5833   1.2329     2         

Number of treatment arms (by study):
                        narms
Albers2018                  2
Alentorn-Geli2008           3
Alfano2001                  2
Alptug2023                  2
Altan2004                   2
Ang2010                     2
Arakaki2021                 2
Ardic2007                   2
Assefi2005                  2
Assis2006                   2
Assumpçao2018               3
Atan2020                    2
Audoux2023                  2
Baelz2022                   2
Barranengoa-Cuadra2021      2
Bircan2008                  2
Boggiss2022                 2
Bongi2010                   2
Bongi2012                   2
Bourgault2015               2
Boyer2014                   2
Bressan2008                 2
Brietzke2019                2
Calandre2009                2
Cao2020                     2
Carretero2009               2
Carson2010                  2
Casanueva2014               2
Castro-Sanchez2019          2
Castro-Sanchez2020          2
Caumo2023                   2
Ceballos-Laita2020          2
Colbert1999                 2
Collado-Mateo2017           2
Coste2021                   2
Da Costa2005                2
Dailey2019                  2
daSilva2008                 2
deMedeiros2020              2
Ekici2008                   2
Ekici2017                   2
Espi-Lopes2016              2
Evcik2002                   2
Fernandes2016               2
Fitzgibbon2018              2
Franco2023                  2
Friedberg2019               2
Giannotti2014               2
Goldway2019                 2
Gomez-Hernandez2019         2
Gowans1999                  2
Gunther1994                 2
Hargrove2012                2
Harris2005                  2
Harte2013                   2
Hsu2010                     2
Izquierdo-Alventosa2020     2
Jamison2021                 2
Jensen2012                  2
Jones2002                   2
Jones2012                   2
Karatay2018                 2
Kayo2012                    3
Lami2018                    2
Lauche2016                  2
Lee2024                     2
Lopes-Rodrigues2012         2
Lopes-Rodrigues2013         2
Luciano2014                 2
Lynch2012                   2
Maestu2013                  2
McCrae2019                  2
Menzies2014                 2
Mhalla2011                  2
Mingorance2021.2            2
Mist2018                    2
Nadal-Nicolas2020           2
Norrengaard1997             3
Oka2019                     2
Paolucci2016                2
Paolucci2022                2
Park2021                    2
Parra-Delgado2013           2
Redondo2004                 2
Rivera2018                  2
Rodriguez-Mansilla2021      3
Ruaro2014                   2
Samartin-Veiga2022          2
Sarmento2020                2
Schachter2003               2
Schulze2023                 3
Sencan2004                  2
Sevimli2015                 3
Silva2019                   2
Sutbeyaz2009                2
Tanwar2020                  2
To2017                      2
Tomas-Carus2007b&c          2
Torres2015                  2
Udina-Cortés2020            2
Ugurlu2017                  2
Valim2003                   2
Vas2016                     2
Verkaik2013                 2
Wicksell2013                2
Wong2018                    2

Results (random effects model):

                        treat1 treat2      MD             95%-CI
Albers2018                 MnT   WlNi -1.6825 [-3.1520; -0.2131]
Alentorn-Geli2008          McT    WBV  0.4991 [-1.1457;  2.1440]
Alentorn-Geli2008          McT   WlNi -1.2167 [-1.8929; -0.5406]
Alentorn-Geli2008          WBV   WlNi -1.7159 [-3.2907; -0.1411]
Alfano2001                 MfT  PlaSh -1.6928 [-2.7756; -0.6099]
Alptug2023               ManTh   WlNi -2.5304 [-4.5731; -0.4877]
Altan2004                 AqET    Bal  1.0434 [-0.5280;  2.6148]
Ang2010                    CBT   WlNi -0.7147 [-1.2553; -0.1740]
Arakaki2021               FlET   ReET  0.7635 [-0.4207;  1.9478]
Ardic2007                  Bal   WlNi -2.8847 [-4.3709; -1.3984]
Assefi2005                 Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Assis2006                 AeET   AqET  0.6326 [-0.3013;  1.5665]
Assumpçao2018             FlET   ReET  0.7635 [-0.4207;  1.9478]
Assumpçao2018             FlET   WlNi -0.5039 [-1.6815;  0.6738]
Assumpçao2018             ReET   WlNi -1.2674 [-2.3388; -0.1960]
Atan2020                  MiET   WlNi -0.8110 [-1.5615; -0.0606]
Audoux2023               ManTh  MasTh  0.8074 [-1.2921;  2.9069]
Baelz2022                  Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Barranengoa-Cuadra2021     CBT   WlNi -0.7147 [-1.2553; -0.1740]
Bircan2008                AeET   ReET  0.0588 [-1.0576;  1.1752]
Boggiss2022                CBT   PbTh  4.0000 [ 0.8280;  7.1720]
Bongi2010                  CBT   WlNi -0.7147 [-1.2553; -0.1740]
Bongi2012                  CBT    McT  0.5021 [-0.2507;  1.2549]
Bourgault2015              McT   WlNi -1.2167 [-1.8929; -0.5406]
Boyer2014                PlaSh   rTMS  1.2745 [ 0.2651;  2.2838]
Bressan2008               AeET   FlET -0.7048 [-1.8382;  0.4286]
Brietzke2019             PlaSh   tDCS  1.3926 [ 0.3449;  2.4402]
Calandre2009              AqET   WlNi -1.8413 [-2.7839; -0.8986]
Cao2020                    Acu   MasT -0.0740 [-1.3556;  1.2077]
Carretero2009            PlaSh   rTMS  1.2745 [ 0.2651;  2.2838]
Carson2010                 McT   WlNi -1.2167 [-1.8929; -0.5406]
Casanueva2014             DryN   WlNi -3.3305 [-4.8468; -1.8142]
Castro-Sanchez2019        DryN   MasT -2.0205 [-3.5873; -0.4537]
Castro-Sanchez2020        DryN   Elec -1.6547 [-3.2336; -0.0758]
Caumo2023                PlaSh   tDCS  1.3926 [ 0.3449;  2.4402]
Ceballos-Laita2020         McT   MiET -0.4057 [-1.3220;  0.5106]
Colbert1999                MfT  PlaSh -1.6928 [-2.7756; -0.6099]
Collado-Mateo2017         MiET   WlNi -0.8110 [-1.5615; -0.0606]
Coste2021                  MnT  PlaSh -1.4860 [-3.0555;  0.0835]
Da Costa2005              MiET   WlNi -0.8110 [-1.5615; -0.0606]
Dailey2019                Elec  PlaSh -1.4793 [-2.6248; -0.3338]
daSilva2008               AqET   Elec -0.1655 [-1.6690;  1.3381]
deMedeiros2020            AqET    Plt -0.0701 [-1.5399;  1.3997]
Ekici2008                 MasT    Plt  0.4611 [-0.8989;  1.8212]
Ekici2017                 MasT    Plt  0.4611 [-0.8989;  1.8212]
Espi-Lopes2016            MiET   WlNi -0.8110 [-1.5615; -0.0606]
Evcik2002                  Bal   WlNi -2.8847 [-4.3709; -1.3984]
Fernandes2016             AeET   AqET  0.6326 [-0.3013;  1.5665]
Fitzgibbon2018           PlaSh   rTMS  1.2745 [ 0.2651;  2.2838]
Franco2023                AeET    Plt  0.5625 [-0.8819;  2.0069]
Friedberg2019              CBT   WlNi -0.7147 [-1.2553; -0.1740]
Giannotti2014              McT   WlNi -1.2167 [-1.8929; -0.5406]
Goldway2019                CBT  PlaSh -0.5182 [-1.5817;  0.5453]
Gomez-Hernandez2019       AeET   MiET -0.3976 [-1.3464;  0.5512]
Gowans1999                 McT   WlNi -1.2167 [-1.8929; -0.5406]
Gunther1994                Bal    CBT -2.1700 [-3.6985; -0.6414]
Hargrove2012             PlaSh   tDCS  1.3926 [ 0.3449;  2.4402]
Harris2005                 Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Harte2013                  Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Hsu2010                    CBT   WlNi -0.7147 [-1.2553; -0.1740]
Izquierdo-Alventosa2020   MiET   WlNi -0.8110 [-1.5615; -0.0606]
Jamison2021               Elec  PlaSh -1.4793 [-2.6248; -0.3338]
Jensen2012                 CBT   WlNi -0.7147 [-1.2553; -0.1740]
Jones2002                  McT   ReET  0.0507 [-1.1123;  1.2136]
Jones2012                  CBT    McT  0.5021 [-0.2507;  1.2549]
Karatay2018                Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Kayo2012                  AeET   ReET  0.0588 [-1.0576;  1.1752]
Kayo2012                  AeET   WlNi -1.2086 [-2.0827; -0.3346]
Kayo2012                  ReET   WlNi -1.2674 [-2.3388; -0.1960]
Lami2018                   CBT   WlNi -0.7147 [-1.2553; -0.1740]
Lauche2016                MasT  PlaSh -1.1135 [-2.2973;  0.0703]
Lee2024                    CBT    McT  0.5021 [-0.2507;  1.2549]
Lopes-Rodrigues2012       AqET   FlET -1.3374 [-2.4821; -0.1927]
Lopes-Rodrigues2013       AqET   FlET -1.3374 [-2.4821; -0.1927]
Luciano2014                CBT   WlNi -0.7147 [-1.2553; -0.1740]
Lynch2012                  McT   WlNi -1.2167 [-1.8929; -0.5406]
Maestu2013               PlaSh   rTMS  1.2745 [ 0.2651;  2.2838]
McCrae2019                 CBT   WlNi -0.7147 [-1.2553; -0.1740]
Menzies2014                CBT   WlNi -0.7147 [-1.2553; -0.1740]
Mhalla2011               PlaSh   rTMS  1.2745 [ 0.2651;  2.2838]
Mingorance2021.2           WBV   WlNi -1.7159 [-3.2907; -0.1411]
Mist2018                   Acu    CBT -0.6692 [-1.8633;  0.5248]
Nadal-Nicolas2020         MasT  PlaSh -1.1135 [-2.2973;  0.0703]
Norrengaard1997           AeET    HtT  0.0205 [-2.2977;  2.3387]
Norrengaard1997           AeET   MiET -0.3976 [-1.3464;  0.5512]
Norrengaard1997            HtT   MiET -0.4181 [-2.6570;  1.8208]
Oka2019                    MfT  PlaSh -1.6928 [-2.7756; -0.6099]
Paolucci2016               MfT  PlaSh -1.6928 [-2.7756; -0.6099]
Paolucci2022               CBT   MiET  0.0964 [-0.7508;  0.9435]
Park2021                  FlET   ReET  0.7635 [-0.4207;  1.9478]
Parra-Delgado2013          CBT   WlNi -0.7147 [-1.2553; -0.1740]
Redondo2004                CBT   MiET  0.0964 [-0.7508;  0.9435]
Rivera2018                 Cry   WlNi -1.9000 [-4.2920;  0.4920]
Rodriguez-Mansilla2021     McT   MiET -0.4057 [-1.3220;  0.5106]
Rodriguez-Mansilla2021    MiET   WlNi -0.8110 [-1.5615; -0.0606]
Rodriguez-Mansilla2021     McT   WlNi -1.2167 [-1.8929; -0.5406]
Ruaro2014                  PbT  PlaSh -2.3000 [-4.6762;  0.0762]
Samartin-Veiga2022       PlaSh   tDCS  1.3926 [ 0.3449;  2.4402]
Sarmento2020               McT  PlaSh -1.0202 [-2.1790;  0.1386]
Schachter2003             AeET   WlNi -1.2086 [-2.0827; -0.3346]
Schulze2023             FlexEx  MasTh  2.7789 [ 0.6511;  4.9068]
Schulze2023              MasTh   WlNi -3.3378 [-5.2250; -1.4506]
Schulze2023             FlexEx   WlNi -0.5589 [-2.6868;  1.5689]
Sencan2004                AeET  PlaSh -1.0121 [-2.1765;  0.1522]
Sevimli2015               AeET   AqET  0.6326 [-0.3013;  1.5665]
Sevimli2015               AeET   MiET -0.3976 [-1.3464;  0.5512]
Sevimli2015               AqET   MiET -1.0302 [-2.0941;  0.0337]
Silva2019                  CBT   ReET  0.5527 [-0.5641;  1.6695]
Sutbeyaz2009               MfT  PlaSh -1.6928 [-2.7756; -0.6099]
Tanwar2020               PlaSh   rTMS  1.2745 [ 0.2651;  2.2838]
To2017                   PlaSh   tDCS  1.3926 [ 0.3449;  2.4402]
Tomas-Carus2007b&c        AqET   WlNi -1.8413 [-2.7839; -0.8986]
Torres2015                 CBT    MnT  0.9679 [-0.4990;  2.4347]
Udina-Cortés2020          Elec  PlaSh -1.4793 [-2.6248; -0.3338]
Ugurlu2017                 Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Valim2003                 AeET   FlET -0.7048 [-1.8382;  0.4286]
Vas2016                    Acu  PlaSh -1.1874 [-2.0078; -0.3671]
Verkaik2013                CBT   WlNi -0.7147 [-1.2553; -0.1740]
Wicksell2013               CBT   WlNi -0.7147 [-1.2553; -0.1740]
Wong2018                   McT   WlNi -1.2167 [-1.8929; -0.5406]

Number of studies: k = 106
Number of pairwise comparisons: m = 120
Number of observations: o = 6143
Number of treatments: n = 27
Number of designs: d = 53

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD             95%-CI     z  p-value
Acu    -1.3839 [-2.5896; -0.1783] -2.25   0.0245
AeET   -1.2086 [-2.0827; -0.3346] -2.71   0.0067
AqET   -1.8413 [-2.7839; -0.8986] -3.83   0.0001
Bal    -2.8847 [-4.3709; -1.3984] -3.80   0.0001
CBT    -0.7147 [-1.2553; -0.1740] -2.59   0.0096
Cry    -1.9000 [-4.2920;  0.4920] -1.56   0.1195
DryN   -3.3305 [-4.8468; -1.8142] -4.31 < 0.0001
Elec   -1.6758 [-3.0833; -0.2683] -2.33   0.0196
FlET   -0.5039 [-1.6815;  0.6738] -0.84   0.4017
FlexEx -0.5589 [-2.6868;  1.5689] -0.51   0.6067
HtT    -1.2291 [-3.5457;  1.0874] -1.04   0.2984
ManTh  -2.5304 [-4.5731; -0.4877] -2.43   0.0152
MasT   -1.3100 [-2.6708;  0.0508] -1.89   0.0592
MasTh  -3.3378 [-5.2250; -1.4506] -3.47   0.0005
McT    -1.2167 [-1.8929; -0.5406] -3.53   0.0004
MfT    -1.8893 [-3.4052; -0.3733] -2.44   0.0146
MiET   -0.8110 [-1.5615; -0.0606] -2.12   0.0342
MnT    -1.6825 [-3.1520; -0.2131] -2.24   0.0248
PbT    -2.4965 [-5.0988;  0.1058] -1.88   0.0601
PbTh   -4.7147 [-7.9324; -1.4970] -2.87   0.0041
PlaSh  -0.1965 [-1.2575;  0.8645] -0.36   0.7166
Plt    -1.7711 [-3.2552; -0.2870] -2.34   0.0193
ReET   -1.2674 [-2.3388; -0.1960] -2.32   0.0204
rTMS   -1.4710 [-2.9354; -0.0066] -1.97   0.0490
tDCS   -1.5891 [-3.0801; -0.0980] -2.09   0.0367
WBV    -1.7159 [-3.2907; -0.1411] -2.14   0.0327
WlNi         .                  .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 1.1798; tau = 1.0862; I^2 = 83.6% [80.3%; 86.4%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           531.18   87 < 0.0001
Within designs  285.41   53 < 0.0001
Between designs 245.77   34 < 0.0001

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr)

Forest plot of treatment effects for Network



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr, ci = TRUE)
League table (random effects model):
                                                      
                        Acu                          .
 -0.1753 [-1.4889;  1.1383]                       AeET
  0.4573 [-0.9197;  1.8344]  0.6326 [-0.3013;  1.5665]
  1.5007 [-0.3553;  3.3568]  1.6760 [ 0.0392;  3.3128]
 -0.6692 [-1.8633;  0.5248] -0.4939 [-1.4502;  0.4624]
  0.5161 [-2.1626;  3.1948]  0.6914 [-1.8553;  3.2381]
  1.9466 [ 0.3028;  3.5903]  2.1219 [ 0.4820;  3.7618]
  0.2919 [-1.0809;  1.6646]  0.4672 [-1.0220;  1.9564]
 -0.8801 [-2.4493;  0.6891] -0.7048 [-1.8382;  0.4286]
 -0.8250 [-3.2707;  1.6207] -0.6497 [-2.9501;  1.6506]
 -0.1548 [-2.7097;  2.4001]  0.0205 [-2.2977;  2.3387]
  1.1465 [-1.2255;  3.5184]  1.3218 [-0.9001;  3.5436]
 -0.0740 [-1.3556;  1.2077]  0.1013 [-1.3128;  1.5155]
  1.9539 [-0.2856;  4.1934]  2.1292 [ 0.0494;  4.2090]
 -0.1672 [-1.4649;  1.1306]  0.0081 [-1.0239;  1.0402]
  0.5053 [-0.8532;  1.8638]  0.6806 [-0.9094;  2.2707]
 -0.5729 [-1.9180;  0.7722] -0.3976 [-1.3464;  0.5512]
  0.2986 [-1.4013;  1.9985]  0.4739 [-1.1699;  2.1177]
  1.1126 [-1.4013;  3.6264]  1.2879 [-1.3583;  3.9340]
  3.3308 [-0.0585;  6.7200]  3.5061 [ 0.1931;  6.8190]
 -1.1874 [-2.0078; -0.3671] -1.0121 [-2.1765;  0.1522]
  0.3872 [-1.2167;  1.9911]  0.5625 [-0.8819;  2.0069]
 -0.1165 [-1.6291;  1.3961]  0.0588 [-1.0576;  1.1752]
  0.0870 [-1.2136;  1.3877]  0.2623 [-1.2786;  1.8033]
  0.2051 [-1.1255;  1.5358]  0.3804 [-1.1859;  1.9468]
  0.3319 [-1.6368;  2.3007]  0.5073 [-1.2828;  2.2973]
 -1.3839 [-2.5896; -0.1783] -1.2086 [-2.0827; -0.3346]
                                                      
                          .                          .
  0.3190 [-1.0302;  1.6682]                          .
                       AqET  0.1800 [-2.3014;  2.6614]
  1.0434 [-0.5280;  2.6148]                        Bal
 -1.1266 [-2.1531; -0.1001] -2.1700 [-3.6985; -0.6414]
  0.0587 [-2.5123;  2.6298] -0.9847 [-3.8008;  1.8315]
  1.4892 [-0.1806;  3.1591]  0.4458 [-1.6376;  2.5292]
 -0.1655 [-1.6690;  1.3381] -1.2089 [-3.1923;  0.7745]
 -1.3374 [-2.4821; -0.1927] -2.3808 [-4.1805; -0.5811]
 -1.2823 [-3.6096;  1.0449] -2.3257 [-4.9213;  0.2698]
 -0.6121 [-3.0199;  1.7957] -1.6555 [-4.3743;  1.0632]
  0.6891 [-1.5606;  2.9388] -0.3543 [-2.8805;  2.1719]
 -0.5313 [-1.9903;  0.9277] -1.5747 [-3.5252;  0.3758]
  1.4966 [-0.6130;  3.6061]  0.4532 [-1.9490;  2.8554]
 -0.6245 [-1.7281;  0.4791] -1.6679 [-3.2757; -0.0602]
  0.0480 [-1.5987;  1.6947] -0.9954 [-3.0658;  1.0750]
 -1.0302 [-2.0941;  0.0337] -2.0736 [-3.6969; -0.4503]
 -0.1587 [-1.8471;  1.5297] -1.2021 [-3.2610;  0.8568]
  0.6552 [-2.0253;  3.3358] -0.3882 [-3.3479;  2.5716]
  2.8734 [-0.4605;  6.2073]  1.8300 [-1.6910;  5.3511]
 -1.6448 [-2.8854; -0.4041] -2.6882 [-4.4528; -0.9235]
 -0.0701 [-1.5399;  1.3997] -1.1135 [-3.1279;  0.9008]
 -0.5739 [-1.8040;  0.6563] -1.6173 [-3.3891;  0.1546]
 -0.3703 [-1.9696;  1.2291] -1.4137 [-3.4466;  0.6192]
 -0.2522 [-1.8760;  1.3716] -1.2956 [-3.3478;  0.7566]
 -0.1254 [-1.9519;  1.7011] -1.1688 [-3.3294;  0.9919]
 -1.8413 [-2.7839; -0.8986] -2.8847 [-4.3709; -1.3984]
                                                      
 -1.6000 [-3.7619;  0.5619]                          .
                          .                          .
                          .                          .
 -1.1200 [-4.2829;  2.0429]                          .
                        CBT                          .
  1.1853 [-1.2670;  3.6377]                        Cry
  2.6158 [ 1.0551;  4.1766]  1.4305 [-1.4016;  4.2626]
  0.9611 [-0.4650;  2.3872] -0.2242 [-2.9996;  2.5512]
 -0.2108 [-1.4499;  1.0282] -1.3961 [-4.0624;  1.2701]
 -0.1558 [-2.3512;  2.0397] -1.3411 [-4.5426;  1.8604]
  0.5145 [-1.8350;  2.8639] -0.6709 [-4.0008;  2.6590]
  1.8157 [-0.2973;  3.9288]  0.6304 [-2.5151;  3.7759]
  0.5953 [-0.7861;  1.9767] -0.5900 [-3.3420;  2.1620]
  2.6231 [ 0.6600;  4.5863]  1.4378 [-1.6090;  4.4847]
  0.5021 [-0.2507;  1.2549] -0.6833 [-3.1690;  1.8025]
  1.1746 [-0.3432;  2.6923] -0.0107 [-2.8427;  2.8212]
  0.0964 [-0.7508;  0.9435] -1.0890 [-3.5959;  1.4180]
  0.9679 [-0.4990;  2.4347] -0.2175 [-3.0248;  2.5899]
  1.7818 [-0.8215;  4.3852]  0.5965 [-2.9381;  4.1311]
  4.0000 [ 0.8280;  7.1720]  2.8147 [-1.1947;  6.8241]
 -0.5182 [-1.5817;  0.5453] -1.7035 [-4.3203;  0.9133]
  1.0564 [-0.4629;  2.5757] -0.1289 [-2.9439;  2.6861]
  0.5527 [-0.5641;  1.6695] -0.6326 [-3.2536;  1.9884]
  0.7563 [-0.7099;  2.2225] -0.4290 [-3.2337;  2.3756]
  0.8744 [-0.6185;  2.3673] -0.3109 [-3.1296;  2.5077]
  1.0012 [-0.6499;  2.6522] -0.1841 [-3.0480;  2.6797]
 -0.7147 [-1.2553; -0.1740] -1.9000 [-4.2920;  0.4920]
                                                      
                          .                          .
                          .                          .
                          .  3.2000 [ 0.0410;  6.3590]
                          .                          .
                          .                          .
                          .                          .
                       DryN -2.6800 [-4.9745; -0.3855]
 -1.6547 [-3.2336; -0.0758]                       Elec
 -2.8266 [-4.6661; -0.9872] -1.1719 [-2.8813;  0.5374]
 -2.7716 [-5.3844; -0.1587] -1.1169 [-3.6681;  1.4343]
 -2.1013 [-4.8312;  0.6285] -0.4466 [-3.1001;  2.2068]
 -0.8001 [-3.3441;  1.7439]  0.8546 [-1.6260;  3.3353]
 -2.0205 [-3.5873; -0.4537] -0.3658 [-1.8961;  1.1645]
  0.0073 [-2.4135;  2.4282]  1.6620 [-0.6922;  4.0163]
 -2.1137 [-3.7344; -0.4931] -0.4590 [-1.9541;  1.0360]
 -1.4412 [-3.3106;  0.4281]  0.2135 [-1.3628;  1.7897]
 -2.5194 [-4.1679; -0.8710] -0.8648 [-2.3918;  0.6623]
 -1.6479 [-3.6605;  0.3647]  0.0068 [-1.8591;  1.8726]
 -0.8340 [-3.6568;  1.9888]  0.8207 [-1.8172;  3.4586]
  1.3842 [-2.1509;  4.9193]  3.0389 [-0.4389;  6.5167]
 -3.1340 [-4.6578; -1.6102] -1.4793 [-2.6248; -0.3338]
 -1.5594 [-3.4144;  0.2957]  0.0953 [-1.6769;  1.8676]
 -2.0631 [-3.8585; -0.2677] -0.4084 [-2.0821;  1.2653]
 -1.8595 [-3.6873; -0.0317] -0.2048 [-1.7315;  1.3219]
 -1.7414 [-3.5906;  0.1078] -0.0867 [-1.6391;  1.4656]
 -1.6146 [-3.7932;  0.5640]  0.0401 [-2.0598;  2.1400]
 -3.3305 [-4.8468; -1.8142] -1.6758 [-3.0833; -0.2683]
                                                      
                          .                          .
  0.3683 [-1.5690;  2.3055]                          .
 -2.3377 [-4.0027; -0.6726]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                       FlET                          .
  0.0551 [-2.3769;  2.4871]                     FlexEx
  0.7253 [-1.7824;  3.2329]  0.6702 [-2.4753;  3.8157]
  2.0265 [-0.3313;  4.3844]  1.9715 [-0.6813;  4.6243]
  0.8061 [-0.8552;  2.4675]  0.7511 [-1.7747;  3.2768]
  2.8340 [ 0.6095;  5.0585]  2.7789 [ 0.6511;  4.9068]
  0.7129 [-0.5816;  2.0074]  0.6578 [-1.5749;  2.8905]
  1.3854 [-0.4262;  3.1970]  1.3303 [-1.2823;  3.9430]
  0.3072 [-0.9798;  1.5941]  0.2521 [-2.0042;  2.5084]
  1.1787 [-0.6560;  3.0134]  1.1236 [-1.4623;  3.7095]
  1.9926 [-0.7923;  4.7776]  1.9376 [-1.4239;  5.2991]
  4.2108 [ 0.8055;  7.6162]  4.1558 [ 0.2981;  8.0134]
 -0.3074 [-1.7597;  1.1450] -0.3624 [-2.7401;  2.0153]
  1.2673 [-0.4355;  2.9700]  1.2122 [-1.3821;  3.8065]
  0.7635 [-0.4207;  1.9478]  0.7085 [-1.6739;  3.0909]
  0.9671 [-0.8015;  2.7358]  0.9121 [-1.6710;  3.4951]
  1.0852 [-0.7056;  2.8760]  1.0301 [-1.5681;  3.6284]
  1.2120 [-0.7435;  3.1676]  1.1570 [-1.4902;  3.8042]
 -0.5039 [-1.6815;  0.6738] -0.5589 [-2.6868;  1.5689]
                                                      
                          .                          .
  1.0000 [-2.1019;  4.1019]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                        HtT                          .
  1.3013 [-1.7873;  4.3898]                      ManTh
  0.0808 [-2.5407;  2.7024] -1.2204 [-3.6749;  1.2340]
  2.1087 [-0.8793;  5.0967]  0.8074 [-1.2921;  2.9069]
 -0.0124 [-2.3894;  2.3646] -1.3137 [-3.4654;  0.8381]
  0.6601 [-2.0516;  3.3719] -0.6411 [-3.1849;  1.9026]
 -0.4181 [-2.6570;  1.8208] -1.7194 [-3.8956;  0.4568]
  0.4534 [-2.2626;  3.1694] -0.8479 [-3.3642;  1.6685]
  1.2674 [-2.1717;  4.7065] -0.0339 [-3.3422;  3.2744]
  3.4855 [-0.4618;  7.4328]  2.1843 [-1.6271;  5.9956]
 -1.0326 [-3.5188;  1.4535] -2.3339 [-4.6357; -0.0321]
  0.5420 [-2.1217;  3.2057] -0.7593 [-3.2842;  1.7656]
  0.0383 [-2.4414;  2.5179] -1.2630 [-3.5696;  1.0436]
  0.2418 [-2.4414;  2.9251] -1.0594 [-3.5728;  1.4540]
  0.3599 [-2.3380;  3.0578] -0.9413 [-3.4704;  1.5877]
  0.4867 [-2.3066;  3.2800] -0.8145 [-3.3938;  1.7648]
 -1.2291 [-3.5457;  1.0874] -2.5304 [-4.5731; -0.4877]
                                                      
 -0.2200 [-2.4539;  2.0139]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
 -2.9300 [-5.2344; -0.6256]                          .
                          .                          .
                          .                          .
                          .  2.4500 [ 0.2495;  4.6505]
                          .                          .
                          .  1.8000 [-0.8967;  4.4967]
                       MasT                          .
  2.0279 [-0.2988;  4.3545]                      MasTh
 -0.0932 [-1.5476;  1.3612] -2.1211 [-4.1258; -0.1164]
  0.5793 [-1.0251;  2.1836] -1.4486 [-3.8693;  0.9721]
 -0.4989 [-1.9769;  0.9790] -2.5268 [-4.5577; -0.4959]
  0.3726 [-1.4777;  2.2228] -1.6553 [-4.0471;  0.7365]
  1.1865 [-1.4682;  3.8413] -0.8413 [-4.0559;  2.3732]
  3.4047 [-0.0550;  6.8644]  1.3769 [-2.3534;  5.1072]
 -1.1135 [-2.2973;  0.0703] -3.1413 [-5.3063; -0.9763]
  0.4611 [-0.8989;  1.8212] -1.5667 [-3.9676;  0.8341]
 -0.0426 [-1.6685;  1.5833] -2.0704 [-4.2406;  0.0997]
  0.1610 [-1.3947;  1.7167] -1.8669 [-4.2556;  0.5219]
  0.2791 [-1.3017;  1.8599] -1.7488 [-4.1539;  0.6564]
  0.4059 [-1.6636;  2.4754] -1.6220 [-4.0799;  0.8360]
 -1.3100 [-2.6708;  0.0508] -3.3378 [-5.2250; -1.4506]
                                                      
                          .                          .
                          .                          .
                          .                          .
                          .                          .
  0.3908 [-0.9254;  1.7070]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                        McT                          .
  0.6725 [-0.9135;  2.2585]                        MfT
 -0.4057 [-1.3220;  0.5106] -1.0782 [-2.7047;  0.5483]
  0.4658 [-1.1073;  2.0389] -0.2067 [-2.1135;  1.7001]
  1.2798 [-1.3639;  3.9235]  0.6072 [-2.0040;  3.2185]
  3.4979 [ 0.2379;  6.7580]  2.8254 [-0.6910;  6.3418]
 -1.0202 [-2.1790;  0.1386] -1.6928 [-2.7756; -0.6099]
  0.5544 [-1.0239;  2.1327] -0.1181 [-1.9740;  1.7378]
  0.0507 [-1.1123;  1.2136] -0.6218 [-2.3877;  1.1440]
  0.2542 [-1.2825;  1.7910] -0.4183 [-1.8986;  1.0620]
  0.3723 [-1.1899;  1.9345] -0.3002 [-1.8069;  1.2065]
  0.4991 [-1.1457;  2.1440] -0.1734 [-2.3453;  1.9986]
 -1.2167 [-1.8929; -0.5406] -1.8893 [-3.4052; -0.3733]
                                                      
                          .                          .
 -0.3099 [-1.6897;  1.0699]                          .
 -2.4400 [-4.6701; -0.2099]                          .
                          .                          .
 -0.4832 [-2.4245;  1.4582]  1.6700 [-0.6847;  4.0247]
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
  0.0000 [-2.4055;  2.4055]                          .
                          .                          .
                          .                          .
                          .                          .
 -1.2974 [-3.0715;  0.4768]                          .
                          .                          .
                       MiET                          .
  0.8715 [-0.7423;  2.4853]                        MnT
  1.6855 [-0.9827;  4.3536]  0.8140 [-2.0338;  3.6617]
  3.9036 [ 0.6205;  7.1868]  3.0321 [-0.4626;  6.5268]
 -0.6145 [-1.8282;  0.5991] -1.4860 [-3.0555;  0.0835]
  0.9601 [-0.6101;  2.5303]  0.0886 [-1.9008;  2.0780]
  0.4564 [-0.7574;  1.6702] -0.4151 [-2.1853;  1.3551]
  0.6599 [-0.9185;  2.2384] -0.2116 [-2.0776;  1.6545]
  0.7780 [-0.8252;  2.3813] -0.0935 [-1.9805;  1.7936]
  0.9048 [-0.8264;  2.6361]  0.0333 [-2.1122;  2.1789]
 -0.8110 [-1.5615; -0.0606] -1.6825 [-3.1520; -0.2131]
                                                      
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .  4.0000 [ 0.8280;  7.1720]
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                        PbT                          .
  2.2182 [-1.8853;  6.3217]                       PbTh
 -2.3000 [-4.6762;  0.0762] -4.5182 [-7.8637; -1.1727]
 -0.7254 [-3.5393;  2.0885] -2.9436 [-6.4606;  0.5735]
 -1.2291 [-3.9844;  1.5262] -3.4473 [-6.8101; -0.0845]
 -1.0255 [-3.6072;  1.5562] -3.2437 [-6.7382;  0.2507]
 -0.9074 [-3.5043;  1.6895] -3.1256 [-6.6313;  0.3801]
 -0.7806 [-3.8123;  2.2511] -2.9988 [-6.5747;  0.5771]
 -2.4965 [-5.0988;  0.1058] -4.7147 [-7.9324; -1.4970]
                                                      
 -0.9964 [-1.9109; -0.0820]                          .
 -2.1500 [-4.4566;  0.1566]  1.2000 [-1.1938;  3.5938]
                          . -0.6000 [-3.0381;  1.8381]
                          .                          .
  0.8200 [-1.8126;  3.4526]                          .
                          .                          .
                          .                          .
 -1.2324 [-2.5488;  0.0840]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
 -1.6819 [-3.4669;  0.1030]  0.4003 [-1.2578;  2.0584]
                          .                          .
 -3.7000 [-6.4086; -0.9914]                          .
 -1.6928 [-2.7756; -0.6099]                          .
                          .                          .
 -0.2900 [-2.7758;  2.1958]                          .
 -2.3000 [-4.6762;  0.0762]                          .
                          .                          .
                      PlaSh                          .
  1.5746 [ 0.0674;  3.0819]                        Plt
  1.0709 [-0.3239;  2.4657] -0.5037 [-2.2002;  1.1928]
  1.2745 [ 0.2651;  2.2838] -0.3001 [-2.1141;  1.5138]
  1.3926 [ 0.3449;  2.4402] -0.1821 [-2.0177;  1.6535]
  1.5194 [-0.3634;  3.4021] -0.0552 [-2.2093;  2.0988]
 -0.1965 [-1.2575;  0.8645] -1.7711 [-3.2552; -0.2870]
                                                      
                          .                          .
 -0.7062 [-2.4919;  1.0795]                          .
                          .                          .
                          .                          .
  1.0400 [-1.3518;  3.4318]                          .
                          .                          .
                          .                          .
                          .                          .
  0.7829 [-0.7720;  2.3378]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
  0.5300 [-1.8701;  2.9301]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .  1.2745 [ 0.2651;  2.2838]
                          .                          .
                       ReET                          .
  0.2036 [-1.5181;  1.9253]                       rTMS
  0.3217 [-1.4228;  2.0661]  0.1181 [-1.3367;  1.5729]
  0.4485 [-1.4393;  2.3363]  0.2449 [-1.8913;  2.3812]
 -1.2674 [-2.3388; -0.1960] -1.4710 [-2.9354; -0.0066]
                                                      
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .  1.8100 [-0.7735;  4.3935]
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
  1.3926 [ 0.3449;  2.4402]                          .
                          .                          .
                          .                          .
                          .                          .
                       tDCS                          .
  0.1268 [-2.0278;  2.2814]                        WBV
 -1.5891 [-3.0801; -0.0980] -1.7159 [-3.2907; -0.1411]
                           
                          .
 -1.4165 [-3.1429;  0.3099]
 -0.9074 [-2.6479;  0.8331]
 -4.0137 [-6.1597; -1.8678]
 -0.8331 [-1.4820; -0.1841]
 -1.9000 [-4.2920;  0.4920]
 -1.5000 [-3.7363;  0.7363]
                          .
 -1.8000 [-4.6961;  1.0961]
 -0.2300 [-2.4305;  1.9705]
                          .
 -3.4000 [-5.9241; -0.8759]
                          .
 -2.6800 [-4.8754; -0.4846]
 -0.9506 [-1.8191; -0.0822]
                          .
 -1.2193 [-2.2171; -0.2214]
 -2.0900 [-4.5575;  0.3775]
                          .
                          .
                          .
                          .
 -1.2106 [-3.1301;  0.7089]
                          .
                          .
 -1.5284 [-3.2078;  0.1511]
                       WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr <- netrank(nma_sr, small.values = "good")
print(ranking_sr)
       P-score
PbTh    0.9408
DryN    0.8917
MasTh   0.8728
Bal     0.8252
ManTh   0.7280
PbT     0.7060
AqET    0.6133
MfT     0.6115
Cry     0.5764
Plt     0.5752
WBV     0.5497
Elec    0.5463
MnT     0.5445
tDCS    0.5171
rTMS    0.4780
Acu     0.4492
MasT    0.4229
ReET    0.4168
HtT     0.4137
McT     0.3968
AeET    0.3916
MiET    0.2523
FlexEx  0.2474
CBT     0.2149
FlET    0.1766
PlaSh   0.0916
WlNi    0.0495



Code 
# Rankogram
ran_sr <- rankogram(nma_sr)
plot(ran_sr)

Rankogram of treatments network



Code 
# Design decomposition
decomp_sr <- decomp.design(nma_sr)
print(decomp_sr)
Q statistics to assess homogeneity / consistency

                     Q df  p-value
Total           531.18 87 < 0.0001
Within designs  285.41 53 < 0.0001
Between designs 245.77 34 < 0.0001

Design-specific decomposition of within-designs Q statistic

     Design     Q df  p-value
 PlaSh:rTMS 71.74  5 < 0.0001
   WlNi:CBT 83.37 12 < 0.0001
  Acu:PlaSh 42.88  6 < 0.0001
  WlNi:MiET 24.29  4 < 0.0001
  MfT:PlaSh 15.09  4   0.0045
    CBT:McT  8.27  2   0.0160
 PlaSh:tDCS 11.61  4   0.0205
  WlNi:AqET  4.87  1   0.0274
  FlET:ReET  4.25  1   0.0393
 MasT:PlaSh  3.43  1   0.0641
 Elec:PlaSh  4.93  2   0.0851
   CBT:MiET  2.28  1   0.1312
   WlNi:McT  7.93  5   0.1600
  AqET:FlET  0.26  1   0.6118
   WlNi:Bal  0.20  1   0.6548
  AeET:FlET  0.02  1   0.8964
   MasT:Plt  0.00  1   0.9551
  AeET:AqET  0.00  1   1.0000

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from < 0.0001)

 Detached design      Q df  p-value
  AeET:AqET:MiET 153.82 32 < 0.0001
       AeET:MiET 165.62 33 < 0.0001
       WlNi:DryN 216.35 33 < 0.0001
         Acu:CBT 223.60 33 < 0.0001
      AeET:PlaSh 232.23 33 < 0.0001
        WlNi:WBV 233.52 33 < 0.0001
       Acu:PlaSh 234.22 33 < 0.0001
       AqET:Elec 234.46 33 < 0.0001
       DryN:MasT 234.65 33 < 0.0001
       McT:PlaSh 234.80 33 < 0.0001
    WlNi:McT:WBV 233.46 32 < 0.0001
        McT:MiET 236.20 33 < 0.0001
       AqET:FlET 237.29 33 < 0.0001
        WlNi:Bal 237.95 33 < 0.0001
       DryN:Elec 238.39 33 < 0.0001
       WlNi:AqET 238.49 33 < 0.0001
       MnT:PlaSh 240.05 33 < 0.0001
     ManTh:MasTh 240.76 33 < 0.0001
      WlNi:ManTh 240.76 33 < 0.0001
       AeET:FlET 241.03 33 < 0.0001
   WlNi:McT:MiET 238.70 32 < 0.0001
        CBT:MiET 241.04 33 < 0.0001
        AqET:Bal 241.49 33 < 0.0001
        WlNi:CBT 242.01 33 < 0.0001
         CBT:McT 242.90 33 < 0.0001
       CBT:PlaSh 243.18 33 < 0.0001
       WlNi:MiET 243.35 33 < 0.0001
        Acu:MasT 243.53 33 < 0.0001
         CBT:MnT 244.03 33 < 0.0001
        McT:ReET 244.32 33 < 0.0001
       AeET:ReET 244.46 33 < 0.0001
        CBT:ReET 244.55 33 < 0.0001
         Bal:CBT 244.55 33 < 0.0001
        AeET:Plt 244.58 33 < 0.0001
  WlNi:FlET:ReET 242.25 32 < 0.0001
       AeET:AqET 244.64 33 < 0.0001
      Elec:PlaSh 244.65 33 < 0.0001
       WlNi:AeET 244.67 33 < 0.0001
      MasT:PlaSh 244.90 33 < 0.0001
  WlNi:AeET:ReET 242.65 32 < 0.0001
        WlNi:MnT 245.04 33 < 0.0001
        AqET:Plt 245.14 33 < 0.0001
        MasT:Plt 245.67 33 < 0.0001
       FlET:ReET 245.74 33 < 0.0001
        WlNi:McT 245.77 33 < 0.0001

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                    Q df p-value tau.within tau2.within
Between designs 43.86 34  0.1199     0.9850      0.9702



Code 
# Node-splitting analysis to detect inconsistency
split_sr <- netsplit(nma_sr)
print(split_sr)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

   comparison  k prop     nma  direct  indir.    Diff     z p-value
      Acu:CBT  1 0.31 -0.6692 -1.6000 -0.2606 -1.3394 -1.01  0.3114
     Acu:MasT  1 0.33 -0.0740 -0.2200 -0.0023 -0.2177 -0.16  0.8757
    Acu:PlaSh  7 0.80 -1.1874 -0.9964 -1.9752  0.9788  0.93  0.3541
    AeET:AqET  3 0.48  0.6326  0.3190  0.9212 -0.6021 -0.63  0.5279
    AeET:FlET  2 0.34 -0.7048  0.3683 -1.2632  1.6315  1.34  0.1807
     AeET:HtT  1 0.56  0.0205  1.0000 -1.2188  2.2188  0.93  0.3516
    AeET:MiET  3 0.47 -0.3976 -0.3099 -0.4762  0.1664  0.17  0.8638
   AeET:PlaSh  1 0.25 -1.0121 -2.1500 -0.6230 -1.5270 -1.12  0.2627
     AeET:Plt  1 0.36  0.5625  1.2000  0.1975  1.0025  0.65  0.5128
    AeET:ReET  2 0.39  0.0588 -0.7062  0.5496 -1.2558 -1.08  0.2820
    AeET:WlNi  2 0.26 -1.2086 -1.4165 -1.1370 -0.2795 -0.27  0.7843
     AqET:Bal  1 0.40  1.0434  0.1800  1.6214 -1.4414 -0.88  0.3782
    AqET:Elec  1 0.23 -0.1655  3.2000 -1.1512  4.3512  2.37  0.0176
    AqET:FlET  2 0.47 -1.3374 -2.3377 -0.4409 -1.8967 -1.62  0.1049
    AqET:MiET  1 0.23 -1.0302 -2.4400 -0.6148 -1.8252 -1.41  0.1586
     AqET:Plt  1 0.36 -0.0701 -0.6000  0.2323 -0.8323 -0.53  0.5934
    AqET:WlNi  2 0.29 -1.8413 -0.9074 -2.2289  1.3215  1.25  0.2109
      Bal:CBT  1 0.23 -2.1700 -1.1200 -2.4899  1.3699  0.74  0.4574
     Bal:WlNi  2 0.48 -2.8847 -4.0137 -1.8437 -2.1700 -1.43  0.1528
      CBT:McT  3 0.33  0.5021  0.3908  0.5562 -0.1654 -0.20  0.8399
     CBT:MiET  2 0.19  0.0964 -0.4832  0.2327 -0.7159 -0.65  0.5155
      CBT:MnT  1 0.39  0.9679  1.6700  0.5226  1.1474  0.75  0.4550
    CBT:PlaSh  1 0.16 -0.5182  0.8200 -0.7792  1.5992  1.09  0.2761
     CBT:ReET  1 0.22  0.5527  1.0400  0.4169  0.6231  0.45  0.6516
     CBT:WlNi 13 0.69 -0.7147 -0.8331 -0.4461 -0.3870 -0.65  0.5180
    DryN:Elec  1 0.47 -1.6547 -2.6800 -0.7324 -1.9476 -1.21  0.2274
    DryN:MasT  1 0.46 -2.0205 -2.9300 -1.2385 -1.6915 -1.05  0.2915
    DryN:WlNi  1 0.46 -3.3305 -1.5000 -4.8881  3.3881  2.18  0.0291
   Elec:PlaSh  3 0.76 -1.4793 -1.2324 -2.2494  1.0170  0.75  0.4556
    FlET:ReET  3 0.58  0.7635  0.7829  0.7368  0.0462  0.04  0.9699
    FlET:WlNi  1 0.17 -0.5039 -1.8000 -0.2471 -1.5529 -0.96  0.3370
 FlexEx:MasTh  1 0.94  2.7789  2.4500  7.5136 -5.0636 -1.15  0.2504
  FlexEx:WlNi  1 0.94 -0.5589 -0.2300 -5.2936  5.0636  1.15  0.2504
     HtT:MiET  1 0.87 -0.4181  0.0000 -3.1260  3.1260  0.93  0.3516
  ManTh:MasTh  1 0.61  0.8074  1.8000 -0.7200  2.5200  1.15  0.2504
   ManTh:WlNi  1 0.65 -2.5304 -3.4000 -0.8800 -2.5200 -1.15  0.2504
   MasT:PlaSh  2 0.44 -1.1135 -1.6819 -0.6671 -1.0148 -0.83  0.4043
     MasT:Plt  2 0.67  0.4611  0.4003  0.5862 -0.1858 -0.13  0.9000
   MasTh:WlNi  1 0.74 -3.3378 -2.6800 -5.2000  2.5200  1.15  0.2504
     McT:MiET  2 0.27 -0.4057 -1.2974 -0.0814 -1.2160 -1.15  0.2500
    McT:PlaSh  1 0.18 -1.0202 -3.7000 -0.4199 -3.2801 -2.15  0.0319
     McT:ReET  1 0.23  0.0507  0.5300 -0.0964  0.6264  0.45  0.6545
      McT:WBV  1 0.41  0.4991  1.8100 -0.3944  2.2044  1.29  0.1972
     McT:WlNi  8 0.61 -1.2167 -0.9506 -1.6265  0.6758  0.96  0.3385
    MiET:WlNi  6 0.57 -0.8110 -1.2193 -0.2796 -0.9397 -1.22  0.2238
    MnT:PlaSh  1 0.40 -1.4860 -0.2900 -2.2789  1.9889  1.22  0.2240
     MnT:WlNi  1 0.35 -1.6825 -2.0900 -1.4586 -0.6314 -0.40  0.6870
    ReET:WlNi  2 0.31 -1.2674 -1.2106 -1.2931  0.0825  0.07  0.9443
     WBV:WlNi  2 0.88 -1.7159 -1.5284 -3.0817  1.5534  0.63  0.5288

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr)

Forest plot of node-splitting for Network



Code 
# Heatmap
netheat(nma_sr)

Heatmap of contribution matrix for Network



Code 
# Funnel plot
funnel(nma_sr,
    order = "WlNi",
)

Funnel plot for Network (P | Sh)





Code 
# Read data
data_lg <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "P | Lg") |>
    mutate(
        Mean1 = as.numeric(Mean1),
        Mean2 = as.numeric(Mean2),
        Mean3 = as.numeric(Mean3),
        SD1 = as.numeric(SD1),
        SD2 = as.numeric(SD2),
        SD3 = as.numeric(SD3),
    )


# Transform to contrast-based
pw <- pairwise(
    treat = list(Treat1, Treat2, Treat3),
    n = list(N1, N2, N3),
    mean = list(Mean1, Mean2, Mean3),
    sd = list(SD1, SD2, SD3),
    studlab = StudyID,
    data = data_lg,
    sm      = "MD"
)

# Check network connections
net_con <- netconnection(pw)
net_con
Number of studies: k = 25
Number of pairwise comparisons: m = 29
Number of treatments: n = 15
Number of designs: d = 16
Number of networks: 3

Details on subnetworks: 
 subnetwork  k  m n
          1 20 24 9
          2  1  1 2
          3  4  4 4


There are three sub-networks:

Subnet 1:
- 20 studies - 24 comparisons - 9 treatments

Subnet 2:
- 1 studies
- 1 comparisons
- 2 treatments

Subnet 3:
- 4 studies
- 4 comparisons
- 4 treatments

Tip

There are Three treatment sub-networks that do not connect.

Note

Please: Select the treatment sub-networks before proceeding.

Select the procedures performed

Important

the first subnet contains 20 studies, 24 comparisons and 9 treatments.

Code 
# Filter data for subnet 1
sr1 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 1)

# Display comparison table
sr1



Code 
# Unique treatments in subnet 1
unique_treat1 <- sr1$treat1 |> unique()
unique_treat2 <- sr1$treat2 |> unique()

# Combination of all unique treatments
trat_sr1 <- unique(c(unique_treat1, unique_treat2))
print(trat_sr1)
[1] "AeET"   "AqET"   "ReET"   "McT"    "CBT"    "MiET"   "WlNi"   "FlET"  
[9] "FlexEx"
Code 
# Total number of treatments
length(trat_sr1)
[1] 9



Code 
# Filter pairwise object only for comparisons within subnet 1
pw_plg_sr1 <- pw %>%
    filter(treat1 %in% trat_sr1 & treat2 %in% trat_sr1)

# Number of comparisons in subnet 1
nrow(pw_plg_sr1)
[1] 24



Code 
# Fit NMA model for subnet 1
nma_sr1 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_plg_sr1,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    sm = "MD", # can be "MD" or "SMD"
    ref = "WlNi" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr1)
Number of studies: k = 20
Number of pairwise comparisons: m = 24
Number of observations: o = 1270
Number of treatments: n = 9
Number of designs: d = 12

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD             95%-CI     z p-value
AeET   -1.3607 [-2.1240; -0.5974] -3.49  0.0005
AqET   -1.4645 [-2.2660; -0.6631] -3.58  0.0003
CBT    -0.2492 [-1.5519;  1.0535] -0.37  0.7077
FlET   -0.1807 [-2.2805;  1.9192] -0.17  0.8661
FlexEx  1.6208 [-1.1658;  4.4074]  1.14  0.2543
McT    -0.4904 [-1.8095;  0.8287] -0.73  0.4662
MiET   -1.1425 [-2.4020;  0.1170] -1.78  0.0754
ReET   -2.4558 [-4.0166; -0.8949] -3.08  0.0020
WlNi         .                  .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.6311; tau = 0.7944; I^2 = 67.2% [43.7%; 80.9%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f.  p-value
Total           42.69   14 < 0.0001
Within designs  31.37    8   0.0001
Between designs 11.32    6   0.0789

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(
    nma_sr1,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 1 (P | Lg)



Code 
# Detailed model summary
summary(nma_sr1)
Original data (with adjusted standard errors for multi-arm studies):

                       treat1 treat2      TE   seTE seTE.adj narms multiarm
Acosta-Gallego2018       AeET   AqET  0.5000 0.4574   0.9167     2         
Andrade2019              AqET   WlNi -1.0000 0.6137   1.0039     2         
Assis2006                AeET   AqET  0.0000 0.5601   0.9720     2         
Baptista2012             AeET   WlNi -2.9000 0.3860   0.8832     2         
Hakkinen2001             ReET   WlNi -3.9200 1.1181   1.3716     2         
Kayo2012                 AeET   ReET  0.3700 0.7979   1.4272     3        *
Kayo2012                 AeET   WlNi -1.3700 0.7203   1.2892     3        *
Kayo2012                 ReET   WlNi -1.7400 0.7288   1.3018     3        *
Larsson2015               McT   MiET  1.6100 0.4798   0.9280     2         
Letieri2013              AqET   WlNi -2.0800 0.3616   0.8728     2         
Mannerkorpi2000           McT   WlNi -0.5000 0.6372   1.0184     2         
Mengshoel1992            AeET   WlNi -0.6500 0.8641   1.1738     2         
Munguia-Izquierdo 2007   AqET   WlNi -0.9700 0.5334   0.9569     2         
Rooks2007                 CBT    McT  1.0000 0.5752   1.2481     3        *
Rooks2007                 CBT   MiET  0.9000 0.5016   1.1373     3        *
Rooks2007                 McT   MiET -0.1000 0.4732   1.1051     3        *
Sanudo2015               MiET   WlNi -0.3000 0.7371   1.0837     2         
Schachter2003            AeET   WlNi -0.0400 0.4272   0.9020     2         
Tomas-Carus2008          AqET   WlNi -1.3000 0.5888   0.9888     2         
Valim2003                AeET   FlET -1.1800 0.6042   0.9981     2         
Valkeinen2008            MiET   WlNi -1.7100 1.4134   1.6213     2         
Williams2010              CBT   WlNi -0.6000 0.2855   0.8442     2         
Hernando-Garijo2021      AeET   WlNi -1.5400 0.6724   1.0408     2         
Saranya2022               CBT FlexEx -1.8700 0.9740   1.2569     2         

Number of treatment arms (by study):
                       narms
Acosta-Gallego2018         2
Andrade2019                2
Assis2006                  2
Baptista2012               2
Hakkinen2001               2
Kayo2012                   3
Larsson2015                2
Letieri2013                2
Mannerkorpi2000            2
Mengshoel1992              2
Munguia-Izquierdo 2007     2
Rooks2007                  3
Sanudo2015                 2
Schachter2003              2
Tomas-Carus2008            2
Valim2003                  2
Valkeinen2008              2
Williams2010               2
Hernando-Garijo2021        2
Saranya2022                2

Results (random effects model):

                       treat1 treat2      MD             95%-CI
Acosta-Gallego2018       AeET   AqET  0.1039 [-0.8083;  1.0160]
Andrade2019              AqET   WlNi -1.4645 [-2.2660; -0.6631]
Assis2006                AeET   AqET  0.1039 [-0.8083;  1.0160]
Baptista2012             AeET   WlNi -1.3607 [-2.1240; -0.5974]
Hakkinen2001             ReET   WlNi -2.4558 [-4.0166; -0.8949]
Kayo2012                 AeET   ReET  1.0951 [-0.5371;  2.7273]
Kayo2012                 AeET   WlNi -1.3607 [-2.1240; -0.5974]
Kayo2012                 ReET   WlNi -2.4558 [-4.0166; -0.8949]
Larsson2015               McT   MiET  0.6521 [-0.5045;  1.8087]
Letieri2013              AqET   WlNi -1.4645 [-2.2660; -0.6631]
Mannerkorpi2000           McT   WlNi -0.4904 [-1.8095;  0.8287]
Mengshoel1992            AeET   WlNi -1.3607 [-2.1240; -0.5974]
Munguia-Izquierdo 2007   AqET   WlNi -1.4645 [-2.2660; -0.6631]
Rooks2007                 CBT    McT  0.2412 [-1.2075;  1.6899]
Rooks2007                 CBT   MiET  0.8933 [-0.5067;  2.2933]
Rooks2007                 McT   MiET  0.6521 [-0.5045;  1.8087]
Sanudo2015               MiET   WlNi -1.1425 [-2.4020;  0.1170]
Schachter2003            AeET   WlNi -1.3607 [-2.1240; -0.5974]
Tomas-Carus2008          AqET   WlNi -1.4645 [-2.2660; -0.6631]
Valim2003                AeET   FlET -1.1800 [-3.1362;  0.7762]
Valkeinen2008            MiET   WlNi -1.1425 [-2.4020;  0.1170]
Williams2010              CBT   WlNi -0.2492 [-1.5519;  1.0535]
Hernando-Garijo2021      AeET   WlNi -1.3607 [-2.1240; -0.5974]
Saranya2022               CBT FlexEx -1.8700 [-4.3334;  0.5934]

Number of studies: k = 20
Number of pairwise comparisons: m = 24
Number of observations: o = 1270
Number of treatments: n = 9
Number of designs: d = 12

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD             95%-CI     z p-value
AeET   -1.3607 [-2.1240; -0.5974] -3.49  0.0005
AqET   -1.4645 [-2.2660; -0.6631] -3.58  0.0003
CBT    -0.2492 [-1.5519;  1.0535] -0.37  0.7077
FlET   -0.1807 [-2.2805;  1.9192] -0.17  0.8661
FlexEx  1.6208 [-1.1658;  4.4074]  1.14  0.2543
McT    -0.4904 [-1.8095;  0.8287] -0.73  0.4662
MiET   -1.1425 [-2.4020;  0.1170] -1.78  0.0754
ReET   -2.4558 [-4.0166; -0.8949] -3.08  0.0020
WlNi         .                  .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.6311; tau = 0.7944; I^2 = 67.2% [43.7%; 80.9%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f.  p-value
Total           42.69   14 < 0.0001
Within designs  31.37    8   0.0001
Between designs 11.32    6   0.0789

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr1)

Forest plot of treatment effects for Subnet 1



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr1, ci = TRUE)
League table (random effects model):
                                                      
                       AeET  0.2646 [-1.0425;  1.5718]
  0.1039 [-0.8083;  1.0160]                       AqET
 -1.1114 [-2.6213;  0.3984] -1.2153 [-2.7448;  0.3142]
 -1.1800 [-3.1362;  0.7762] -1.2839 [-3.4423;  0.8745]
 -2.9814 [-5.8707; -0.0922] -3.0853 [-5.9849; -0.1857]
 -0.8702 [-2.3942;  0.6538] -0.9741 [-2.5176;  0.5693]
 -0.2181 [-1.6909;  1.2546] -0.3220 [-1.8149;  1.1709]
  1.0951 [-0.5371;  2.7273]  0.9912 [-0.7289;  2.7114]
 -1.3607 [-2.1240; -0.5974] -1.4645 [-2.2660; -0.6631]
                                                      
                          . -1.1800 [-3.1362;  0.7762]
                          .                          .
                        CBT                          .
 -0.0686 [-2.5396;  2.4025]                       FlET
 -1.8700 [-4.3334;  0.5934] -1.8014 [-5.2907;  1.6878]
  0.2412 [-1.2075;  1.6899]  0.3098 [-2.1700;  2.7895]
  0.8933 [-0.5067;  2.2933]  0.9619 [-1.4868;  3.4105]
  2.2066 [ 0.1735;  4.2396]  2.2751 [-0.2726;  4.8228]
 -0.2492 [-1.5519;  1.0535] -0.1807 [-2.2805;  1.9192]
                                                      
                          .                          .
                          .                          .
 -1.8700 [-4.3334;  0.5934]  1.0000 [-0.9223;  2.9223]
                          .                          .
                     FlexEx                          .
  2.1112 [-0.7466;  4.9690]                        McT
  2.7633 [-0.0702;  5.5968]  0.6521 [-0.5045;  1.8087]
  4.0766 [ 0.8826;  7.2706]  1.9654 [-0.0782;  4.0089]
  1.6208 [-1.1658;  4.4074] -0.4904 [-1.8095;  0.8287]
                                                      
                          .  0.3700 [-1.8368;  2.5768]
                          .                          .
  0.9000 [-0.9414;  2.7414]                          .
                          .                          .
                          .                          .
  0.7519 [-0.5320;  2.0357]                          .
                       MiET                          .
  1.3133 [-0.6924;  3.3189]                       ReET
 -1.1425 [-2.4020;  0.1170] -2.4558 [-4.0166; -0.8949]
                           
 -1.3622 [-2.2362; -0.4883]
 -1.3827 [-2.3150; -0.4505]
 -0.6000 [-2.2546;  1.0546]
                          .
                          .
 -0.5000 [-2.4960;  1.4960]
 -0.7354 [-2.5013;  1.0305]
 -2.5725 [-4.2338; -0.9112]
                       WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr1 <- netrank(nma_sr1, small.values = "good")
print(ranking_sr1)
       P-score
ReET    0.9479
AqET    0.7591
AeET    0.7217
MiET    0.6619
McT     0.4152
FlET    0.3492
CBT     0.3410
WlNi    0.2415
FlexEx  0.0624



Code 
# Rankogram
ran_sr1 <- rankogram(nma_sr1)
plot(ran_sr1)

Rankogram of treatments for Subnet 1




Code 
# Design decomposition
decomp_sr1 <- decomp.design(nma_sr1)
print(decomp_sr1)
Q statistics to assess homogeneity / consistency

                    Q df  p-value
Total           42.69 14 < 0.0001
Within designs  31.37  8   0.0001
Between designs 11.32  6   0.0789

Design-specific decomposition of within-designs Q statistic

    Design     Q df  p-value
 WlNi:AeET 25.80  3 < 0.0001
 WlNi:AqET  4.31  3   0.2296
 WlNi:MiET  0.78  1   0.3764
 AeET:AqET  0.48  1   0.4893

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from 0.0789)

 Detached design     Q df p-value
        McT:MiET  4.96  5  0.4202
    CBT:McT:MiET  5.18  4  0.2691
       WlNi:ReET  8.61  5  0.1256
       WlNi:MiET  9.85  5  0.0797
        WlNi:CBT  9.92  5  0.0776
  WlNi:AeET:ReET  8.60  4  0.0719
       AeET:AqET 10.97  5  0.0520
       WlNi:AqET 10.97  5  0.0520
       WlNi:AeET 11.16  5  0.0482
        WlNi:McT 11.31  5  0.0455

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 3.31  6  0.7686     0.9355      0.8752



Code 
# Node-splitting analysis to detect inconsistency
split_sr1 <- netsplit(nma_sr1, show = "all")
print(split_sr1)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

  comparison k prop     nma  direct  indir.    Diff     z p-value
   AeET:AqET 2 0.49  0.1039  0.2646 -0.0487  0.3134  0.34  0.7364
    AeET:CBT 0    0 -1.1114       . -1.1114       .     .       .
   AeET:FlET 1 1.00 -1.1800 -1.1800       .       .     .       .
 AeET:FlexEx 0    0 -2.9814       . -2.9814       .     .       .
    AeET:McT 0    0 -0.8702       . -0.8702       .     .       .
   AeET:MiET 0    0 -0.2181       . -0.2181       .     .       .
   AeET:ReET 1 0.55  1.0951  0.3700  1.9709 -1.6009 -0.96  0.3386
   AeET:WlNi 5 0.76 -1.3607 -1.3622 -1.3555 -0.0067 -0.01  0.9942
    AqET:CBT 0    0 -1.2153       . -1.2153       .     .       .
   AqET:FlET 0    0 -1.2839       . -1.2839       .     .       .
 AqET:FlexEx 0    0 -3.0853       . -3.0853       .     .       .
    AqET:McT 0    0 -0.9741       . -0.9741       .     .       .
   AqET:MiET 0    0 -0.3220       . -0.3220       .     .       .
   AqET:ReET 0    0  0.9912       .  0.9912       .     .       .
   AqET:WlNi 4 0.74 -1.4645 -1.3827 -1.6961  0.3134  0.34  0.7364
    CBT:FlET 0    0 -0.0686       . -0.0686       .     .       .
  CBT:FlexEx 1 1.00 -1.8700 -1.8700       .       .     .       .
     CBT:McT 1 0.57  0.2412  1.0000 -0.7563  1.7563  1.18  0.2392
    CBT:MiET 1 0.58  0.8933  0.9000  0.8841  0.0159  0.01  0.9912
    CBT:ReET 0    0  2.2066       .  2.2066       .     .       .
    CBT:WlNi 1 0.62 -0.2492 -0.6000  0.3229 -0.9229 -0.67  0.5003
 FlET:FlexEx 0    0 -1.8014       . -1.8014       .     .       .
    FlET:McT 0    0  0.3098       .  0.3098       .     .       .
   FlET:MiET 0    0  0.9619       .  0.9619       .     .       .
   FlET:ReET 0    0  2.2751       .  2.2751       .     .       .
   FlET:WlNi 0    0 -0.1807       . -0.1807       .     .       .
  FlexEx:McT 0    0  2.1112       .  2.1112       .     .       .
 FlexEx:MiET 0    0  2.7633       .  2.7633       .     .       .
 FlexEx:ReET 0    0  4.0766       .  4.0766       .     .       .
 FlexEx:WlNi 0    0  1.6208       .  1.6208       .     .       .
    McT:MiET 2 0.81  0.6521  0.7519  0.2222  0.5296  0.35  0.7256
    McT:ReET 0    0  1.9654       .  1.9654       .     .       .
    McT:WlNi 1 0.44 -0.4904 -0.5000 -0.4830 -0.0170 -0.01  0.9900
   MiET:ReET 0    0  1.3133       .  1.3133       .     .       .
   MiET:WlNi 2 0.51 -1.1425 -0.7354 -1.5641  0.8287  0.64  0.5192
   ReET:WlNi 2 0.88 -2.4558 -2.5725 -1.5768 -0.9957 -0.40  0.6875

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr1)

Forest plot of node-splitting for Subnet 1



Code 
# Heatmap
netheat(nma_sr1)

Heatmap of contribution matrix for Subnet 1



Code 
# Funnel plot
funnel(nma_sr1,
    order = "WlNi",
)

Funnel plot for Subnet 1 (P | Lg)





Select the procedures performed

Important

The second subnet contains 1 studies, 1 comparisons and 2 treatments. Due to its limited size, the analysis will be simplified.

Code 
# Filter data for subnet 2
sr2 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 2)

# Display first rows of comparison table
sr2 |> head()



Code 
# Unique treatments in subnet 2
unique_treat1_sr2 <- sr2$treat1 |> unique()
print(unique_treat1_sr2)
[1] "DryN"
Code 
unique_treat2_sr2 <- sr2$treat2 |> unique()
print(unique_treat2_sr2)
[1] "MasT"
Code 
# Combination of all unique treatments
trat_sr2 <- unique(c(unique_treat1_sr2, unique_treat2_sr2))
print(trat_sr2)
[1] "DryN" "MasT"
Code 
# Total number of treatments
length(trat_sr2)
[1] 2



Code 
# Filter pairwise object only for comparisons within subnet 2
pw_plg_sr2 <- pw %>%
    filter(treat1 %in% trat_sr2 & treat2 %in% trat_sr2)

# Number of comparisons in subnet 2
nrow(pw_plg_sr2)
[1] 1
Code 
# Number of unique studies
length(unique(pw_plg_sr2$studlab))
[1] 1



Code 
# Fit NMA model for subnet 2
nma_sr2 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_plg_sr2,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "MasT" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr2)
Number of studies: k = 1
Number of pairwise comparisons: m = 1
Number of observations: o = 59
Number of treatments: n = 2
Number of designs: d = 1

Random effects model

Treatment estimate (sm = 'MD', comparison: 'DryN' vs 'MasT'):
          MD            95%-CI     z p-value
DryN -1.0600 [-3.2020; 1.0820] -0.97  0.3321
MasT       .                 .     .       .

Quantifying heterogeneity:
tau^2 = NA; tau = NA

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2



Code 
# Network plot
netgraph(nma_sr2,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts)

Network plot of treatments for Subnet 2 (P | Lg)



Code 
# Detailed model summary
summary(nma_sr2)
Original data:

                   treat1 treat2      TE   seTE
Castro-Sanchez2011   DryN   MasT -1.0600 1.0929

Number of treatment arms (by study):
                   narms
Castro-Sanchez2011     2

Results (random effects model):

                   treat1 treat2      MD            95%-CI
Castro-Sanchez2011   DryN   MasT -1.0600 [-3.2020; 1.0820]

Number of studies: k = 1
Number of pairwise comparisons: m = 1
Number of observations: o = 59
Number of treatments: n = 2
Number of designs: d = 1

Random effects model

Treatment estimate (sm = 'MD', comparison: 'DryN' vs 'MasT'):
          MD            95%-CI     z p-value
DryN -1.0600 [-3.2020; 1.0820] -0.97  0.3321
MasT       .                 .     .       .

Quantifying heterogeneity:
tau^2 = NA; tau = NA

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2





Select the procedures performed

Important

the third subnet contains 4 studies, 4 comparisons and 4 treatments.

Code 
# Filter data for subnet 3
sr3 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 3)

# Display first rows of comparison table
sr3 |> head()



Code 
# Unique treatments in subnet 3
unique_treat1_sr3 <- sr3$treat1 |> unique()
print(unique_treat1_sr3)
[1] "MfT"  "Acu"  "rTMS"
Code 
unique_treat2_sr3 <- sr3$treat2 |> unique()
print(unique_treat2_sr3)
[1] "PlaSh"
Code 
# Combination of all unique treatments
trat_sr3 <- unique(c(unique_treat1_sr3, unique_treat2_sr3))
print(trat_sr3)
[1] "MfT"   "Acu"   "rTMS"  "PlaSh"
Code 
# Total number of treatments
length(trat_sr3)
[1] 4



Code 
# Filter pairwise object only for comparisons within subnet 3
pw_plg_sr3 <- pw %>%
    filter(treat1 %in% trat_sr3 & treat2 %in% trat_sr3)

# Number of comparisons in subnet 3
nrow(pw_plg_sr3)
[1] 4
Code 
# Number of unique studies
length(unique(pw_plg_sr3$studlab))
[1] 4



Code 
# Fit NMA model for subnet 3
nma_sr3 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_plg_sr3,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "PlaSh" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr3)
Number of studies: k = 4
Number of pairwise comparisons: m = 4
Number of observations: o = 235
Number of treatments: n = 4
Number of designs: d = 3

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'PlaSh'):
           MD             95%-CI     z p-value
Acu   -0.0800 [-1.4610;  1.3010] -0.11  0.9096
MfT   -1.0662 [-2.0393; -0.0931] -2.15  0.0318
PlaSh       .                  .     .       .
rTMS  -1.1700 [-2.0291; -0.3109] -2.67  0.0076

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0%

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           0.73    1  0.3925
Within designs  0.73    1  0.3925
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(nma_sr3,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts)

Network plot of treatments for Subnet 3 (P | Lg)



Code 
# Detailed model summary
summary(nma_sr3)
Original data:

            treat1 treat2      TE   seTE
Alfano2001     MfT  PlaSh -0.8500 0.5572
Colbert1999    MfT  PlaSh -1.9000 1.0942
Harris2005     Acu  PlaSh -0.0800 0.7046
Mhalla2011   PlaSh   rTMS  1.1700 0.4383

Number of treatment arms (by study):
            narms
Alfano2001      2
Colbert1999     2
Harris2005      2
Mhalla2011      2

Results (random effects model):

            treat1 treat2      MD             95%-CI
Alfano2001     MfT  PlaSh -1.0662 [-2.0393; -0.0931]
Colbert1999    MfT  PlaSh -1.0662 [-2.0393; -0.0931]
Harris2005     Acu  PlaSh -0.0800 [-1.4610;  1.3010]
Mhalla2011   PlaSh   rTMS  1.1700 [ 0.3109;  2.0291]

Number of studies: k = 4
Number of pairwise comparisons: m = 4
Number of observations: o = 235
Number of treatments: n = 4
Number of designs: d = 3

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'PlaSh'):
           MD             95%-CI     z p-value
Acu   -0.0800 [-1.4610;  1.3010] -0.11  0.9096
MfT   -1.0662 [-2.0393; -0.0931] -2.15  0.0318
PlaSh       .                  .     .       .
rTMS  -1.1700 [-2.0291; -0.3109] -2.67  0.0076

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0%

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           0.73    1  0.3925
Within designs  0.73    1  0.3925
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr3)

Forest plot of treatment effects for Subnet 3



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr3, ci = TRUE)
League table (random effects model):
                                                      
                        Acu                          .
  0.9862 [-0.7032;  2.6756]                        MfT
 -0.0800 [-1.4610;  1.3010] -1.0662 [-2.0393; -0.0931]
  1.0900 [-0.5364;  2.7164]  0.1038 [-1.1943;  1.4019]
                                                     
 -0.0800 [-1.4610;  1.3010]                         .
 -1.0662 [-2.0393; -0.0931]                         .
                      PlaSh 1.1700 [ 0.3109;  2.0291]
  1.1700 [ 0.3109;  2.0291]                      rTMS

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr3 <- netrank(nma_sr3, small.values = "good")
print(ranking_sr3)
      P-score
rTMS   0.8213
MfT    0.7652
Acu    0.2553
PlaSh  0.1582



Code 
# Rankogram
ran_sr3 <- rankogram(nma_sr3)
plot(ran_sr3)

Rankogram of treatments for Subnet 2



Code 
# Design decomposition
decomp_sr3 <- decomp.design(nma_sr3)
print(decomp_sr3)
Q statistics to assess homogeneity / consistency

                   Q df p-value
Total           0.73  1  0.3925
Within designs  0.73  1  0.3925
Between designs 0.00  0      --

Design-specific decomposition of within-designs Q statistic

    Design    Q df p-value
 PlaSh:MfT 0.73  1  0.3925

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 0.00  0      --          0           0



Code 
# Node-splitting analysis to detect inconsistency
split_sr3 <- netsplit(nma_sr3, show = "all")
print(split_sr3)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop     nma  direct indir. Diff z p-value
    Acu:MfT 0    0  0.9862       . 0.9862    . .       .
  Acu:PlaSh 1 1.00 -0.0800 -0.0800      .    . .       .
   Acu:rTMS 0    0  1.0900       . 1.0900    . .       .
  MfT:PlaSh 2 1.00 -1.0662 -1.0662      .    . .       .
   MfT:rTMS 0    0  0.1038       . 0.1038    . .       .
 rTMS:PlaSh 1 1.00 -1.1700 -1.1700      .    . .       .

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr3)

Forest plot of node-splitting for Subnet 3



Code 
# Heatmap
netheat(nma_sr3)



Code 
# Funnel plot
funnel(nma_sr3,
    order = "PlaSh",
)

Funnel plot for Subnet 3 (P | Lg)





Code 
# Read data
data_qim <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "Q | Im") |>
    mutate(
        Mean1 = as.numeric(Mean1),
        Mean2 = as.numeric(Mean2),
        SD1 = as.numeric(SD1),
        SD2 = as.numeric(SD2)
    )


# Transform to contrast-based
pw <- pairwise(
    treat = list(Treat1, Treat2),
    n = list(N1, N2),
    mean = list(Mean1, Mean2),
    sd = list(SD1, SD2),
    studlab = StudyID,
    data = data_qim
)

# Check network connections
net_con <- netconnection(pw)
net_con
Number of studies: k = 20
Number of pairwise comparisons: m = 20
Number of treatments: n = 11
Number of designs: d = 10
Number of networks: 1


There are network:

Network:
- 20 studies
- 20 comparisons
- 11 treatments



Tip

The network is fully connected.

1.0.2 Network

Select the procedures performed

Important

The network contain 20 studies, 20 comparisons and 11 treatments.

Code 
# Filter data for network
sr <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
)


# Display comparison table
sr



Code 
# Unique treatments in network
unique_treat_sr1 <- sr$treat1 |> unique()
print(unique_treat_sr1)
[1] "MnT"  "PbT"  "CBT"  "rTMS" "tDCS" "HtT"  "Bal"  "McT"  "Cry"
Code 
unique_treat_sr2 <- sr$treat2 |> unique()
print(unique_treat_sr2)
[1] "WlNi"  "PlaSh"
Code 
# Combination of all unique treatments
trat_sr <- unique(c(unique_treat_sr1, unique_treat_sr2))
print(trat_sr)
 [1] "MnT"   "PbT"   "CBT"   "rTMS"  "tDCS"  "HtT"   "Bal"   "McT"   "Cry"  
[10] "WlNi"  "PlaSh"
Code 
# Total number of treatments
length(trat_sr)
[1] 11



Code 
# Filter pairwise object only for comparisons within network
pw_qim <- pw %>%
    filter(treat1 %in% trat_sr & treat2 %in% trat_sr)

# Number of comparisons in network
nrow(pw_qim)
[1] 20



Code 
# Fit NMA model for network
nma_sr <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_qim,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "WlNi" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr)
Number of studies: k = 20
Number of pairwise comparisons: m = 20
Number of observations: o = 886
Number of treatments: n = 11
Number of designs: d = 10

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD               95%-CI     z  p-value
Bal   -15.0330 [-25.0820;  -4.9840] -2.93   0.0034
CBT    -1.1924 [-25.0968;  22.7120] -0.10   0.9221
Cry   -30.1200 [-42.4084; -17.8316] -4.80 < 0.0001
HtT   -24.1300 [-35.8403; -12.4197] -4.04 < 0.0001
McT    -7.1969 [-15.4843;   1.0906] -1.70   0.0887
MnT     1.6600 [-13.9760;  17.2960]  0.21   0.8352
PbT    -3.0576 [-23.6075;  17.4923] -0.29   0.7706
PlaSh   8.4076 [-10.1330;  26.9483]  0.89   0.3741
rTMS   -0.1422 [-19.7652;  19.4808] -0.01   0.9887
tDCS   -5.7600 [-21.9299;  10.4099] -0.70   0.4851
WlNi         .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 30.3434; tau = 5.5085; I^2 = 63% [29.0%; 80.7%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                 Q d.f. p-value
Total           27   10  0.0026
Within designs  27   10  0.0026
Between designs  0    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(nma_sr,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Network (Q | Im)



Code 
# Detailed model summary
summary(nma_sr)
Original data:

               treat1 treat2       TE    seTE
Albers2018        MnT   WlNi   1.6600  5.7706
Armagam2006       PbT  PlaSh  -5.1300  3.5183
Babu2007          CBT  PlaSh  -9.6000  5.3779
Boyer2014       PlaSh   rTMS   1.0000  4.7100
Curatolo2017    PlaSh   tDCS  28.2800  8.5783
Fagerlund2015    tDCS   WlNi  -5.7600  6.1417
Fioravanti2009    HtT   WlNi -24.1300  2.3140
Fioravanti2007    Bal   WlNi -21.3500  4.2760
Gur2002a          PbT  PlaSh -17.2800  2.9780
Hamnes2012        McT   WlNi  -2.7600  2.4785
Lee2012         PlaSh   rTMS   1.4000 16.3233
Mhalla2011      PlaSh   rTMS   9.3000  3.8196
Ozkurt2011        Bal   WlNi  -7.6000  5.1841
Passard2007     PlaSh   rTMS  10.4000  2.7307
Salaffi2015       McT   WlNi -11.4600  2.1713
Short2011       PlaSh   rTMS  11.7600  9.8838
Valle2009       PlaSh   tDCS  15.3100 11.9744
Yagci2014       PlaSh   rTMS  14.0300  6.3821
Loreti2023      PlaSh   tDCS   9.6200  1.2652
Kiyak2022         Cry   WlNi -30.1200  2.9943

Number of treatment arms (by study):
               narms
Albers2018         2
Armagam2006        2
Babu2007           2
Boyer2014          2
Curatolo2017       2
Fagerlund2015      2
Fioravanti2009     2
Fioravanti2007     2
Gur2002a           2
Hamnes2012         2
Lee2012            2
Mhalla2011         2
Ozkurt2011         2
Passard2007        2
Salaffi2015        2
Short2011          2
Valle2009          2
Yagci2014          2
Loreti2023         2
Kiyak2022          2

Results (random effects model):

               treat1 treat2       MD               95%-CI
Albers2018        MnT   WlNi   1.6600 [-13.9760;  17.2960]
Armagam2006       PbT  PlaSh -11.4652 [-20.3277;  -2.6028]
Babu2007          CBT  PlaSh  -9.6000 [-24.6886;   5.4886]
Boyer2014       PlaSh   rTMS   8.5498 [  2.1228;  14.9768]
Curatolo2017    PlaSh   tDCS  14.1676 [  5.0963;  23.2389]
Fagerlund2015    tDCS   WlNi  -5.7600 [-21.9299;  10.4099]
Fioravanti2009    HtT   WlNi -24.1300 [-35.8403; -12.4197]
Fioravanti2007    Bal   WlNi -15.0330 [-25.0820;  -4.9840]
Gur2002a          PbT  PlaSh -11.4652 [-20.3277;  -2.6028]
Hamnes2012        McT   WlNi  -7.1969 [-15.4843;   1.0906]
Lee2012         PlaSh   rTMS   8.5498 [  2.1228;  14.9768]
Mhalla2011      PlaSh   rTMS   8.5498 [  2.1228;  14.9768]
Ozkurt2011        Bal   WlNi -15.0330 [-25.0820;  -4.9840]
Passard2007     PlaSh   rTMS   8.5498 [  2.1228;  14.9768]
Salaffi2015       McT   WlNi  -7.1969 [-15.4843;   1.0906]
Short2011       PlaSh   rTMS   8.5498 [  2.1228;  14.9768]
Valle2009       PlaSh   tDCS  14.1676 [  5.0963;  23.2389]
Yagci2014       PlaSh   rTMS   8.5498 [  2.1228;  14.9768]
Loreti2023      PlaSh   tDCS  14.1676 [  5.0963;  23.2389]
Kiyak2022         Cry   WlNi -30.1200 [-42.4084; -17.8316]

Number of studies: k = 20
Number of pairwise comparisons: m = 20
Number of observations: o = 886
Number of treatments: n = 11
Number of designs: d = 10

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD               95%-CI     z  p-value
Bal   -15.0330 [-25.0820;  -4.9840] -2.93   0.0034
CBT    -1.1924 [-25.0968;  22.7120] -0.10   0.9221
Cry   -30.1200 [-42.4084; -17.8316] -4.80 < 0.0001
HtT   -24.1300 [-35.8403; -12.4197] -4.04 < 0.0001
McT    -7.1969 [-15.4843;   1.0906] -1.70   0.0887
MnT     1.6600 [-13.9760;  17.2960]  0.21   0.8352
PbT    -3.0576 [-23.6075;  17.4923] -0.29   0.7706
PlaSh   8.4076 [-10.1330;  26.9483]  0.89   0.3741
rTMS   -0.1422 [-19.7652;  19.4808] -0.01   0.9887
tDCS   -5.7600 [-21.9299;  10.4099] -0.70   0.4851
WlNi         .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 30.3434; tau = 5.5085; I^2 = 63% [29.0%; 80.7%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                 Q d.f. p-value
Total           27   10  0.0026
Within designs  27   10  0.0026
Between designs  0    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr)

Forest plot of treatment effects for network



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr, ci = TRUE)
League table (random effects model):
                                                           
                           Bal                            .
 -13.8406 [-39.7713;  12.0901]                          CBT
  15.0870 [ -0.7871;  30.9611] 28.9276 [  2.0496;  55.8056]
   9.0970 [ -6.3339;  24.5279] 22.9376 [ -3.6810;  49.5563]
  -7.8361 [-20.8616;   5.1894]  6.0045 [-19.2957;  31.3047]
 -16.6930 [-35.2797;   1.8937] -2.8524 [-31.4164;  25.7117]
 -11.9754 [-34.8507;  10.8999]  1.8652 [-15.6335;  19.3640]
 -23.4406 [-44.5294;  -2.3518] -9.6000 [-24.6886;   5.4886]
 -14.8908 [-36.9372;   7.1556] -1.0502 [-17.4506;  15.3502]
  -9.2730 [-28.3111;   9.7651]  4.5676 [-13.0379;  22.1731]
 -15.0330 [-25.0820;  -4.9840] -1.1924 [-25.0968;  22.7120]
                                                            
                             .                             .
                             .                             .
                           Cry                             .
  -5.9900 [-22.9646;  10.9846]                           HtT
 -22.9231 [-37.7450;  -8.1013] -16.9331 [-31.2793;  -2.5869]
 -31.7800 [-51.6669; -11.8931] -25.7900 [-45.3250;  -6.2550]
 -27.0624 [-51.0061;  -3.1186] -21.0724 [-44.7247;   2.5799]
 -38.5276 [-60.7709; -16.2844] -32.5376 [-54.4668; -10.6085]
 -29.9778 [-53.1310;  -6.8247] -23.9878 [-46.8394;  -1.1363]
 -24.3600 [-44.6694;  -4.0506] -18.3700 [-38.3349;   1.5949]
 -30.1200 [-42.4084; -17.8316] -24.1300 [-35.8403; -12.4197]
                                                           
                             .                            .
                             .                            .
                             .                            .
                             .                            .
                           McT                            .
  -8.8569 [-26.5534;   8.8396]                          MnT
  -4.1393 [-26.2973;  18.0188]  4.7176 [-21.1045;  30.5397]
 -15.6045 [-35.9130;   4.7041] -6.7476 [-31.0013;  17.5060]
  -7.0547 [-28.3560;  14.2466]  1.8022 [-23.2886;  26.8929]
  -1.4369 [-19.6069;  16.7331]  7.4200 [-15.0734;  29.9134]
  -7.1969 [-15.4843;   1.0906]  1.6600 [-13.9760;  17.2960]
                                                            
                             .                             .
                             .  -9.6000 [-24.6886;   5.4886]
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                           PbT -11.4652 [-20.3277;  -2.6028]
 -11.4652 [-20.3277;  -2.6028]                         PlaSh
  -2.9154 [-13.8630;   8.0321]   8.5498 [  2.1228;  14.9768]
   2.7024 [ -9.9795;  15.3843]  14.1676 [  5.0963;  23.2389]
  -3.0576 [-23.6075;  17.4923]   8.4076 [-10.1330;  26.9483]
                                                          
                            .                            .
                            .                            .
                            .                            .
                            .                            .
                            .                            .
                            .                            .
                            .                            .
  8.5498 [  2.1228;  14.9768] 14.1676 [  5.0963;  23.2389]
                         rTMS                            .
  5.6178 [ -5.4995;  16.7352]                         tDCS
 -0.1422 [-19.7652;  19.4808] -5.7600 [-21.9299;  10.4099]
                              
 -15.0330 [-25.0820;  -4.9840]
                             .
 -30.1200 [-42.4084; -17.8316]
 -24.1300 [-35.8403; -12.4197]
  -7.1969 [-15.4843;   1.0906]
   1.6600 [-13.9760;  17.2960]
                             .
                             .
                             .
  -5.7600 [-21.9299;  10.4099]
                          WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr <- netrank(nma_sr, small.values = "good")
print(ranking_sr)
      P-score
Cry    0.9676
HtT    0.8962
Bal    0.7418
McT    0.5482
tDCS   0.5346
PbT    0.4432
CBT    0.3815
rTMS   0.3345
WlNi   0.3025
MnT    0.2819
PlaSh  0.0680



Code 
# Rankogram
ran_sr <- rankogram(nma_sr)
plot(ran_sr)

Rankogram of treatments network



Code 
# Design decomposition
decomp_sr <- decomp.design(nma_sr)
print(decomp_sr)
Q statistics to assess homogeneity / consistency

                    Q df p-value
Total           27.00 10  0.0026
Within designs  27.00 10  0.0026
Between designs  0.00  0      --

Design-specific decomposition of within-designs Q statistic

     Design    Q df p-value
   WlNi:McT 6.97  1  0.0083
  PbT:PlaSh 6.95  1  0.0084
   WlNi:Bal 4.19  1  0.0407
 PlaSh:tDCS 4.82  2  0.0896
 PlaSh:rTMS 4.07  5  0.5398

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 0.00  0      --     5.5085     30.3434



Code 
# Node-splitting analysis to detect inconsistency
split_sr <- netsplit(nma_sr, show = "all")
print(split_sr)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop      nma   direct   indir. Diff z p-value
    Bal:CBT 0    0 -13.8406        . -13.8406    . .       .
    Bal:Cry 0    0  15.0870        .  15.0870    . .       .
    Bal:HtT 0    0   9.0970        .   9.0970    . .       .
    Bal:McT 0    0  -7.8361        .  -7.8361    . .       .
    Bal:MnT 0    0 -16.6930        . -16.6930    . .       .
    Bal:PbT 0    0 -11.9754        . -11.9754    . .       .
  Bal:PlaSh 0    0 -23.4406        . -23.4406    . .       .
   Bal:rTMS 0    0 -14.8908        . -14.8908    . .       .
   Bal:tDCS 0    0  -9.2730        .  -9.2730    . .       .
   Bal:WlNi 2 1.00 -15.0330 -15.0330        .    . .       .
    CBT:Cry 0    0  28.9276        .  28.9276    . .       .
    CBT:HtT 0    0  22.9376        .  22.9376    . .       .
    CBT:McT 0    0   6.0045        .   6.0045    . .       .
    CBT:MnT 0    0  -2.8524        .  -2.8524    . .       .
    CBT:PbT 0    0   1.8652        .   1.8652    . .       .
  CBT:PlaSh 1 1.00  -9.6000  -9.6000        .    . .       .
   CBT:rTMS 0    0  -1.0502        .  -1.0502    . .       .
   CBT:tDCS 0    0   4.5676        .   4.5676    . .       .
   CBT:WlNi 0    0  -1.1924        .  -1.1924    . .       .
    Cry:HtT 0    0  -5.9900        .  -5.9900    . .       .
    Cry:McT 0    0 -22.9231        . -22.9231    . .       .
    Cry:MnT 0    0 -31.7800        . -31.7800    . .       .
    Cry:PbT 0    0 -27.0624        . -27.0624    . .       .
  Cry:PlaSh 0    0 -38.5276        . -38.5276    . .       .
   Cry:rTMS 0    0 -29.9778        . -29.9778    . .       .
   Cry:tDCS 0    0 -24.3600        . -24.3600    . .       .
   Cry:WlNi 1 1.00 -30.1200 -30.1200        .    . .       .
    HtT:McT 0    0 -16.9331        . -16.9331    . .       .
    HtT:MnT 0    0 -25.7900        . -25.7900    . .       .
    HtT:PbT 0    0 -21.0724        . -21.0724    . .       .
  HtT:PlaSh 0    0 -32.5376        . -32.5376    . .       .
   HtT:rTMS 0    0 -23.9878        . -23.9878    . .       .
   HtT:tDCS 0    0 -18.3700        . -18.3700    . .       .
   HtT:WlNi 1 1.00 -24.1300 -24.1300        .    . .       .
    McT:MnT 0    0  -8.8569        .  -8.8569    . .       .
    McT:PbT 0    0  -4.1393        .  -4.1393    . .       .
  McT:PlaSh 0    0 -15.6045        . -15.6045    . .       .
   McT:rTMS 0    0  -7.0547        .  -7.0547    . .       .
   McT:tDCS 0    0  -1.4369        .  -1.4369    . .       .
   McT:WlNi 2 1.00  -7.1969  -7.1969        .    . .       .
    MnT:PbT 0    0   4.7176        .   4.7176    . .       .
  MnT:PlaSh 0    0  -6.7476        .  -6.7476    . .       .
   MnT:rTMS 0    0   1.8022        .   1.8022    . .       .
   MnT:tDCS 0    0   7.4200        .   7.4200    . .       .
   MnT:WlNi 1 1.00   1.6600   1.6600        .    . .       .
  PbT:PlaSh 2 1.00 -11.4652 -11.4652        .    . .       .
   PbT:rTMS 0    0  -2.9154        .  -2.9154    . .       .
   PbT:tDCS 0    0   2.7024        .   2.7024    . .       .
   PbT:WlNi 0    0  -3.0576        .  -3.0576    . .       .
 PlaSh:rTMS 6 1.00   8.5498   8.5498        .    . .       .
 PlaSh:tDCS 3 1.00  14.1676  14.1676        .    . .       .
 PlaSh:WlNi 0    0   8.4076        .   8.4076    . .       .
  rTMS:tDCS 0    0   5.6178        .   5.6178    . .       .
  rTMS:WlNi 0    0  -0.1422        .  -0.1422    . .       .
  tDCS:WlNi 1 1.00  -5.7600  -5.7600        .    . .       .

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr)

Forest plot of node-splitting for Network



Code 
# Heatmap
netheat(nma_sr)



Code 
# Funnel plot
funnel(nma_sr,
    order = "WlNi",
)

Funnel plot for Network (Q | Im)





Code 
# Read data
data_qsh <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "Q | Sh") |>
    mutate(
        Mean1 = as.numeric(Mean1),
        Mean2 = as.numeric(Mean2),
        Mean3 = as.numeric(Mean3),
        SD1 = as.numeric(SD1),
        SD2 = as.numeric(SD2),
        SD3 = as.numeric(SD3),
    )


# Transform to contrast-based
pw <- pairwise(
    treat = list(Treat1, Treat2, Treat3),
    n = list(N1, N2, N3),
    mean = list(Mean1, Mean2, Mean3),
    sd = list(SD1, SD2, SD3),
    studlab = StudyID,
    data = data_qsh,
    sm      = "MD"
)

# Check network connections
net_con <- netconnection(pw)
net_con
Number of studies: k = 99
Number of pairwise comparisons: m = 115
Number of treatments: n = 25
Number of designs: d = 49
Number of networks: 1


There are network:

Network:
- 99 studies
- 115 comparisons
- 25 treatments



Tip

The network is fully connected.

1.0.3 Network

Select the procedures performed

Important

The network contain 99 studies, 115 comparisons and 26 treatments.

Code 
# Filter data for network
sr <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
)


# Display comparison table
sr



Code 
# Unique treatments in network
unique_treat_sr1 <- sr$treat1 |> unique()
print(unique_treat_sr1)
 [1] "MnT"    "McT"    "WBV"    "MfT"    "AqET"   "Bal"    "AeET"   "FlET"  
 [9] "ReET"   "CBT"    "rTMS"   "DryN"   "MiET"   "Elec"   "MasT"   "tDCS"  
[17] "Acu"    "PbT"    "ManTh"  "MasTh"  "MiEx"   "FlexEx"
Code 
unique_treat_sr2 <- sr$treat2 |> unique()
print(unique_treat_sr2)
 [1] "WlNi"   "WBV"    "PlaSh"  "Bal"    "AqET"   "ReET"   "McT"    "FlET"  
 [9] "MasT"   "Plt"    "CBT"    "MiET"   "ManTh"  "MiEx"   "FlexEx"
Code 
# Combination of all unique treatments
trat_sr <- unique(c(unique_treat_sr1, unique_treat_sr2))
print(trat_sr)
 [1] "MnT"    "McT"    "WBV"    "MfT"    "AqET"   "Bal"    "AeET"   "FlET"  
 [9] "ReET"   "CBT"    "rTMS"   "DryN"   "MiET"   "Elec"   "MasT"   "tDCS"  
[17] "Acu"    "PbT"    "ManTh"  "MasTh"  "MiEx"   "FlexEx" "WlNi"   "PlaSh" 
[25] "Plt"
Code 
# Total number of treatments
length(trat_sr)
[1] 25



Code 
# Filter pairwise object only for comparisons within network
pw_qsh <- pw %>%
    filter(treat1 %in% trat_sr & treat2 %in% trat_sr)

# Number of comparisons in network
nrow(pw_qsh)
[1] 115



Code 
# Fit NMA model for network
nma_sr <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_qsh,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "WlNi" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr)
Number of studies: k = 99
Number of pairwise comparisons: m = 115
Number of observations: o = 6658
Number of treatments: n = 25
Number of designs: d = 49

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
             MD               95%-CI     z  p-value
Acu    -19.8814 [-31.8617;  -7.9011] -3.25   0.0011
AeET   -12.1494 [-18.5910;  -5.7077] -3.70   0.0002
AqET   -13.4467 [-20.4760;  -6.4175] -3.75   0.0002
Bal    -15.1868 [-25.4178;  -4.9557] -2.91   0.0036
CBT     -7.3401 [-11.3520;  -3.3282] -3.59   0.0003
DryN   -18.9003 [-33.3019;  -4.4986] -2.57   0.0101
Elec   -14.5898 [-30.6576;   1.4781] -1.78   0.0751
FlET    -5.1373 [-14.0671;   3.7926] -1.13   0.2595
FlexEx -16.2765 [-32.8737;   0.3206] -1.92   0.0546
ManTh  -23.8265 [-40.2174;  -7.4355] -2.85   0.0044
MasT    -5.1238 [-18.4460;   8.1983] -0.75   0.4510
MasTh  -33.8132 [-48.6401; -18.9863] -4.47 < 0.0001
McT    -12.7318 [-17.2173;  -8.2463] -5.56 < 0.0001
MfT    -19.1477 [-33.8644;  -4.4310] -2.55   0.0108
MiET    -9.0967 [-14.3450;  -3.8485] -3.40   0.0007
MiEx   -22.0943 [-38.3981;  -5.7906] -2.66   0.0079
MnT     -6.0107 [-20.6275;   8.6062] -0.81   0.4203
PbT    -15.7777 [-36.7570;   5.2016] -1.47   0.1405
PlaSh   -3.1777 [-13.4826;   7.1271] -0.60   0.5456
Plt    -16.0174 [-28.5529;  -3.4819] -2.50   0.0123
ReET   -19.7226 [-27.8471; -11.5980] -4.76 < 0.0001
rTMS   -11.1423 [-25.2615;   2.9769] -1.55   0.1219
tDCS    -7.5281 [-22.4400;   7.3838] -0.99   0.3224
WBV    -12.4979 [-21.6558;  -3.3401] -2.67   0.0075
WlNi          .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 71.7470; tau = 8.4704; I^2 = 82.7% [79.0%; 85.7%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           478.62   83 < 0.0001
Within designs  290.45   50 < 0.0001
Between designs 188.18   33 < 0.0001

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(nma_sr,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Network (Q | Sh)



Code 
# Detailed model summary
summary(nma_sr)
Original data (with adjusted standard errors for multi-arm studies):

                        treat1 treat2       TE    seTE seTE.adj narms multiarm
Albers2018                 MnT   WlNi  -8.3900  5.6141  10.1619     2         
Alentorn-Geli2008          McT    WBV   6.4100  6.4532  12.5201     3        *
Alentorn-Geli2008          McT   WlNi  -9.4400  7.3279  13.6918     3        *
Alentorn-Geli2008          WBV   WlNi -15.8500  7.9606  14.9142     3        *
Alfano2001                 MfT  PlaSh  -4.6400  3.5345   9.1782     2         
Altan2004                 AqET    Bal  -1.8800  4.7088   9.6912     2         
Ardic2007                  Bal   WlNi  -8.6800  4.3832   9.5372     2         
Assis2006                 AeET   AqET   3.0000  5.0248   9.8486     2         
Assumpçao2018             FlET   ReET   9.1000  9.5318  16.6511     3        *
Assumpçao2018             FlET   WlNi -14.8000  8.1936  14.0155     3        *
Assumpçao2018             ReET   WlNi -23.9000  8.2018  14.0272     3        *
Astin2003                  CBT    McT   1.3000  4.1904   9.4502     2         
Baumueller2017             CBT   WlNi   2.3700  6.6855  10.7909     2         
Bongi2012                  CBT    McT  10.0900  6.8643  10.9025     2         
Bongi2010                  CBT   WlNi -13.9000  5.6413  10.1770     2         
Bourgault2015              McT   WlNi  -1.5700  4.9106   9.7909     2         
Boyer2014                PlaSh   rTMS  11.6000  4.3853   9.5382     2         
Calandre2009              AqET   FlET  -4.7200  4.2444   9.4743     2         
Carson2010                 McT   WlNi -13.2000  5.0135   9.8429     2         
Casanueva2014             DryN   WlNi  -9.7000  3.3866   9.1223     2         
Castro-Sanchez2019        DryN   MasT -23.8200  4.3700   9.5312     2         
Collado-Mateo2017         MiET  PlaSh  -6.9300  3.3233   9.0990     2         
daCosta2005               MiET   WlNi  -7.3000  4.2695   9.4856     2         
Dailey2019                Elec  PlaSh -56.0600 23.1621  24.6623     2         
deMedeiros2020            AqET    Plt   7.0000  5.0943   9.8843     2         
Ekici2017                 MasT    Plt   6.5600  3.3208   9.0980     2         
Espi-Lopes2016            MiET   WlNi   1.7600  7.0148  10.9979     2         
Evcik2002                  Bal   WlNi -33.8000 10.9424  13.8378     2         
Fernandes2016             AeET   AqET   3.4800  4.1605   9.4370     2         
Fitzgibbon2018           PlaSh   rTMS   3.0700  7.9323  11.6047     2         
Fonseca2019               AqET    CBT  13.6000  4.3355   9.5154     2         
Garcia2006                 CBT   WlNi -13.8800  9.9308  13.0525     2         
Garcia-Martinez2012       MiET   WlNi -18.2100  7.4089  11.2534     2         
Giannotti2014              McT   WlNi   4.5300  5.6870  10.2024     2         
Glasgow2017               ReET   WlNi -30.0000  7.0456  11.0176     2         
Gomez-Hernandez2019       AeET   MiET  10.6200  0.8775   8.5157     2         
Gowans2001                AqET   WlNi  -6.7300  5.8527  10.2957     2         
Hargrove2012             PlaSh   tDCS   9.9000  4.5112   9.5967     2         
Jones2002                  McT   ReET   5.5500  4.8917   9.7814     2         
Jones2012                  CBT    McT  13.4000  6.5801  10.7259     2         
Karatay2018                Acu  PlaSh -17.1100  4.8992   9.7852     2         
Kayo2012                  AeET   ReET  -9.7400  5.4131  12.3649     3        *
Kayo2012                  AeET   WlNi -16.1300  5.3516  12.2826     3        *
Kayo2012                  ReET   WlNi  -6.3900  5.2328  12.1306     3        *
King2002                   CBT    McT  11.6000  4.8603   9.7657     2         
Kurt2016                   Bal   MiET  -7.1000  2.5883   8.8570     2         
Lami2018                   CBT   WlNi   1.4400  3.3937   9.1249     2         
Lauche2016                MasT  PlaSh  -6.6000  2.8655   8.9419     2         
Lopes-Rodrigues2012       AqET   FlET -17.0700  4.6996   9.6868     2         
Lopes-Rodrigues2013       AqET   FlET -14.7900  4.2189   9.4629     2         
Luciano2014                CBT   WlNi -18.9800  1.5949   8.6192     2         
Lynch2012                  McT   WlNi -17.5200  3.2954   9.0888     2         
Mhalla2011               PlaSh   rTMS  10.7000  4.4529   9.5695     2         
Mist2018                   Acu    CBT -22.4000  5.0071   9.8396     2         
Olivares2011               WBV   WlNi  -3.7300  3.6133   9.2088     2         
Paolucci2016               MfT  PlaSh -22.3000  4.2735   9.4874     2         
Paolucci2015              MiET   WlNi  -9.7000  3.6907   9.2395     2         
Parra-Delgado2013          CBT   WlNi  -4.4300  5.5637  10.1342     2         
Pereira-Pernambuco2018     McT   WlNi -37.5900  3.2725   9.0805     2         
Perez-Aranda2019           CBT   WlNi  -6.8600  2.9360   8.9648     2         
Picard2013                 CBT   WlNi  -1.3500  4.6479   9.6618     2         
Redondo2004                CBT   MiET   4.3600  5.5606  10.1325     2         
Richards2002              AeET    McT   0.3000  2.6343   8.8705     2         
Rivera2018                 WBV   WlNi -22.0000  4.7523   9.7124     2         
Ruaro2014                  PbT  PlaSh -12.6000  3.8967   9.3237     2         
Salaffi2015                McT   WlNi  -8.2400  2.1713   8.7442     2         
Schachter2003             AeET   WlNi -10.1900  3.3527   9.1098     2         
Schmidt2011                CBT   WlNi  -3.0300  2.4137   8.8075     2         
Sevimli2015               AeET   AqET   1.7000  4.6428  11.8469     3        *
Sevimli2015               AeET   MiET -26.3000  4.4976  11.6804     3        *
Sevimli2015               AqET   MiET -28.0000  4.6973  11.9126     3        *
Silva2019                  CBT   ReET  25.7400  4.1233   9.4207     2         
Simister2018               CBT   WlNi -16.2300  3.2949   9.0886     2         
Soares2002                 CBT   WlNi  -1.8400  1.6938   8.6381     2         
Sutbeyaz2009               MfT  PlaSh -21.4000  3.5877   9.1988     2         
Tomas-Carus2007b&c        AqET   WlNi  -8.0000  6.1835  10.4872     2         
Ugurlu2017                 Acu  PlaSh -26.0300  3.5736   9.1933     2         
Valim2003                 AeET   FlET  -3.3100  4.8020   9.7369     2         
Vallejo2015                CBT   WlNi  -2.7600  4.8915   9.7813     2         
Vas2016                    Acu  PlaSh  -8.5000  2.5814   8.8550     2         
Verkaik2013                CBT   WlNi  -3.8000  3.3368   9.1039     2         
Wang2018                   McT   MiET  -6.8800  2.9934   8.9837     2         
Wicksell2013               CBT   WlNi  -4.8000  3.6440   9.2209     2         
Arakaki2021               FlET   ReET  15.7100  5.6273  10.1693     2         
Atan2020                  MiET   WlNi -31.0800  4.3638   9.5284     2         
Barranengoa-Cuadra2021     CBT   WlNi -24.1000  3.0388   8.9990     2         
Ceballos-Laita2020         McT   MiET  -0.3500  7.7076  11.4522     2         
Coste2021                  MnT  PlaSh  -0.8000  4.0600   9.3931     2         
Izquierdo-Alventosa2020   MiET   WlNi  -5.5800  5.9339  10.3421     2         
Jamison2021               Elec  PlaSh  -7.4700  2.4770   8.8251     2         
Mingorance2021.2           WBV   WlNi  -8.2000  2.5870   8.8566     2         
Rodriguez-Mansilla2021     McT   MiET  -0.0800  4.2198  12.0236     3        *
Rodriguez-Mansilla2021    MiET   WlNi -11.6600  3.2126  10.9511     3        *
Rodriguez-Mansilla2021     McT   WlNi -11.7400  2.9326  10.7426     3        *
Sarmento2020               McT  PlaSh -18.0000  9.1302  12.4542     2         
Udina-Cortés2020          Elec  PlaSh  -9.3000  4.5740   9.6264     2         
Lacroix2022              PlaSh   rTMS   5.1500  3.5083   9.1682     2         
Paolucci2022               CBT   MiET  -8.5000  6.9387  10.9496     2         
Park2021                  FlET   ReET  11.3000  6.5679  10.7184     2         
Samartin-Veiga2022       PlaSh   tDCS   1.3400  5.3236  10.0044     2         
Alptug2023               ManTh   WlNi -24.1000  5.9968  10.3783     2         
Audoux2023               ManTh  MasTh  10.3000  7.1849  11.1072     2         
Baelz2022                  Acu  PlaSh  -2.6000  7.3763  11.2320     2         
Caumo2023                PlaSh   tDCS   1.8800  3.1792   9.0473     2         
Franco2023                AeET    Plt   4.5000  4.2791   9.4899     2         
Rodríguez-Mansilla2023    AeET    McT   0.0900  3.2027  11.2562     3        *
Rodríguez-Mansilla2023    AeET   WlNi -10.4800  2.6296  10.7871     3        *
Rodríguez-Mansilla2023     McT   WlNi -10.5700  2.6113  10.7745     3        *
Patru2021                  McT   MiEx  11.8000  4.6757  11.9824     3        *
Patru2021                  McT   WlNi  -8.1000  4.5444  11.8201     3        *
Patru2021                 MiEx   WlNi -19.9000  4.1244  11.3690     3        *
Lee2024                    CBT    McT   0.1000  2.6946   8.8886     2         
Schulze2023             FlexEx  MasTh  17.4400  2.1681  10.7182     3        *
Schulze2023              MasTh   WlNi -33.6200  2.0780  10.6647     3        *
Schulze2023             FlexEx   WlNi -16.1800  2.1603  10.7134     3        *

Number of treatment arms (by study):
                        narms
Albers2018                  2
Alentorn-Geli2008           3
Alfano2001                  2
Altan2004                   2
Ardic2007                   2
Assis2006                   2
Assumpçao2018               3
Astin2003                   2
Baumueller2017              2
Bongi2012                   2
Bongi2010                   2
Bourgault2015               2
Boyer2014                   2
Calandre2009                2
Carson2010                  2
Casanueva2014               2
Castro-Sanchez2019          2
Collado-Mateo2017           2
daCosta2005                 2
Dailey2019                  2
deMedeiros2020              2
Ekici2017                   2
Espi-Lopes2016              2
Evcik2002                   2
Fernandes2016               2
Fitzgibbon2018              2
Fonseca2019                 2
Garcia2006                  2
Garcia-Martinez2012         2
Giannotti2014               2
Glasgow2017                 2
Gomez-Hernandez2019         2
Gowans2001                  2
Hargrove2012                2
Jones2002                   2
Jones2012                   2
Karatay2018                 2
Kayo2012                    3
King2002                    2
Kurt2016                    2
Lami2018                    2
Lauche2016                  2
Lopes-Rodrigues2012         2
Lopes-Rodrigues2013         2
Luciano2014                 2
Lynch2012                   2
Mhalla2011                  2
Mist2018                    2
Olivares2011                2
Paolucci2016                2
Paolucci2015                2
Parra-Delgado2013           2
Pereira-Pernambuco2018      2
Perez-Aranda2019            2
Picard2013                  2
Redondo2004                 2
Richards2002                2
Rivera2018                  2
Ruaro2014                   2
Salaffi2015                 2
Schachter2003               2
Schmidt2011                 2
Sevimli2015                 3
Silva2019                   2
Simister2018                2
Soares2002                  2
Sutbeyaz2009                2
Tomas-Carus2007b&c          2
Ugurlu2017                  2
Valim2003                   2
Vallejo2015                 2
Vas2016                     2
Verkaik2013                 2
Wang2018                    2
Wicksell2013                2
Arakaki2021                 2
Atan2020                    2
Barranengoa-Cuadra2021      2
Ceballos-Laita2020          2
Coste2021                   2
Izquierdo-Alventosa2020     2
Jamison2021                 2
Mingorance2021.2            2
Rodriguez-Mansilla2021      3
Sarmento2020                2
Udina-Cortés2020            2
Lacroix2022                 2
Paolucci2022                2
Park2021                    2
Samartin-Veiga2022          2
Alptug2023                  2
Audoux2023                  2
Baelz2022                   2
Caumo2023                   2
Franco2023                  2
Rodríguez-Mansilla2023      3
Patru2021                   3
Lee2024                     2
Schulze2023                 3

Results (random effects model):

                        treat1 treat2       MD               95%-CI
Albers2018                 MnT   WlNi  -6.0107 [-20.6275;   8.6062]
Alentorn-Geli2008          McT    WBV  -0.2339 [-10.1539;   9.6861]
Alentorn-Geli2008          McT   WlNi -12.7318 [-17.2173;  -8.2463]
Alentorn-Geli2008          WBV   WlNi -12.4979 [-21.6558;  -3.3401]
Alfano2001                 MfT  PlaSh -15.9700 [-26.4767;  -5.4632]
Altan2004                 AqET    Bal   1.7401 [ -9.3409;  12.8210]
Ardic2007                  Bal   WlNi -15.1868 [-25.4178;  -4.9557]
Assis2006                 AeET   AqET   1.2974 [ -6.0259;   8.6206]
Assumpçao2018             FlET   ReET  14.5853 [  5.1075;  24.0631]
Assumpçao2018             FlET   WlNi  -5.1373 [-14.0671;   3.7926]
Assumpçao2018             ReET   WlNi -19.7226 [-27.8471; -11.5980]
Astin2003                  CBT    McT   5.3917 [  0.2470;  10.5365]
Baumueller2017             CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Bongi2012                  CBT    McT   5.3917 [  0.2470;  10.5365]
Bongi2010                  CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Bourgault2015              McT   WlNi -12.7318 [-17.2173;  -8.2463]
Boyer2014                PlaSh   rTMS   7.9646 [ -1.6874;  17.6166]
Calandre2009              AqET   FlET  -8.3095 [-16.6617;   0.0427]
Carson2010                 McT   WlNi -12.7318 [-17.2173;  -8.2463]
Casanueva2014             DryN   WlNi -18.9003 [-33.3019;  -4.4986]
Castro-Sanchez2019        DryN   MasT -13.7764 [-28.4456;   0.8927]
Collado-Mateo2017         MiET  PlaSh  -5.9190 [-16.4771;   4.6391]
daCosta2005               MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Dailey2019                Elec  PlaSh -11.4120 [-23.7403;   0.9162]
deMedeiros2020            AqET    Plt   2.5707 [ -9.8486;  14.9900]
Ekici2017                 MasT    Plt  10.8936 [ -2.8804;  24.6675]
Espi-Lopes2016            MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Evcik2002                  Bal   WlNi -15.1868 [-25.4178;  -4.9557]
Fernandes2016             AeET   AqET   1.2974 [ -6.0259;   8.6206]
Fitzgibbon2018           PlaSh   rTMS   7.9646 [ -1.6874;  17.6166]
Fonseca2019               AqET    CBT  -6.1066 [-13.6750;   1.4617]
Garcia2006                 CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Garcia-Martinez2012       MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Giannotti2014              McT   WlNi -12.7318 [-17.2173;  -8.2463]
Glasgow2017               ReET   WlNi -19.7226 [-27.8471; -11.5980]
Gomez-Hernandez2019       AeET   MiET  -3.0526 [-10.2506;   4.1453]
Gowans2001                AqET   WlNi -13.4467 [-20.4760;  -6.4175]
Hargrove2012             PlaSh   tDCS   4.3504 [ -6.4281;  15.1289]
Jones2002                  McT   ReET   6.9907 [ -1.6346;  15.6160]
Jones2012                  CBT    McT   5.3917 [  0.2470;  10.5365]
Karatay2018                Acu  PlaSh -16.7037 [-25.4358;  -7.9715]
Kayo2012                  AeET   ReET   7.5732 [ -1.6669;  16.8132]
Kayo2012                  AeET   WlNi -12.1494 [-18.5910;  -5.7077]
Kayo2012                  ReET   WlNi -19.7226 [-27.8471; -11.5980]
King2002                   CBT    McT   5.3917 [  0.2470;  10.5365]
Kurt2016                   Bal   MiET  -6.0900 [-16.6036;   4.4235]
Lami2018                   CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Lauche2016                MasT  PlaSh  -1.9461 [-15.2520;  11.3599]
Lopes-Rodrigues2012       AqET   FlET  -8.3095 [-16.6617;   0.0427]
Lopes-Rodrigues2013       AqET   FlET  -8.3095 [-16.6617;   0.0427]
Luciano2014                CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Lynch2012                  McT   WlNi -12.7318 [-17.2173;  -8.2463]
Mhalla2011               PlaSh   rTMS   7.9646 [ -1.6874;  17.6166]
Mist2018                   Acu    CBT -12.5413 [-24.5415;  -0.5411]
Olivares2011               WBV   WlNi -12.4979 [-21.6558;  -3.3401]
Paolucci2016               MfT  PlaSh -15.9700 [-26.4767;  -5.4632]
Paolucci2015              MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Parra-Delgado2013          CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Pereira-Pernambuco2018     McT   WlNi -12.7318 [-17.2173;  -8.2463]
Perez-Aranda2019           CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Picard2013                 CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Redondo2004                CBT   MiET   1.7566 [ -4.2562;   7.7695]
Richards2002              AeET    McT   0.5824 [ -6.4077;   7.5726]
Rivera2018                 WBV   WlNi -12.4979 [-21.6558;  -3.3401]
Ruaro2014                  PbT  PlaSh -12.6000 [-30.8741;   5.6741]
Salaffi2015                McT   WlNi -12.7318 [-17.2173;  -8.2463]
Schachter2003             AeET   WlNi -12.1494 [-18.5910;  -5.7077]
Schmidt2011                CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Sevimli2015               AeET   AqET   1.2974 [ -6.0259;   8.6206]
Sevimli2015               AeET   MiET  -3.0526 [-10.2506;   4.1453]
Sevimli2015               AqET   MiET  -4.3500 [-12.2392;   3.5392]
Silva2019                  CBT   ReET  12.3825 [  3.8710;  20.8939]
Simister2018               CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Soares2002                 CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Sutbeyaz2009               MfT  PlaSh -15.9700 [-26.4767;  -5.4632]
Tomas-Carus2007b&c        AqET   WlNi -13.4467 [-20.4760;  -6.4175]
Ugurlu2017                 Acu  PlaSh -16.7037 [-25.4358;  -7.9715]
Valim2003                 AeET   FlET  -7.0121 [-16.2065;   2.1823]
Vallejo2015                CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Vas2016                    Acu  PlaSh -16.7037 [-25.4358;  -7.9715]
Verkaik2013                CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Wang2018                   McT   MiET  -3.6351 [ -9.6881;   2.4180]
Wicksell2013               CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Arakaki2021               FlET   ReET  14.5853 [  5.1075;  24.0631]
Atan2020                  MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Barranengoa-Cuadra2021     CBT   WlNi  -7.3401 [-11.3520;  -3.3282]
Ceballos-Laita2020         McT   MiET  -3.6351 [ -9.6881;   2.4180]
Coste2021                  MnT  PlaSh  -2.8329 [-17.1617;  11.4959]
Izquierdo-Alventosa2020   MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Jamison2021               Elec  PlaSh -11.4120 [-23.7403;   0.9162]
Mingorance2021.2           WBV   WlNi -12.4979 [-21.6558;  -3.3401]
Rodriguez-Mansilla2021     McT   MiET  -3.6351 [ -9.6881;   2.4180]
Rodriguez-Mansilla2021    MiET   WlNi  -9.0967 [-14.3450;  -3.8485]
Rodriguez-Mansilla2021     McT   WlNi -12.7318 [-17.2173;  -8.2463]
Sarmento2020               McT  PlaSh  -9.5541 [-20.1833;   1.0752]
Udina-Cortés2020          Elec  PlaSh -11.4120 [-23.7403;   0.9162]
Lacroix2022              PlaSh   rTMS   7.9646 [ -1.6874;  17.6166]
Paolucci2022               CBT   MiET   1.7566 [ -4.2562;   7.7695]
Park2021                  FlET   ReET  14.5853 [  5.1075;  24.0631]
Samartin-Veiga2022       PlaSh   tDCS   4.3504 [ -6.4281;  15.1289]
Alptug2023               ManTh   WlNi -23.8265 [-40.2174;  -7.4355]
Audoux2023               ManTh  MasTh   9.9867 [ -6.8526;  26.8260]
Baelz2022                  Acu  PlaSh -16.7037 [-25.4358;  -7.9715]
Caumo2023                PlaSh   tDCS   4.3504 [ -6.4281;  15.1289]
Franco2023                AeET    Plt   3.8680 [ -8.4000;  16.1360]
Rodríguez-Mansilla2023    AeET    McT   0.5824 [ -6.4077;   7.5726]
Rodríguez-Mansilla2023    AeET   WlNi -12.1494 [-18.5910;  -5.7077]
Rodríguez-Mansilla2023     McT   WlNi -12.7318 [-17.2173;  -8.2463]
Patru2021                  McT   MiEx   9.3625 [ -6.9736;  25.6986]
Patru2021                  McT   WlNi -12.7318 [-17.2173;  -8.2463]
Patru2021                 MiEx   WlNi -22.0943 [-38.3981;  -5.7906]
Lee2024                    CBT    McT   5.3917 [  0.2470;  10.5365]
Schulze2023             FlexEx  MasTh  17.5366 [  0.9365;  34.1367]
Schulze2023              MasTh   WlNi -33.8132 [-48.6401; -18.9863]
Schulze2023             FlexEx   WlNi -16.2765 [-32.8737;   0.3206]

Number of studies: k = 99
Number of pairwise comparisons: m = 115
Number of observations: o = 6658
Number of treatments: n = 25
Number of designs: d = 49

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
             MD               95%-CI     z  p-value
Acu    -19.8814 [-31.8617;  -7.9011] -3.25   0.0011
AeET   -12.1494 [-18.5910;  -5.7077] -3.70   0.0002
AqET   -13.4467 [-20.4760;  -6.4175] -3.75   0.0002
Bal    -15.1868 [-25.4178;  -4.9557] -2.91   0.0036
CBT     -7.3401 [-11.3520;  -3.3282] -3.59   0.0003
DryN   -18.9003 [-33.3019;  -4.4986] -2.57   0.0101
Elec   -14.5898 [-30.6576;   1.4781] -1.78   0.0751
FlET    -5.1373 [-14.0671;   3.7926] -1.13   0.2595
FlexEx -16.2765 [-32.8737;   0.3206] -1.92   0.0546
ManTh  -23.8265 [-40.2174;  -7.4355] -2.85   0.0044
MasT    -5.1238 [-18.4460;   8.1983] -0.75   0.4510
MasTh  -33.8132 [-48.6401; -18.9863] -4.47 < 0.0001
McT    -12.7318 [-17.2173;  -8.2463] -5.56 < 0.0001
MfT    -19.1477 [-33.8644;  -4.4310] -2.55   0.0108
MiET    -9.0967 [-14.3450;  -3.8485] -3.40   0.0007
MiEx   -22.0943 [-38.3981;  -5.7906] -2.66   0.0079
MnT     -6.0107 [-20.6275;   8.6062] -0.81   0.4203
PbT    -15.7777 [-36.7570;   5.2016] -1.47   0.1405
PlaSh   -3.1777 [-13.4826;   7.1271] -0.60   0.5456
Plt    -16.0174 [-28.5529;  -3.4819] -2.50   0.0123
ReET   -19.7226 [-27.8471; -11.5980] -4.76 < 0.0001
rTMS   -11.1423 [-25.2615;   2.9769] -1.55   0.1219
tDCS    -7.5281 [-22.4400;   7.3838] -0.99   0.3224
WBV    -12.4979 [-21.6558;  -3.3401] -2.67   0.0075
WlNi          .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 71.7470; tau = 8.4704; I^2 = 82.7% [79.0%; 85.7%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           478.62   83 < 0.0001
Within designs  290.45   50 < 0.0001
Between designs 188.18   33 < 0.0001

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr)

Forest plot of treatment effects for network



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr, ci = TRUE)
League table (random effects model):
                                                            
                           Acu                             .
  -7.7320 [-20.8393;   5.3753]                          AeET
  -6.4347 [-19.8449;   6.9756]   1.2974 [ -6.0259;   8.6206]
  -4.6946 [-20.1360;  10.7468]   3.0374 [ -8.3908;  14.4657]
 -12.5413 [-24.5415;  -0.5411]  -4.8093 [-11.9538;   2.3353]
  -0.9811 [-18.5629;  16.6007]   6.7509 [ -8.6379;  22.1396]
  -5.2916 [-20.3991;   9.8159]   2.4404 [-14.4369;  19.3177]
 -14.7441 [-29.3170;  -0.1713]  -7.0121 [-16.2065;   2.1823]
  -3.6048 [-24.0742;  16.8645]   4.1272 [-13.6762;  21.9306]
   3.9451 [-16.3574;  24.2476]  11.6771 [ -5.9342;  29.2884]
 -14.7576 [-30.0397;   0.5246]  -7.0256 [-20.9429;   6.8918]
  13.9318 [ -5.1304;  32.9939]  21.6638 [  5.4980;  37.8295]
  -7.1496 [-19.4383;   5.1392]   0.5824 [ -6.4077;   7.5726]
  -0.7337 [-14.3954;  12.9280]   6.9983 [ -8.5981;  22.5948]
 -10.7846 [-23.1003;   1.5310]  -3.0526 [-10.2506;   4.1453]
   2.2129 [-17.8708;  22.2966]   9.9450 [ -7.4120;  27.3019]
 -13.8707 [-30.1076;   2.3662]  -6.1387 [-21.8597;   9.5823]
  -4.1037 [-24.3569;  16.1496]   3.6284 [-17.9772;  25.2339]
 -16.7037 [-25.4358;  -7.9715]  -8.9716 [-20.4980;   2.5547]
  -3.8640 [-20.0084;  12.2804]   3.8680 [ -8.4000;  16.1360]
  -0.1588 [-14.3194;  14.0017]   7.5732 [ -1.6669;  16.8132]
  -8.7391 [-21.7549;   4.2768]  -1.0071 [-16.0410;  14.0269]
 -12.3533 [-26.2250;   1.5185]  -4.6212 [-20.4020;  11.1595]
  -7.3835 [-22.4049;   7.6380]   0.3486 [-10.7687;  11.4658]
 -19.8814 [-31.8617;  -7.9011] -12.1494 [-18.5910;  -5.7077]
                                                            
                             .                             .
   2.7351 [ -8.1778;  13.6481]                             .
                          AqET  -1.8800 [-20.8744;  17.1144]
   1.7401 [ -9.3409;  12.8210]                           Bal
  -6.1066 [-13.6750;   1.4617]  -7.8467 [-18.6240;   2.9306]
   5.4535 [-10.1683;  21.0754]   3.7135 [-13.7870;  21.2139]
   1.1430 [-15.9832;  18.2693]  -0.5970 [-19.3546;  18.1606]
  -8.3095 [-16.6617;   0.0427] -10.0495 [-22.8788;   2.7798]
   2.8298 [-15.1945;  20.8541]   1.0897 [-18.4074;  20.5869]
  10.3797 [ -7.4549;  28.2144]   8.6397 [-10.6823;  27.9616]
  -8.3229 [-22.4710;   5.8252] -10.0630 [-26.4943;   6.3684]
  20.3664 [  3.9577;  36.7752]  18.6264 [  0.6122;  36.6406]
  -0.7149 [ -8.5139;   7.0841]  -2.4550 [-13.3594;   8.4494]
   5.7010 [-10.1645;  21.5665]   3.9609 [-13.6531;  21.5749]
  -4.3500 [-12.2392;   3.5392]  -6.0900 [-16.6036;   4.4235]
   8.6476 [ -8.9904;  26.2856]   6.9075 [-12.2679;  26.0830]
  -7.4361 [-23.4161;   8.5440]  -9.1761 [-26.8508;   8.4985]
   2.3310 [-19.4695;  24.1315]   0.5909 [-22.5133;  23.6951]
 -10.2690 [-22.1569;   1.6189] -12.0091 [-26.1463;   2.1282]
   2.5707 [ -9.8486;  14.9900]   0.8306 [-14.7469;  16.4081]
   6.2758 [ -3.2524;  15.8040]   4.5358 [ -8.1696;  17.2411]
  -2.3044 [-17.6173;  13.0084]  -4.0445 [-21.1624;  13.0735]
  -5.9186 [-21.9653;  10.1281]  -7.6587 [-25.4361;  10.1188]
  -0.9488 [-12.4410;  10.5434]  -2.6889 [-16.3901;  11.0124]
 -13.4467 [-20.4760;  -6.4175] -15.1868 [-25.4178;  -4.9557]
                                                            
 -22.4000 [-41.6853;  -3.1147]                             .
                             .                             .
  13.6000 [ -5.0499;  32.2499]                             .
                             .                             .
                           CBT                             .
  11.5602 [ -3.2648;  26.3851]                          DryN
   7.2497 [ -8.9564;  23.4557]  -4.3105 [-24.6724;  16.0514]
  -2.2028 [-11.5842;   7.1785] -13.7630 [-30.4276;   2.9016]
   8.9364 [ -8.1387;  26.0116]  -2.6237 [-24.5981;  19.3506]
  16.4864 [ -0.3884;  33.3611]   4.9262 [-16.8928;  26.7452]
  -2.2163 [-15.8466;  11.4141] -13.7764 [-28.4456;   0.8927]
  26.4731 [ 11.1130;  41.8331]  14.9129 [ -5.7569;  35.5828]
   5.3917 [  0.2470;  10.5365]  -6.1684 [-21.0990;   8.7621]
  11.8076 [ -3.0599;  26.6751]   0.2475 [-19.0661;  19.5610]
   1.7566 [ -4.2562;   7.7695]  -9.8035 [-24.8882;   5.2812]
  14.7542 [ -1.8978;  31.4062]   3.1941 [-18.5093;  24.8975]
  -1.3294 [-16.2784;  13.6196] -12.8896 [-32.7282;   6.9490]
   8.4376 [-12.6477;  29.5230]  -3.1225 [-27.5472;  21.3021]
  -4.1624 [-14.6814;   6.3567] -15.7225 [-31.9281;   0.4831]
   8.6773 [ -4.1961;  21.5507]  -2.8829 [-20.0663;  14.3006]
  12.3825 [  3.8710;  20.8939]   0.8223 [-15.5503;  17.1949]
   3.8022 [-10.4741;  18.0785]  -7.7579 [-26.6202;  11.1043]
   0.1880 [-14.8727;  15.2488] -11.3721 [-30.8348;   8.0906]
   5.1578 [ -4.7724;  15.0881]  -6.4023 [-23.4503;  10.6457]
  -7.3401 [-11.3520;  -3.3282] -18.9003 [-33.3019;  -4.4986]
                                                            
                             .                             .
                             .  -3.3100 [-22.3939;  15.7739]
                             . -12.1240 [-22.9189;  -1.3290]
                             .                             .
                             .                             .
                             .                             .
                          Elec                             .
  -9.4525 [-27.5156;   8.6106]                          FlET
   1.6868 [-21.4139;  24.7875]  11.1393 [ -7.7077;  29.9862]
   9.2367 [-13.7163;  32.1897]  18.6892 [  0.0236;  37.3548]
  -9.4660 [-27.6053;   8.6733]  -0.0134 [-15.4237;  15.3969]
  19.2234 [ -2.6401;  41.0869]  28.6759 [ 11.3676;  45.9843]
  -1.8579 [-18.1357;  14.4198]   7.5946 [ -1.9047;  17.0939]
   4.5579 [-11.6401;  20.7560]  14.0105 [ -2.8620;  30.8829]
  -5.4930 [-21.7244;  10.7384]   3.9595 [ -5.8022;  13.7211]
   7.5046 [-15.2479;  30.2570]  16.9571 [ -1.5090;  35.4231]
  -8.5791 [-27.4815;  10.3233]   0.8734 [-16.0711;  17.8179]
   1.1880 [-20.8558;  23.2317]  10.6405 [-11.9035;  33.1844]
 -11.4120 [-23.7403;   0.9162]  -1.9595 [-15.1614;  11.2423]
   1.4276 [-17.7419;  20.5972]  10.8801 [ -3.2393;  24.9996]
   5.1328 [-12.6246;  22.8901]  14.5853 [  5.1075;  24.0631]
  -3.4475 [-19.1046;  12.2097]   6.0051 [-10.3489;  22.3590]
  -7.0616 [-23.4373;   9.3140]   2.3909 [-14.6521;  19.4339]
  -2.0918 [-20.5362;  16.3525]   7.3607 [ -5.3780;  20.0993]
 -14.5898 [-30.6576;   1.4781]  -5.1373 [-14.0671;   3.7926]
                                                            
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                        FlexEx                             .
   7.5499 [-13.4669;  28.5667]                         ManTh
 -11.1527 [-32.4352;  10.1298] -18.7027 [-39.8247;   2.4194]
  17.5366 [  0.9365;  34.1367]   9.9867 [ -6.8526;  26.8260]
  -3.5447 [-20.7373;  13.6479] -11.0946 [-28.0883;   5.8990]
   2.8712 [-19.3110;  25.0533]  -4.6788 [-26.7070;  17.3495]
  -7.1798 [-24.5870;  10.2274] -14.7297 [-31.9404;   2.4809]
   5.8178 [-17.4476;  29.0832]  -1.7321 [-24.8509;  21.3866]
 -10.2659 [-32.3819;  11.8501] -17.8158 [-39.7775;   4.1458]
  -0.4988 [-27.2495;  26.2518]  -8.0487 [-34.6719;  18.5745]
 -13.0988 [-32.6348;   6.4372] -20.6487 [-40.0098;  -1.2876]
  -0.2592 [-21.0583;  20.5400]  -7.8091 [-28.4440;  12.8259]
   3.4460 [-15.0330;  21.9250]  -4.1039 [-22.3979;  14.1901]
  -5.1342 [-26.9245;  16.6561] -12.6842 [-34.3178;   8.9495]
  -8.7484 [-31.0605;  13.5637] -16.2983 [-38.4575;   5.8608]
  -3.7786 [-22.7347;  15.1774] -11.3285 [-30.1043;   7.4472]
 -16.2765 [-32.8737;   0.3206] -23.8265 [-40.2174;  -7.4355]
                                                            
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
 -23.8200 [-42.5008;  -5.1392]                             .
                             .                             .
                             .                             .
                             .  17.4400 [  0.3032;  34.5768]
                             .  10.3000 [-11.4697;  32.0697]
                          MasT                             .
  28.6894 [  8.7566;  48.6221]                         MasTh
   7.6080 [ -6.1021;  21.3181] -21.0813 [-36.5719;  -5.5908]
  14.0239 [ -2.9302;  30.9779] -14.6655 [-35.5561;   6.2252]
   3.9729 [ -9.7945;  17.7403] -24.7164 [-40.4447;  -8.9881]
  16.9705 [ -3.9753;  37.9164] -11.7188 [-33.7563;  10.3186]
   0.8868 [-17.3788;  19.1525] -27.8025 [-48.6229;  -6.9821]
  10.6539 [-11.9512;  33.2590] -18.0354 [-43.7253;   7.6544]
  -1.9461 [-15.2520;  11.3599] -30.6354 [-48.6916; -12.5792]
  10.8936 [ -2.8804;  24.6675] -17.7958 [-37.2116;   1.6201]
  14.5987 [ -0.6423;  29.8398] -14.0906 [-30.9975;   2.8163]
   6.0185 [-10.4196;  22.4566] -22.6709 [-43.1449;  -2.1968]
   2.4043 [-14.7195;  19.5281] -26.2850 [-47.3136;  -5.2564]
   7.3741 [ -8.7507;  23.4989] -21.3152 [-38.7423;  -3.8882]
  -5.1238 [-18.4460;   8.1983] -33.8132 [-48.6401; -18.9863]
                                                            
                             .                             .
   0.1972 [-12.2228;  12.6172]                             .
                             .                             .
                             .                             .
   6.5860 [ -2.0552;  15.2272]                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                           McT                             .
   6.4159 [ -8.5298;  21.3615]                           MfT
  -3.6351 [ -9.6881;   2.4180] -10.0510 [-24.9461;   4.8441]
   9.3625 [ -6.9736;  25.6986]   2.9466 [-18.8726;  24.7658]
  -6.7212 [-21.7739;   8.3315] -13.1371 [-30.9052;   4.6311]
   3.0459 [-18.0946;  24.1865]  -3.3700 [-24.4492;  17.7092]
  -9.5541 [-20.1833;   1.0752] -15.9700 [-26.4767;  -5.4632]
   3.2856 [ -9.6323;  16.2035]  -3.1303 [-21.1824;  14.9218]
   6.9907 [ -1.6346;  15.6160]   0.5748 [-15.9699;  17.1196]
  -1.5895 [-15.9472;  12.7682]  -8.0054 [-22.2726;   6.2618]
  -5.2037 [-20.3416;   9.9342] -11.6196 [-26.6717;   3.4326]
  -0.2339 [-10.1539;   9.6861]  -6.6498 [-23.9298;  10.6302]
 -12.7318 [-17.2173;  -8.2463] -19.1477 [-33.8644;  -4.4310]
                                                            
                             .                             .
  -5.6563 [-18.1368;   6.8241]                             .
 -28.0000 [-46.9835;  -9.0165]                             .
  -7.1000 [-24.4594;  10.2594]                             .
  -1.5723 [-16.1483;  13.0036]                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
  -2.8481 [-13.9475;   8.2513]  11.8000 [ -7.1630;  30.7630]
                             .                             .
                          MiET                             .
  12.9976 [ -3.9769;  29.9721]                          MiEx
  -3.0861 [-18.2251;  12.0530] -16.0837 [-37.9024;   5.7351]
   6.6810 [-14.4239;  27.7858]  -6.3166 [-32.7671;  20.1339]
  -5.9190 [-16.4771;   4.6391] -18.9166 [-38.0395;   0.2064]
   6.9206 [ -6.0738;  19.9150]  -6.0769 [-26.5227;  14.3688]
  10.6258 [  1.3865;  19.8652]  -2.3718 [-20.4345;  15.6909]
   2.0456 [-12.2595;  16.3506] -10.9520 [-32.3728;  10.4687]
  -1.5686 [-16.6566;  13.5194] -14.5662 [-36.5176;   7.3852]
   3.4012 [ -7.0813;  13.8836]  -9.5964 [-28.2253;   9.0325]
  -9.0967 [-14.3450;  -3.8485] -22.0943 [-38.3981;  -5.7906]
                                                           
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                          MnT                             .
  9.7671 [-13.4548;  32.9890]                           PbT
 -2.8329 [-17.1617;  11.4959] -12.6000 [-30.8741;   5.6741]
 10.0067 [ -8.5672;  28.5807]   0.2397 [-23.2002;  23.6795]
 13.7119 [ -2.8677;  30.2914]   3.9448 [-18.3550;  26.2446]
  5.1317 [-12.1448;  22.4081]  -4.6354 [-25.3019;  16.0311]
  1.5175 [-16.4127;  19.4476]  -8.2496 [-29.4656;  12.9664]
  6.4873 [-10.7325;  23.7070]  -3.2798 [-26.1304;  19.5708]
 -6.0107 [-20.6275;   8.6062] -15.7777 [-36.7570;   5.2016]
                                                            
 -14.3332 [-23.7898;  -4.8765]                             .
                             .   4.5000 [-14.0998;  23.0998]
                             .   7.0000 [-12.3729;  26.3729]
                             .                             .
                             .                             .
                             .                             .
 -11.4120 [-23.7403;   0.9162]                             .
                             .                             .
                             .                             .
                             .                             .
  -6.6000 [-24.1259;  10.9259]   6.5600 [-11.2718;  24.3918]
                             .                             .
 -18.0000 [-42.4098;   6.4098]                             .
 -15.9700 [-26.4767;  -5.4632]                             .
  -6.9300 [-24.7636;  10.9036]                             .
                             .                             .
  -0.8000 [-19.2101;  17.6101]                             .
 -12.6000 [-30.8741;   5.6741]                             .
                         PlaSh                             .
  12.8397 [ -1.8398;  27.5191]                           Plt
  16.5448 [  3.7644;  29.3252]   3.7052 [-10.5848;  17.9951]
   7.9646 [ -1.6874;  17.6166]  -4.8751 [-22.4435;  12.6933]
   4.3504 [ -6.4281;  15.1289]  -8.4893 [-26.7008;   9.7223]
   9.3202 [ -4.3987;  23.0391]  -3.5195 [-18.9973;  11.9584]
  -3.1777 [-13.4826;   7.1271] -16.0174 [-28.5529;  -3.4819]
                                                            
                             .                             .
  -9.7400 [-29.4421;   9.9621]                             .
                             .                             .
                             .                             .
  25.7400 [  7.2759;  44.2041]                             .
                             .                             .
                             .                             .
  12.4872 [ -0.0284;  25.0027]                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
   5.5500 [-13.6212;  24.7212]                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .   7.9646 [ -1.6874;  17.6166]
                             .                             .
                          ReET                             .
  -8.5802 [-24.5958;   7.4354]                          rTMS
 -12.1944 [-28.9131;   4.5242]  -3.6142 [-18.0827;  10.8543]
  -7.2246 [-19.4003;   4.9511]   1.3556 [-15.4185;  18.1297]
 -19.7226 [-27.8471; -11.5980] -11.1423 [-25.2615;   2.9769]
                                                           
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .   6.4100 [-14.4607;  27.2807]
                            .                             .
                            .                             .
                            .                             .
                            .                             .
                            .                             .
  4.3504 [ -6.4281;  15.1289]                             .
                            .                             .
                            .                             .
                            .                             .
                         tDCS                             .
  4.9698 [-12.4768;  22.4164]                           WBV
 -7.5281 [-22.4400;   7.3838] -12.4979 [-21.6558;  -3.3401]
                              
                             .
 -12.0002 [-22.5182;  -1.4822]
  -7.3533 [-21.7530;   7.0465]
 -16.7697 [-32.1609;  -1.3786]
  -7.5546 [-12.3436;  -2.7657]
  -9.7000 [-27.5794;   8.1794]
                             .
 -14.8000 [-37.8978;   8.2978]
 -16.1800 [-33.3130;   0.9530]
 -24.1000 [-44.4411;  -3.7589]
                             .
 -33.6200 [-50.7139; -16.5261]
 -11.8990 [-17.7649;  -6.0330]
                             .
 -12.0292 [-19.3569;  -4.7014]
 -19.9000 [-38.3651;  -1.4349]
  -8.3900 [-28.3070;  11.5270]
                             .
                             .
                             .
 -18.9474 [-31.2166;  -6.6783]
                             .
                             .
 -11.7305 [-21.2330;  -2.2281]
                          WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr <- netrank(nma_sr, small.values = "good")
print(ranking_sr)
       P-score
MasTh   0.9658
ManTh   0.8050
MiEx    0.7683
ReET    0.7552
Acu     0.7497
MfT     0.7126
DryN    0.6975
Plt     0.6134
FlexEx  0.5978
Bal     0.5871
PbT     0.5786
Elec    0.5540
AqET    0.5253
McT     0.4954
WBV     0.4799
AeET    0.4659
rTMS    0.4291
MiET    0.3251
tDCS    0.3006
MnT     0.2548
CBT     0.2498
MasT    0.2146
FlET    0.1942
PlaSh   0.1292
WlNi    0.0510



Code 
# Rankogram
ran_sr <- rankogram(nma_sr)
plot(ran_sr)

Rankogram of treatments network




Code 
# Design decomposition
decomp_sr <- decomp.design(nma_sr)
print(decomp_sr)
Q statistics to assess homogeneity / consistency

                     Q df  p-value
Total           478.62 83 < 0.0001
Within designs  290.45 50 < 0.0001
Between designs 188.18 33 < 0.0001

Design-specific decomposition of within-designs Q statistic

     Design      Q df  p-value
   WlNi:CBT 115.30 14 < 0.0001
   WlNi:McT  77.12  5 < 0.0001
  WlNi:MiET  26.23  5 < 0.0001
  Acu:PlaSh  18.66  3   0.0003
  MfT:PlaSh  14.67  2   0.0007
   WlNi:WBV   9.70  2   0.0078
   WlNi:Bal   4.54  1   0.0331
    CBT:McT   7.78  4   0.0999
  AqET:FlET   4.54  2   0.1033
 Elec:PlaSh   4.41  2   0.1101
   CBT:MiET   2.09  1   0.1481
 PlaSh:tDCS   2.40  2   0.3006
   McT:MiET   0.62  1   0.4297
 PlaSh:rTMS   2.09  3   0.5546
  FlET:ReET   0.26  1   0.6101
  WlNi:AqET   0.02  1   0.8814
  AeET:AqET   0.01  1   0.9413

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from < 0.0001)

 Detached design      Q df  p-value
  AeET:AqET:MiET 118.76 31 < 0.0001
       AeET:MiET 120.88 32 < 0.0001
  WlNi:AeET:ReET 165.20 31 < 0.0001
        CBT:ReET 169.79 32 < 0.0001
       DryN:MasT 170.84 32 < 0.0001
       WlNi:DryN 170.84 32 < 0.0001
        AqET:CBT 171.29 32 < 0.0001
      MasT:PlaSh 178.29 32 < 0.0001
        McT:MiET 180.86 32 < 0.0001
         Acu:CBT 181.13 32 < 0.0001
       Acu:PlaSh 181.13 32 < 0.0001
        AeET:McT 181.25 32 < 0.0001
        Bal:MiET 182.12 32 < 0.0001
       AqET:FlET 184.91 32 < 0.0001
        AqET:Bal 185.15 32 < 0.0001
   WlNi:AeET:McT 183.17 31 < 0.0001
       WlNi:ReET 185.77 32 < 0.0001
        WlNi:McT 185.84 32 < 0.0001
        WlNi:WBV 186.19 32 < 0.0001
        WlNi:Bal 186.49 32 < 0.0001
        CBT:MiET 186.55 32 < 0.0001
       WlNi:AeET 186.60 32 < 0.0001
        AqET:Plt 186.62 32 < 0.0001
       McT:PlaSh 186.97 32 < 0.0001
       WlNi:AqET 187.03 32 < 0.0001
       FlET:ReET 187.06 32 < 0.0001
      MiET:PlaSh 187.35 32 < 0.0001
        AeET:Plt 187.57 32 < 0.0001
       AeET:AqET 187.64 32 < 0.0001
  WlNi:FlET:ReET 185.62 31 < 0.0001
       MnT:PlaSh 187.93 32 < 0.0001
        WlNi:MnT 187.93 32 < 0.0001
        WlNi:CBT 188.03 32 < 0.0001
        MasT:Plt 188.06 32 < 0.0001
       WlNi:MiET 188.06 32 < 0.0001
        McT:ReET 188.08 32 < 0.0001
    WlNi:McT:WBV 185.97 31 < 0.0001
       AeET:FlET 188.15 32 < 0.0001
     ManTh:MasTh 188.17 32 < 0.0001
      WlNi:ManTh 188.17 32 < 0.0001
         CBT:McT 188.17 32 < 0.0001
   WlNi:McT:MiET 187.71 31 < 0.0001

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                    Q df p-value tau.within tau2.within
Between designs 29.31 33  0.6516     8.5426     72.9764



Code 
# Node-splitting analysis to detect inconsistency
split_sr <- netsplit(nma_sr,) #show = "all")
print(split_sr)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

   comparison  k prop      nma   direct   indir.     Diff     z p-value
      Acu:CBT  1 0.39 -12.5413 -22.4000  -6.3123 -16.0877 -1.28  0.2006
    Acu:PlaSh  4 0.85 -16.7037 -14.3332 -30.4208  16.0877  1.28  0.2006
    AeET:AqET  3 0.45   1.2974   2.7351   0.1195   2.6157  0.35  0.7276
    AeET:FlET  1 0.23  -7.0121  -3.3100  -8.1312   4.8212  0.43  0.6644
     AeET:McT  2 0.32   0.5824   0.1972   0.7611  -0.5639 -0.07  0.9414
    AeET:MiET  2 0.33  -3.0526  -5.6563  -1.7549  -3.9014 -0.50  0.6167
     AeET:Plt  1 0.44   3.8680   4.5000   3.3814   1.1186  0.09  0.9294
    AeET:ReET  1 0.22   7.5732  -9.7400  12.4549 -22.1949 -1.95  0.0512
    AeET:WlNi  3 0.38 -12.1494 -12.0002 -12.2389   0.2387  0.04  0.9720
     AqET:Bal  1 0.34   1.7401  -1.8800   3.6077  -5.4877 -0.46  0.6456
     AqET:CBT  1 0.16  -6.1066  13.6000  -9.9918  23.5918  2.27  0.0235
    AqET:FlET  3 0.60  -8.3095 -12.1240  -2.6202  -9.5037 -1.09  0.2743
    AqET:MiET  1 0.17  -4.3500 -28.0000   0.5873 -28.5873 -2.68  0.0073
     AqET:Plt  1 0.41   2.5707   7.0000  -0.5197   7.5197  0.58  0.5593
    AqET:WlNi  2 0.24 -13.4467  -7.3533 -15.3530   7.9997  0.95  0.3420
     Bal:MiET  1 0.37  -6.0900  -7.1000  -5.5050  -1.5950 -0.14  0.8861
     Bal:WlNi  2 0.44 -15.1868 -16.7697 -13.9336  -2.8362 -0.27  0.7873
      CBT:McT  5 0.35   5.3917   6.5860   4.7359   1.8501  0.34  0.7360
     CBT:MiET  2 0.17   1.7566  -1.5723   2.4393  -4.0116 -0.49  0.6232
     CBT:ReET  1 0.21  12.3825  25.7400   8.7781  16.9619  1.60  0.1101
     CBT:WlNi 15 0.70  -7.3401  -7.5546  -6.8352  -0.7195 -0.16  0.8723
    DryN:MasT  1 0.62 -13.7764 -23.8200   2.3775 -26.1975 -1.70  0.0888
    DryN:WlNi  1 0.65 -18.9003  -9.7000 -35.8975  26.1975  1.70  0.0888
    FlET:ReET  3 0.57  14.5853  12.4872  17.4063  -4.9191 -0.50  0.6149
    FlET:WlNi  1 0.15  -5.1373 -14.8000  -3.4392 -11.3608 -0.89  0.3740
 FlexEx:MasTh  1 0.94  17.5366  17.4400  19.0072  -1.5672 -0.04  0.9645
  FlexEx:WlNi  1 0.94 -16.2765 -16.1800 -17.7479   1.5679  0.04  0.9645
  ManTh:MasTh  1 0.60   9.9867  10.3000   9.5200   0.7800  0.04  0.9645
   ManTh:WlNi  1 0.65 -23.8265 -24.1000 -23.3200  -0.7800 -0.04  0.9645
   MasT:PlaSh  1 0.58  -1.9461  -6.6000   4.3869 -10.9869 -0.80  0.4239
     MasT:Plt  1 0.60  10.8936   6.5600  17.3041 -10.7441 -0.75  0.4533
   MasTh:WlNi  1 0.75 -33.8132 -33.6200 -34.4000   0.7800  0.04  0.9645
     McT:MiET  3 0.30  -3.6351  -2.8481  -3.9682   1.1201  0.17  0.8683
     McT:MiEx  1 0.74   9.3625  11.8000   2.3473   9.4527  0.50  0.6198
    McT:PlaSh  1 0.19  -9.5541 -18.0000  -7.5779 -10.4221 -0.75  0.4513
     McT:ReET  1 0.20   6.9907   5.5500   7.3564  -1.8064 -0.16  0.8690
      McT:WBV  1 0.23  -0.2339   6.4100  -2.1730   8.5830  0.71  0.4782
     McT:WlNi 10 0.58 -12.7318 -11.8990 -13.9045   2.0056  0.43  0.6659
   MiET:PlaSh  1 0.35  -5.9190  -6.9300  -5.3734  -1.5566 -0.14  0.8903
    MiET:WlNi  7 0.51  -9.0967 -12.0292  -6.0083  -6.0208 -1.12  0.2611
    MiEx:WlNi  1 0.78 -22.0943 -19.9000 -29.8561   9.9561  0.50  0.6198
    MnT:PlaSh  1 0.61  -2.8329  -0.8000  -5.9566   5.1566  0.34  0.7303
     MnT:WlNi  1 0.54  -6.0107  -8.3900  -3.2334  -5.1566 -0.34  0.7303
    ReET:WlNi  3 0.44 -19.7226 -18.9474 -20.3279   1.3805  0.17  0.8687
     WBV:WlNi  4 0.93 -12.4979 -11.7305 -22.5055  10.7750  0.59  0.5531

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr)

Forest plot of node-splitting for Network



Code 
# Heatmap
netheat(nma_sr)

Heatmap of contribution matrix for Network



Code 
# Funnel plot
funnel(nma_sr,
    order = "WlNi",
)

Funnel plot for Network (Q | sh)





Code 
# Read data
data_qlg <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "Q | Lg") |>
    mutate(
        Mean1 = as.numeric(Mean1),
        Mean2 = as.numeric(Mean2),
        Mean3 = as.numeric(Mean3),
        SD1 = as.numeric(SD1),
        SD2 = as.numeric(SD2),
        SD3 = as.numeric(SD3)
    )


# Transform to contrast-based
pw <- pairwise(
    treat = list(Treat1, Treat2, Treat3),
    n = list(N1, N2, N3),
    mean = list(Mean1, Mean2, Mean3),
    sd = list(SD1, SD2, SD3),
    studlab = StudyID,
    data = data_qlg,
    sm      = "MD"
)

# Check network connections
net_con <- netconnection(pw)
net_con
Number of studies: k = 23
Number of pairwise comparisons: m = 27
Number of treatments: n = 12
Number of designs: d = 13
Number of networks: 2

Details on subnetworks: 
 subnetwork  k  m n
          1  2  2 3
          2 21 25 9


There are two sub-networks:

Subnet 1:
- 2 studies
- 2 comparisons
- 3 treatments

Subnet 2:
- 21 studies
- 25 comparisons
- 9 treatments

Tip

There are two treatment sub-networks that do not connect.

Note

Please: Select the treatment sub-networks before proceeding.



Select the procedures performed

Important

The first subnet contains 2 studies, 2 comparisons and 3 treatments.

Code 
# Filter data for subnet 1
sr1 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 1)

# Display comparison table
sr1



Code 
# Unique treatments in subnet 1
unique_treat1 <- sr1$treat1 |> unique()
unique_treat2 <- sr1$treat2 |> unique()

# Combination of all unique treatments
trat_sr1 <- unique(c(unique_treat1, unique_treat2))
print(trat_sr1)
[1] "MfT"   "rTMS"  "PlaSh"
Code 
# Total number of treatments
length(trat_sr1)
[1] 3



Code 
# Filter pairwise object only for comparisons within subnet 1
pw_qlg_sr1 <- pw %>%
    filter(treat1 %in% trat_sr1 & treat2 %in% trat_sr1)

# Number of comparisons in subnet 1
nrow(pw_qlg_sr1)
[1] 2



Code 
# Fit NMA model for subnet 1
nma_sr1 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_qlg_sr1,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    sm = "MD", # can be "MD" or "SMD"
    ref = "PlaSh" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr1)
Number of studies: k = 2
Number of pairwise comparisons: m = 2
Number of observations: o = 134
Number of treatments: n = 3
Number of designs: d = 2

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'PlaSh'):
           MD             95%-CI     z p-value
MfT   -5.5600 [-13.2259; 2.1059] -1.42  0.1552
PlaSh       .                  .     .       .
rTMS  -7.3000 [-17.4681; 2.8681] -1.41  0.1594

Quantifying heterogeneity / inconsistency:
tau^2 = NA; tau = NA

Tests of heterogeneity (within designs) and inconsistency (between designs):
                Q d.f. p-value
Total           0    0      --
Within designs  0    0      --
Between designs 0    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2



Code 
# Network plot
netgraph(
    nma_sr1,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 1 (Q | Lg)



Code 
# Detailed model summary
summary(nma_sr1)
Original data:

           treat1 treat2      TE   seTE
Alfano2001    MfT  PlaSh -5.5600 3.9112
Mhalla2011  PlaSh   rTMS  7.3000 5.1879

Number of treatment arms (by study):
           narms
Alfano2001     2
Mhalla2011     2

Results (random effects model):

           treat1 treat2      MD              95%-CI
Alfano2001    MfT  PlaSh -5.5600 [-13.2259;  2.1059]
Mhalla2011  PlaSh   rTMS  7.3000 [ -2.8681; 17.4681]

Number of studies: k = 2
Number of pairwise comparisons: m = 2
Number of observations: o = 134
Number of treatments: n = 3
Number of designs: d = 2

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'PlaSh'):
           MD             95%-CI     z p-value
MfT   -5.5600 [-13.2259; 2.1059] -1.42  0.1552
PlaSh       .                  .     .       .
rTMS  -7.3000 [-17.4681; 2.8681] -1.41  0.1594

Quantifying heterogeneity / inconsistency:
tau^2 = NA; tau = NA

Tests of heterogeneity (within designs) and inconsistency (between designs):
                Q d.f. p-value
Total           0    0      --
Within designs  0    0      --
Between designs 0    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2



Code 
# Forest plot
forest(nma_sr1)

Forest plot of treatment effects for Subnet 1



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr1, ci = TRUE)
League table (random effects model):
                                                        
                         MfT -5.5600 [-13.2259;  2.1059]
 -5.5600 [-13.2259;  2.1059]                       PlaSh
  1.7400 [-10.9941; 14.4741]  7.3000 [ -2.8681; 17.4681]
                           
                          .
 7.3000 [ -2.8681; 17.4681]
                       rTMS

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr1 <- netrank(nma_sr1, small.values = "good")
print(ranking_sr1)
      P-score
rTMS   0.7629
MfT    0.6584
PlaSh  0.0786



Code 
# Rankogram
ran_sr1 <- rankogram(nma_sr1)
plot(ran_sr1)

Rankogram of treatments for Subnet 1



Code 
# Design decomposition
decomp_sr1 <- decomp.design(nma_sr1)
print(decomp_sr1)
Q statistics to assess homogeneity / consistency

                   Q df p-value
Total           0.00  0      --
Within designs  0.00  0      --
Between designs 0.00  0      --

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 0.00  0      --          0           0



Code 
# Node-splitting analysis to detect inconsistency
split_sr1 <- netsplit(nma_sr1, show = "all")
print(split_sr1)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop     nma  direct indir. Diff z p-value
  MfT:PlaSh 1 1.00 -5.5600 -5.5600      .    . .       .
   MfT:rTMS 0    0  1.7400       . 1.7400    . .       .
 rTMS:PlaSh 1 1.00 -7.3000 -7.3000      .    . .       .

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr1)

Forest plot of node-splitting for Subnet 1



Code 
# Heatmap
netheat(nma_sr1)



Code 
# Funnel plot
funnel(nma_sr1,
    order = "PlaSh",
)

Funnel plot for Subnet 1 (Q | Lg)





Select the procedures performed

Important

The second subnet is more robust, containing 21 studies, 25 comparisons and 9 treatments. This is the main analysis network.

Code 
# Filter data for subnet 2
sr2 <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 2)

# Display first rows of comparison table
sr2 |> head()



Code 
# Unique treatments in subnet 2
unique_treat1_sr2 <- sr2$treat1 |> unique()
print(unique_treat1_sr2)
[1] "AeET" "AqET" "MiET" "ReET" "McT"  "CBT"
Code 
unique_treat2_sr2 <- sr2$treat2 |> unique()
print(unique_treat2_sr2)
[1] "AqET"   "WlNi"   "ReET"   "MiET"   "McT"    "FlET"   "FlexEx"
Code 
# Combination of all unique treatments
trat_sr2 <- unique(c(unique_treat1_sr2, unique_treat2_sr2))
print(trat_sr2)
[1] "AeET"   "AqET"   "MiET"   "ReET"   "McT"    "CBT"    "WlNi"   "FlET"  
[9] "FlexEx"
Code 
# Total number of treatments
length(trat_sr2)
[1] 9



Code 
# Filter pairwise object only for comparisons within subnet 2
pw_qlg_sr2 <- pw %>%
    filter(treat1 %in% trat_sr2 & treat2 %in% trat_sr2)

# Number of unique studies
length(unique(pw_qlg_sr2$studlab))
[1] 21



Code 
# Fit NMA model for subnet 2
nma_sr2 <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_qlg_sr2,
    n1 = N1,
    n2 = N2,
    random = TRUE,
    common = FALSE,
    sm = "MD",
    ref = "WlNi" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr2)
Number of studies: k = 21
Number of pairwise comparisons: m = 25
Number of observations: o = 1321
Number of treatments: n = 9
Number of designs: d = 11

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
             MD               95%-CI     z p-value
AeET   -11.7228 [-21.7124;  -1.7332] -2.30  0.0214
AqET   -13.9973 [-24.9856;  -3.0091] -2.50  0.0125
CBT    -14.9648 [-39.4427;   9.5132] -1.20  0.2308
FlET    -2.6328 [-29.7684;  24.5028] -0.19  0.8492
FlexEx  -8.1548 [-42.5145;  26.2050] -0.47  0.6418
McT    -18.9581 [-32.5559;  -5.3603] -2.73  0.0063
MiET   -23.9122 [-36.1811; -11.6432] -3.82  0.0001
ReET    -9.8992 [-33.3322;  13.5338] -0.83  0.4077
WlNi          .                    .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 148.7710; tau = 12.1972; I^2 = 89.4% [84.5%; 92.8%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           142.15   15 < 0.0001
Within designs   60.07   10 < 0.0001
Between designs  82.08    5 < 0.0001

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(nma_sr2,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 2 (Q | Lg)



Code 
# Detailed model summary
summary(nma_sr2)
Original data (with adjusted standard errors for multi-arm studies):

                       treat1 treat2       TE   seTE seTE.adj narms multiarm
Acosta-Gallego2018       AeET   AqET   8.1000 4.1615  12.8875     2         
Andrade2019              AqET   WlNi -14.6000 3.3374  12.6455     2         
Assis2006                AeET   AqET   4.4600 5.1075  13.2234     2         
Baptista2012             AeET   WlNi -17.6300 3.3515  12.6492     2         
Etnier2009               MiET   WlNi -25.1800 9.0950  15.2148     2         
Kayo2012                 AeET   ReET  -5.6500 6.0952  17.1183     3        *
Kayo2012                 AeET   WlNi -18.9200 4.8426  15.8269     3        *
Kayo2012                 ReET   WlNi -13.2700 5.1235  16.0670     3        *
Larsson2015               McT   MiET   4.9000 3.3376  12.6456     2         
Letieri2013              AqET   WlNi -24.2400 7.3707  14.2513     2         
Mannerkorpi2000           McT   WlNi -11.9400 4.6207  13.0431     2         
Mannerkorpi2004           McT   WlNi   1.8300 5.4792  13.3713     2         
Munguia-Izquierdo 2007   AqET   WlNi   0.4000 3.4557  12.6773     2         
Rooks2007                 CBT    McT   8.3000 3.6542  15.7234     3        *
Rooks2007                 CBT   MiET   4.7500 3.3682  15.5227     3        *
Rooks2007                 McT   MiET  -3.5500 2.7539  15.1667     3        *
Sanudo2010b              AeET   MiET   0.0000 3.7033  12.7470     2         
Sanudo2011               MiET   WlNi -64.8400 5.5331  13.3935     2         
Sanudo2010c              AeET   MiET  11.9900 5.8375  13.5221     2         
Schachter2003            AeET   WlNi  -2.3000 2.8448  12.5245     2         
Tomas-Carus2008          AqET   WlNi -11.9400 4.4726  12.9914     2         
Valim2003                AeET   FlET  -9.0900 4.1151  12.8726     2         
Wang2018                  McT   MiET -11.6700 3.5984  12.7169     2         
Hernando-Garijo2021      AeET   WlNi  -2.9000 6.1852  13.6758     2         
Saranya2022               CBT FlexEx  -6.8100 1.6075  12.3027     2         

Number of treatment arms (by study):
                       narms
Acosta-Gallego2018         2
Andrade2019                2
Assis2006                  2
Baptista2012               2
Etnier2009                 2
Kayo2012                   3
Larsson2015                2
Letieri2013                2
Mannerkorpi2000            2
Mannerkorpi2004            2
Munguia-Izquierdo 2007     2
Rooks2007                  3
Sanudo2010b                2
Sanudo2011                 2
Sanudo2010c                2
Schachter2003              2
Tomas-Carus2008            2
Valim2003                  2
Wang2018                   2
Hernando-Garijo2021        2
Saranya2022                2

Results (random effects model):

                       treat1 treat2       MD               95%-CI
Acosta-Gallego2018       AeET   AqET   2.2745 [-10.1235;  14.6725]
Andrade2019              AqET   WlNi -13.9973 [-24.9856;  -3.0091]
Assis2006                AeET   AqET   2.2745 [-10.1235;  14.6725]
Baptista2012             AeET   WlNi -11.7228 [-21.7124;  -1.7332]
Etnier2009               MiET   WlNi -23.9122 [-36.1811; -11.6432]
Kayo2012                 AeET   ReET  -1.8236 [-25.3911;  21.7438]
Kayo2012                 AeET   WlNi -11.7228 [-21.7124;  -1.7332]
Kayo2012                 ReET   WlNi  -9.8992 [-33.3322;  13.5338]
Larsson2015               McT   MiET   4.9541 [ -7.2252;  17.1333]
Letieri2013              AqET   WlNi -13.9973 [-24.9856;  -3.0091]
Mannerkorpi2000           McT   WlNi -18.9581 [-32.5559;  -5.3603]
Mannerkorpi2004           McT   WlNi -18.9581 [-32.5559;  -5.3603]
Munguia-Izquierdo 2007   AqET   WlNi -13.9973 [-24.9856;  -3.0091]
Rooks2007                 CBT    McT   3.9934 [-18.5188;  26.5055]
Rooks2007                 CBT   MiET   8.9474 [-13.5223;  31.4172]
Rooks2007                 McT   MiET   4.9541 [ -7.2252;  17.1333]
Sanudo2010b              AeET   MiET  12.1893 [ -0.8236;  25.2023]
Sanudo2011               MiET   WlNi -23.9122 [-36.1811; -11.6432]
Sanudo2010c              AeET   MiET  12.1893 [ -0.8236;  25.2023]
Schachter2003            AeET   WlNi -11.7228 [-21.7124;  -1.7332]
Tomas-Carus2008          AqET   WlNi -13.9973 [-24.9856;  -3.0091]
Valim2003                AeET   FlET  -9.0900 [-34.3199;  16.1399]
Wang2018                  McT   MiET   4.9541 [ -7.2252;  17.1333]
Hernando-Garijo2021      AeET   WlNi -11.7228 [-21.7124;  -1.7332]
Saranya2022               CBT FlexEx  -6.8100 [-30.9228;  17.3028]

Number of studies: k = 21
Number of pairwise comparisons: m = 25
Number of observations: o = 1321
Number of treatments: n = 9
Number of designs: d = 11

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
             MD               95%-CI     z p-value
AeET   -11.7228 [-21.7124;  -1.7332] -2.30  0.0214
AqET   -13.9973 [-24.9856;  -3.0091] -2.50  0.0125
CBT    -14.9648 [-39.4427;   9.5132] -1.20  0.2308
FlET    -2.6328 [-29.7684;  24.5028] -0.19  0.8492
FlexEx  -8.1548 [-42.5145;  26.2050] -0.47  0.6418
McT    -18.9581 [-32.5559;  -5.3603] -2.73  0.0063
MiET   -23.9122 [-36.1811; -11.6432] -3.82  0.0001
ReET    -9.8992 [-33.3322;  13.5338] -0.83  0.4077
WlNi          .                    .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 148.7710; tau = 12.1972; I^2 = 89.4% [84.5%; 92.8%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           142.15   15 < 0.0001
Within designs   60.07   10 < 0.0001
Between designs  82.08    5 < 0.0001

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr2)

Forest plot of treatment effects for Subnet 2



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr2, ci = TRUE)
League table (random effects model):
                                                            
                          AeET   6.3268 [-11.7623;  24.4159]
   2.2745 [-10.1235;  14.6725]                          AqET
   3.2419 [-21.9198;  28.4036]   0.9674 [-25.4497;  27.3845]
  -9.0900 [-34.3199;  16.1399] -11.3645 [-39.4761;  16.7470]
  -3.5681 [-38.4183;  31.2821]  -5.8426 [-41.6097;  29.9245]
   7.2353 [ -8.0737;  22.5443]   4.9608 [-12.0331;  21.9546]
  12.1893 [ -0.8236;  25.2023]   9.9148 [ -5.7106;  25.5403]
  -1.8236 [-25.3911;  21.7438]  -4.0981 [-29.3677;  21.1714]
 -11.7228 [-21.7124;  -1.7332] -13.9973 [-24.9856;  -3.0091]
                                                           
                             . -9.0900 [-34.3199;  16.1399]
                             .                            .
                           CBT                            .
 -12.3319 [-47.9642;  23.3003]                         FlET
  -6.8100 [-30.9228;  17.3028]  5.5219 [-37.5023;  48.5461]
   3.9934 [-18.5188;  26.5055] 16.3253 [-13.1860;  45.8365]
   8.9474 [-13.5223;  31.4172] 21.2793 [ -7.1088;  49.6675]
  -5.0655 [-38.4936;  28.3625]  7.2664 [-27.2586;  41.7913]
 -14.9648 [-39.4427;   9.5132] -2.6328 [-29.7684;  24.5028]
                                                           
                            .                             .
                            .                             .
 -6.8100 [-30.9228;  17.3028]   8.3000 [-16.6558;  33.2558]
                            .                             .
                       FlexEx                             .
 10.8034 [-22.1848;  43.7915]                           McT
 15.7574 [-17.2019;  48.7167]   4.9541 [ -7.2252;  17.1333]
  1.7445 [-39.4728;  42.9617]  -9.0589 [-35.7129;  17.5951]
 -8.1548 [-42.5145;  26.2050] -18.9581 [-32.5559;  -5.3603]
                                                           
   5.6415 [-12.5380;  23.8210] -5.6500 [-32.3748;  21.0748]
                             .                            .
   4.7500 [-20.0508;  29.5508]                            .
                             .                            .
                             .                            .
  -3.4103 [-17.6923;  10.8718]                            .
                          MiET                            .
 -14.0130 [-39.7366;  11.7107]                         ReET
 -23.9122 [-36.1811; -11.6432] -9.8992 [-33.3322;  13.5338]
                              
 -10.5228 [-23.2332;   2.1876]
 -11.9577 [-24.7911;   0.8757]
                             .
                             .
                             .
  -5.2261 [-23.5258;  13.0736]
 -47.5247 [-67.2286; -27.8207]
 -13.2700 [-39.1995;  12.6595]
                          WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr2 <- netrank(nma_sr2, small.values = "good")
print(ranking_sr2)
       P-score
MiET    0.8802
McT     0.7166
CBT     0.5841
AqET    0.5665
AeET    0.4824
ReET    0.4479
FlexEx  0.4081
FlET    0.2786
WlNi    0.1356



Code 
# Rankogram
ran_sr2 <- rankogram(nma_sr2)
plot(ran_sr2)

Rankogram of treatments for Subnet 2



Code 
# Design decomposition
decomp_sr2 <- decomp.design(nma_sr2)
print(decomp_sr2)
Q statistics to assess homogeneity / consistency

                     Q df  p-value
Total           142.15 15 < 0.0001
Within designs   60.07 10 < 0.0001
Between designs  82.08  5 < 0.0001

Design-specific decomposition of within-designs Q statistic

    Design     Q df p-value
 WlNi:MiET 13.88  1  0.0002
  McT:MiET 11.40  1  0.0007
 WlNi:AeET 12.95  2  0.0015
 WlNi:AqET 14.84  3  0.0020
  WlNi:McT  3.69  1  0.0547
 AeET:MiET  3.01  1  0.0828
 AeET:AqET  0.31  1  0.5806

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from < 0.0001)

 Detached design     Q df  p-value
       WlNi:MiET  9.51  4   0.0495
        WlNi:McT 57.97  4 < 0.0001
       AeET:MiET 75.03  4 < 0.0001
       AeET:AqET 77.94  4 < 0.0001
       WlNi:AqET 77.94  4 < 0.0001
        McT:MiET 79.16  4 < 0.0001
       WlNi:AeET 79.90  4 < 0.0001

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                    Q df p-value tau.within tau2.within
Between designs 15.45  5  0.0086     9.6818     93.7369



Code 
# Node-splitting analysis to detect inconsistency
split_sr2 <- netsplit(nma_sr2)
print(split_sr2)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop      nma   direct   indir.     Diff     z p-value
  AeET:AqET 2 0.47   2.2745   6.3268  -1.3155   7.6423  0.60  0.5465
  AeET:MiET 2 0.51  12.1893   5.6415  19.0696 -13.4281 -1.01  0.3120
  AeET:ReET 1 0.78  -1.8236  -5.6500  11.5604 -17.2104 -0.60  0.5517
  AeET:WlNi 4 0.62 -11.7228 -10.5228 -13.6618   3.1390  0.30  0.7647
  AqET:WlNi 4 0.73 -13.9973 -11.9577 -19.6000   7.6423  0.60  0.5465
    CBT:McT 1 0.81   3.9934   8.3000 -14.8224  23.1224  0.78  0.4332
   CBT:MiET 1 0.82   8.9474   4.7500  28.1802 -23.4302 -0.78  0.4332
   McT:MiET 3 0.73   4.9541  -3.4103  27.2512 -30.6615 -2.20  0.0280
   McT:WlNi 2 0.55 -18.9581  -5.2261 -35.8876  30.6615  2.20  0.0280
  MiET:WlNi 2 0.39 -23.9122 -47.5247  -8.9605 -38.5642 -3.00  0.0027
  ReET:WlNi 1 0.82  -9.8992 -13.2700   5.1209 -18.3909 -0.60  0.5517

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (MD) in network meta-analysis
 direct     - Estimated treatment effect (MD) derived from direct evidence
 indir.     - Estimated treatment effect (MD) derived from indirect evidence
 Diff       - Difference between direct and indirect treatment estimates
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr2)

Forest plot of node-splitting for Subnet 2



Code 
# Heatmap
netheat(nma_sr2)

Heatmap of contribution matrix for Subnet 2



Code 
# Funnel plot
funnel(nma_sr2,
    order = "WlNi",
)

Funnel plot for Subnet 2 (Q | Lg)







2 NMA for binary outcomes

Note

Please: Select an outcome to proceed.

Code 
# Read data
data_alg <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "A | Lg")

# Transform to contrast-based
pw_alg <- pairwise(
    treat = list(Treat1, Treat2, Treat3),
    event = list(dp1, dp2, dp3), # observed events in each arm
    n = list(nRT1, nRT2, nRT3), # total number of patients in each arm
    studlab = StudyID,
    data = data_alg,
    sm = "OR" # Medida de efeito (OR = Odds Ratio, pode ser "RR" ou "RD" se preferir)
)

# Check network connections
net_con <- netconnection(pw_alg)
net_con
Number of studies: k = 27
Number of pairwise comparisons: m = 31
Number of treatments: n = 14
Number of designs: d = 15
Number of networks: 3

Details on subnetworks: 
 subnetwork  k  m n
          1 22 26 8
          2  1  1 2
          3  4  4 4


There are three sub-networks:

Subnet 1:
- 22 studies
- 26 comparisons
- 8 treatments

Subnet 2:
- 1 study
- 1 comparison
- 2 treatments

Subnet 3:
- 4 studies
- 4 comparisons
- 4 treatments

Tip

There are three treatment sub-networks that do not connect.



Note

Please: Select the treatment sub-networks before proceeding.

Select the procedures performed

Important

The first subnet contains 22 studies, 26 comparisons and 8 treatments. This is the main analysis network for binary outcomes.

Code 
# Filter data for subnet 1
sr1_alg <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 1)

# Display first rows of comparison table
sr1_alg |> head()



Code 
# Unique treatments in subnet 1
unique_treat1_alg <- sr1_alg$treat1 |> unique()
unique_treat2_alg <- sr1_alg$treat2 |> unique()

# Combination of all unique treatments
trat_sr1_alg <- unique(c(unique_treat1_alg, unique_treat2_alg))
print(trat_sr1_alg)
[1] "AeET" "AqET" "ReET" "McT"  "CBT"  "MiET" "WlNi" "FlET"
Code 
# Total number of treatments
length(trat_sr1_alg)
[1] 8



Code 
# Filter pairwise object only for comparisons within subnet 1
pw_sr1_alg <- pw_alg %>%
    filter(treat1 %in% trat_sr1_alg & treat2 %in% trat_sr1_alg)

# Number of comparisons in subnet 1
nrow(pw_sr1_alg)
[1] 29
Code 
# Number of unique studies
length(unique(pw_sr1_alg$studlab))
[1] 25



Code 
# Fit NMA model for subnet 1
nma_sr1_alg <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_sr1_alg,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    ref = "WlNi" # Reference treatment (change if you want another control)
)
Comparisons not considered in network meta-analysis:
      studlab treat1 treat2 TE seTE
   Etnier2009   MiET   WlNi NA   NA
 Hakkinen2001   ReET   WlNi NA   NA
   Sanudo2015   MiET   WlNi NA   NA
Code 
# Basic model summary
print(nma_sr1_alg)
Number of studies: k = 22
Number of pairwise comparisons: m = 26
Number of observations: o = 1685
Number of treatments: n = 8
Number of designs: d = 11

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'WlNi'):
         OR            95%-CI    z p-value
AeET 1.8941 [1.0374;  3.4583] 2.08  0.0376
AqET 1.5725 [0.6805;  3.6338] 1.06  0.2895
CBT  1.6064 [0.6231;  4.1412] 0.98  0.3266
FlET 3.6078 [0.8330; 15.6257] 1.72  0.0862
McT  1.2642 [0.5567;  2.8706] 0.56  0.5753
MiET 1.4730 [0.6380;  3.4012] 0.91  0.3643
ReET 1.6444 [0.4868;  5.5545] 0.80  0.4232
WlNi      .                 .    .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.1313; tau = 0.3624; I^2 = 20.7% [0.0%; 55.0%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f. p-value
Total           21.45   17  0.2070
Within designs  12.01   11  0.3631
Between designs  9.44    6  0.1504

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q
Note

These three studies were excluded from the model because they reported a standard deviation of zero, which makes division by zero impossible.
- Etnier2009: MiET vs WlNi
- Hakkinen2001: ReET vs WlNi
- Sanudo2015: MiET vs WlNi



Code 
# Network plot
netgraph(
    nma_sr1_alg,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 1 (A | Lg)



Code 
# Detailed model summary
summary(nma_sr1_alg)
Original data (with adjusted standard errors for multi-arm studies):

                       treat1 treat2      TE   seTE seTE.adj narms multiarm
Acosta-Gallego2018       AeET   AqET  0.1452 0.5394   0.6498     2         
Andrade2019              AqET   WlNi  0.0000 0.8660   0.9388     2         
Assis2006                AeET   AqET  0.0000 0.7596   0.8416     2         
Baptista2012             AeET   WlNi  0.0000 1.4322   1.4774     2         
Kayo2012                 AeET   ReET -0.1780 0.5973   0.8510     3        *
Kayo2012                 AeET   WlNi  0.0000 0.6105   0.8792     3        *
Kayo2012                 ReET   WlNi  0.1780 0.5973   0.8510     3        *
Larsson2015               McT   MiET  0.3747 0.4479   0.5761     2         
Letieri2013              AqET   WlNi -1.6710 1.5689   1.6103     2         
Mannerkorpi2000           McT   WlNi  1.5731 0.8247   0.9008     2         
Mannerkorpi2004           McT   WlNi -0.1823 0.6849   0.7748     2         
Mengshoel1992            AeET   WlNi  1.5404 0.7918   0.8708     2         
Munguia-Izquierdo 2007   AqET   WlNi  1.6025 1.1148   1.1722     2         
Rooks2007                 CBT    McT  0.6440 0.4070   0.7037     3        *
Rooks2007                 CBT   MiET  0.6224 0.3550   0.6043     3        *
Rooks2007                 McT   MiET -0.0216 0.3615   0.6138     3        *
Sanudo2011               MiET   WlNi  1.2040 1.1995   1.2531     2         
Sanudo2010a              AeET   MiET -0.0572 0.7838   0.8636     2         
Sanudo2010b              AeET   WlNi  1.4917 1.1643   1.2194     2         
Schachter2003            AeET   WlNi  1.1454 0.5236   0.6368     2         
Tomas-Carus2008          AqET   WlNi  0.6931 1.2780   1.3284     2         
Valim2003                AeET   FlET -0.6444 0.5776   0.6819     2         
Valkeinen2008            MiET   WlNi  1.4491 1.6003   1.6408     2         
Wang2018                  McT   MiET -0.8398 0.4465   0.5751     2         
Williams2010              CBT   WlNi -0.7687 0.6425   0.7377     2         
Hernando-Garijo2021      AeET   WlNi  0.0000 0.8997   0.9700     2         

Number of treatment arms (by study):
                       narms
Acosta-Gallego2018         2
Andrade2019                2
Assis2006                  2
Baptista2012               2
Kayo2012                   3
Larsson2015                2
Letieri2013                2
Mannerkorpi2000            2
Mannerkorpi2004            2
Mengshoel1992              2
Munguia-Izquierdo 2007     2
Rooks2007                  3
Sanudo2011                 2
Sanudo2010a                2
Sanudo2010b                2
Schachter2003              2
Tomas-Carus2008            2
Valim2003                  2
Valkeinen2008              2
Wang2018                   2
Williams2010               2
Hernando-Garijo2021        2

Results (random effects model):

                       treat1 treat2     OR           95%-CI
Acosta-Gallego2018       AeET   AqET 1.2045 [0.5384; 2.6950]
Andrade2019              AqET   WlNi 1.5725 [0.6805; 3.6338]
Assis2006                AeET   AqET 1.2045 [0.5384; 2.6950]
Baptista2012             AeET   WlNi 1.8941 [1.0374; 3.4583]
Kayo2012                 AeET   ReET 1.1519 [0.3410; 3.8909]
Kayo2012                 AeET   WlNi 1.8941 [1.0374; 3.4583]
Kayo2012                 ReET   WlNi 1.6444 [0.4868; 5.5545]
Larsson2015               McT   MiET 0.8582 [0.4768; 1.5447]
Letieri2013              AqET   WlNi 1.5725 [0.6805; 3.6338]
Mannerkorpi2000           McT   WlNi 1.2642 [0.5567; 2.8706]
Mannerkorpi2004           McT   WlNi 1.2642 [0.5567; 2.8706]
Mengshoel1992            AeET   WlNi 1.8941 [1.0374; 3.4583]
Munguia-Izquierdo 2007   AqET   WlNi 1.5725 [0.6805; 3.6338]
Rooks2007                 CBT    McT 1.2707 [0.5404; 2.9879]
Rooks2007                 CBT   MiET 1.0905 [0.4721; 2.5192]
Rooks2007                 McT   MiET 0.8582 [0.4768; 1.5447]
Sanudo2011               MiET   WlNi 1.4730 [0.6380; 3.4012]
Sanudo2010a              AeET   MiET 1.2858 [0.5004; 3.3040]
Sanudo2010b              AeET   WlNi 1.8941 [1.0374; 3.4583]
Schachter2003            AeET   WlNi 1.8941 [1.0374; 3.4583]
Tomas-Carus2008          AqET   WlNi 1.5725 [0.6805; 3.6338]
Valim2003                AeET   FlET 0.5250 [0.1380; 1.9979]
Valkeinen2008            MiET   WlNi 1.4730 [0.6380; 3.4012]
Wang2018                  McT   MiET 0.8582 [0.4768; 1.5447]
Williams2010              CBT   WlNi 1.6064 [0.6231; 4.1412]
Hernando-Garijo2021      AeET   WlNi 1.8941 [1.0374; 3.4583]

Number of studies: k = 22
Number of pairwise comparisons: m = 26
Number of observations: o = 1685
Number of treatments: n = 8
Number of designs: d = 11

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'WlNi'):
         OR            95%-CI    z p-value
AeET 1.8941 [1.0374;  3.4583] 2.08  0.0376
AqET 1.5725 [0.6805;  3.6338] 1.06  0.2895
CBT  1.6064 [0.6231;  4.1412] 0.98  0.3266
FlET 3.6078 [0.8330; 15.6257] 1.72  0.0862
McT  1.2642 [0.5567;  2.8706] 0.56  0.5753
MiET 1.4730 [0.6380;  3.4012] 0.91  0.3643
ReET 1.6444 [0.4868;  5.5545] 0.80  0.4232
WlNi      .                 .    .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.1313; tau = 0.3624; I^2 = 20.7% [0.0%; 55.0%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f. p-value
Total           21.45   17  0.2070
Within designs  12.01   11  0.3631
Between designs  9.44    6  0.1504

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr1_alg)

Forest plot of treatment effects for Subnet 1 (A | Lg)



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr1_alg, ci = TRUE)
League table (random effects model):
                                                                           
                     AeET 1.0952 [0.3997;  3.0013]                        .
 1.2045 [0.5384;  2.6950]                     AqET                        .
 1.1791 [0.4036;  3.4444] 0.9789 [0.2835;  3.3795]                      CBT
 0.5250 [0.1380;  1.9979] 0.4359 [0.0916;  2.0749] 0.4453 [0.0803;  2.4699]
 1.4983 [0.5775;  3.8870] 1.2439 [0.3974;  3.8932] 1.2707 [0.5404;  2.9879]
 1.2858 [0.5004;  3.3040] 1.0675 [0.3409;  3.3431] 1.0905 [0.4721;  2.5192]
 1.1519 [0.3410;  3.8909] 0.9563 [0.2345;  3.8995] 0.9769 [0.2127;  4.4859]
 1.8941 [1.0374;  3.4583] 1.5725 [0.6805;  3.6338] 1.6064 [0.6231;  4.1412]
                                                                           
 0.5250 [0.1380;  1.9979]                        . 0.9444 [0.1738;  5.1314]
                        .                        .                        .
                        . 1.9041 [0.6544;  5.5409] 1.8634 [0.6894;  5.0369]
                     FlET                        .                        .
 2.8539 [0.5527; 14.7365]                      McT 0.8594 [0.4603;  1.6046]
 2.4492 [0.4770; 12.5769] 0.8582 [0.4768;  1.5447]                     MiET
 2.1940 [0.3599; 13.3762] 0.7688 [0.1810;  3.2646] 0.8958 [0.2106;  3.8103]
 3.6078 [0.8330; 15.6257] 1.2642 [0.5567;  2.8706] 1.4730 [0.6380;  3.4012]
                                                  
 0.8370 [0.2128;  3.2916] 2.0873 [1.0422;  4.1806]
                        . 1.3839 [0.4303;  4.4511]
                        . 0.4636 [0.1092;  1.9682]
                        .                        .
                        . 1.7579 [0.5559;  5.5594]
                        . 3.6483 [0.5181; 25.6920]
                     ReET 1.1948 [0.3038;  4.6990]
 1.6444 [0.4868;  5.5545]                     WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr1_alg <- netrank(nma_sr1_alg, small.values = "good")
print(ranking_sr1_alg)
     P-score
WlNi  0.8498
McT   0.6669
MiET  0.5327
AqET  0.5026
ReET  0.4813
CBT   0.4734
AeET  0.3524
FlET  0.1407



Code 
# Rankogram
ran_sr1_alg <- rankogram(nma_sr1_alg)
plot(ran_sr1_alg)

Rankogram of treatments for Subnet 1 (A | Lg)



Code 
# Design decomposition
decomp_sr1_alg <- decomp.design(nma_sr1_alg)
print(decomp_sr1_alg)
Q statistics to assess homogeneity / consistency

                    Q df p-value
Total           21.45 17  0.2070
Within designs  12.01 11  0.3631
Between designs  9.44  6  0.1504

Design-specific decomposition of within-designs Q statistic

    Design    Q df p-value
  McT:MiET 3.69  1  0.0548
  WlNi:McT 2.68  1  0.1015
 WlNi:AqET 3.16  3  0.3683
 WlNi:AeET 2.44  4  0.6547
 AeET:AqET 0.02  1  0.8762
 WlNi:MiET 0.02  1  0.9025

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from 0.1504)

 Detached design    Q df p-value
        WlNi:CBT 2.68  5  0.7487
    CBT:McT:MiET 2.42  4  0.6596
       WlNi:AeET 7.08  5  0.2150
       WlNi:MiET 8.14  5  0.1489
        WlNi:McT 8.43  5  0.1341
       AeET:MiET 9.04  5  0.1073
        McT:MiET 9.20  5  0.1015
       AeET:AqET 9.33  5  0.0965
       WlNi:AqET 9.33  5  0.0965

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 8.08  6  0.2321     0.2427      0.0589



Code 
# Node-splitting analysis to detect inconsistency
split_sr1_alg <- netsplit(nma_sr1_alg) # , show = "all")
print(split_sr1_alg)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop    nma direct indir.    RoR     z p-value
  AeET:AqET 2 0.64 1.2045 1.0952 1.4245 0.7688 -0.31  0.7585
  AeET:MiET 1 0.31 1.2858 0.9444 1.4779 0.6390 -0.43  0.6669
  AeET:ReET 1 0.79 1.1519 0.8370 3.8351 0.2182 -1.00  0.3183
  AeET:WlNi 6 0.75 1.8941 2.0873 1.4125 1.4777  0.55  0.5826
  AqET:WlNi 4 0.51 1.5725 1.3839 1.8000 0.7688 -0.31  0.7585
    CBT:McT 1 0.64 1.2707 1.9041 0.6178 3.0823  1.24  0.2157
   CBT:MiET 1 0.71 1.0905 1.8634 0.2956 6.3032  1.96  0.0503
   CBT:WlNi 1 0.43 1.6064 0.4636 4.0867 0.1135 -2.23  0.0258
   McT:MiET 3 0.89 0.8582 0.8594 0.8489 1.0123  0.01  0.9896
   McT:WlNi 2 0.51 1.2642 1.7579 0.9002 1.9529  0.80  0.4239
  MiET:WlNi 2 0.18 1.4730 3.6483 1.2010 3.0378  1.01  0.3135
  ReET:WlNi 1 0.79 1.6444 1.1948 5.4749 0.2182 -1.00  0.3183

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (OR) in network meta-analysis
 direct     - Estimated treatment effect (OR) derived from direct evidence
 indir.     - Estimated treatment effect (OR) derived from indirect evidence
 RoR        - Ratio of Ratios (direct versus indirect)
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr1_alg)

Forest plot of node-splitting for Subnet 1 (A | Lg)



Code 
# Heatmap
netheat(nma_sr1_alg)

Heatmap of contribution matrix for Subnet 1 (A | Lg)



Code 
# Funnel plot
funnel(nma_sr1_alg,
    order = "WlNi",
)

Funnel plot for Subnet 1 (A | Lg)





Select the procedures performed

Important

The second subnet contains only 1 study with 1 comparison between 2 treatments. Due to its limited size, the analysis will be simplified.

Code 
# Filter data for subnet 2
sr2_alg <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 2)

# Display comparison table
sr2_alg



Code 
# Unique treatments in subnet 2
unique_treat1_sr2_alg <- sr2_alg$treat1 |> unique()
unique_treat2_sr2_alg <- sr2_alg$treat2 |> unique()

# Combination of all unique treatments
trat_sr2_alg <- unique(c(unique_treat1_sr2_alg, unique_treat2_sr2_alg))
print(trat_sr2_alg)
[1] "DryN" "MasT"
Code 
# Total number of treatments
length(trat_sr2_alg)
[1] 2



Code 
# Filter pairwise object only for comparisons within subnet 2
pw_sr2_alg <- pw_alg %>%
    filter(treat1 %in% trat_sr2_alg & treat2 %in% trat_sr2_alg)

# Number of comparisons in subnet 2
nrow(pw_sr2_alg)
[1] 1
Code 
# Number of unique studies
length(unique(pw_sr2_alg$studlab))
[1] 1



Code 
# Fit NMA model for subnet 2
nma_sr2_alg <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_sr2_alg,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    ref = "MasT" # First treatment as reference
)

# Basic model summary
print(nma_sr2_alg)
Number of studies: k = 1
Number of pairwise comparisons: m = 1
Number of observations: o = 64
Number of treatments: n = 2
Number of designs: d = 1

Random effects model

Treatment estimate (sm = 'OR', comparison: 'DryN' vs 'MasT'):
         OR           95%-CI     z p-value
DryN 0.6444 [0.1003; 4.1421] -0.46  0.6435
MasT      .                .     .       .

Quantifying heterogeneity:
tau^2 = NA; tau = NA

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2



Code 
# Network plot
netgraph(
    nma_sr2_alg,
    # seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 2 (A | Lg)



Code 
# Detailed model summary
summary(nma_sr2_alg)
Original data:

                   treat1 treat2      TE   seTE
Castro-Sanchez2011   DryN   MasT -0.4394 0.9493

Number of treatment arms (by study):
                   narms
Castro-Sanchez2011     2

Results (random effects model):

                   treat1 treat2     OR           95%-CI
Castro-Sanchez2011   DryN   MasT 0.6444 [0.1003; 4.1421]

Number of studies: k = 1
Number of pairwise comparisons: m = 1
Number of observations: o = 64
Number of treatments: n = 2
Number of designs: d = 1

Random effects model

Treatment estimate (sm = 'OR', comparison: 'DryN' vs 'MasT'):
         OR           95%-CI     z p-value
DryN 0.6444 [0.1003; 4.1421] -0.46  0.6435
MasT      .                .     .       .

Quantifying heterogeneity:
tau^2 = NA; tau = NA

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2





Select the procedures performed

Important

The third subnet contains 4 studies, 4 comparisons and 4 treatments.

Code 
# Filter data for subnet 3
sr3_alg <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 3)

# Display comparison table
sr3_alg



Code 
# Unique treatments in subnet 3
unique_treat1_sr3_alg <- sr3_alg$treat1 |> unique()
unique_treat2_sr3_alg <- sr3_alg$treat2 |> unique()

# Combination of all unique treatments
trat_sr3_alg <- unique(c(unique_treat1_sr3_alg, unique_treat2_sr3_alg))
print(trat_sr3_alg)
[1] "MfT"   "Acu"   "rTMS"  "PlaSh"
Code 
# Total number of treatments
length(trat_sr3_alg)
[1] 4



Code 
# Filter pairwise object only for comparisons within subnet 3
pw_sr3_alg <- pw_alg %>%
    filter(treat1 %in% trat_sr3_alg & treat2 %in% trat_sr3_alg)

# Number of comparisons in subnet 3
nrow(pw_sr3_alg)
[1] 4
Code 
# Number of unique studies
length(unique(pw_sr3_alg$studlab))
[1] 4



Code 
# Fit NMA model for subnet 3
nma_sr3_alg <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_sr3_alg,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    ref = "PlaSh" # Reference treatment (change if you want another control)
)

# Basic model summary
print(nma_sr3_alg)
Number of studies: k = 4
Number of pairwise comparisons: m = 4
Number of observations: o = 295
Number of treatments: n = 4
Number of designs: d = 3

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'PlaSh'):
          OR           95%-CI     z p-value
Acu   0.7683 [0.3521; 1.6766] -0.66  0.5079
MfT   1.0559 [0.4113; 2.7111]  0.11  0.9100
PlaSh      .                .     .       .
rTMS  0.5833 [0.1362; 2.4976] -0.73  0.4676

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0%

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           0.38    1  0.5363
Within designs  0.38    1  0.5363
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Network plot
netgraph(
    nma_sr3_alg,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 3 (A | Lg)



Code 
# Detailed model summary
summary(nma_sr3_alg)
Original data:

            treat1 treat2      TE   seTE
Alfano2001     MfT  PlaSh  0.2184 0.5493
Colbert1999    MfT  PlaSh -0.4855 0.9968
Harris2005     Acu  PlaSh -0.2636 0.3981
Mhalla2011   PlaSh   rTMS  0.5390 0.7420

Number of treatment arms (by study):
            narms
Alfano2001      2
Colbert1999     2
Harris2005      2
Mhalla2011      2

Results (random effects model):

            treat1 treat2     OR           95%-CI
Alfano2001     MfT  PlaSh 1.0559 [0.4113; 2.7111]
Colbert1999    MfT  PlaSh 1.0559 [0.4113; 2.7111]
Harris2005     Acu  PlaSh 0.7683 [0.3521; 1.6766]
Mhalla2011   PlaSh   rTMS 1.7143 [0.4004; 7.3399]

Number of studies: k = 4
Number of pairwise comparisons: m = 4
Number of observations: o = 295
Number of treatments: n = 4
Number of designs: d = 3

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'PlaSh'):
          OR           95%-CI     z p-value
Acu   0.7683 [0.3521; 1.6766] -0.66  0.5079
MfT   1.0559 [0.4113; 2.7111]  0.11  0.9100
PlaSh      .                .     .       .
rTMS  0.5833 [0.1362; 2.4976] -0.73  0.4676

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0%

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           0.38    1  0.5363
Within designs  0.38    1  0.5363
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr3_alg)

Forest plot of treatment effects for Subnet 3 (A | Lg)



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr3_alg, ci = TRUE)
League table (random effects model):
                                                                           
                      Acu                        .  0.7683 [0.3521; 1.6766]
 0.7276 [0.2140;  2.4743]                      MfT  1.0559 [0.4113; 2.7111]
 0.7683 [0.3521;  1.6766] 1.0559 [0.4113;  2.7111]                    PlaSh
 1.3171 [0.2528;  6.8611] 1.8101 [0.3199; 10.2437] 1.7143 [0.4004;  7.3399]
                        
                       .
                       .
 1.7143 [0.4004; 7.3399]
                    rTMS

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr3_alg <- netrank(nma_sr3_alg, small.values = "good")
print(ranking_sr3_alg)
      P-score
rTMS   0.7144
Acu    0.6042
PlaSh  0.3443
MfT    0.3371



Code 
# Rankogram
ran_sr3_alg <- rankogram(nma_sr3_alg)
plot(ran_sr3_alg)

Rankogram of treatments for Subnet 3 (A | Lg)



Code 
# Design decomposition
decomp_sr3_alg <- decomp.design(nma_sr3_alg)
print(decomp_sr3_alg)
Q statistics to assess homogeneity / consistency

                   Q df p-value
Total           0.38  1  0.5363
Within designs  0.38  1  0.5363
Between designs 0.00  0      --

Design-specific decomposition of within-designs Q statistic

    Design    Q df p-value
 PlaSh:MfT 0.38  1  0.5363

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 0.00  0      --          0           0



Code 
# Node-splitting analysis to detect inconsistency
split_sr3_alg <- netsplit(nma_sr3_alg, show = "all")
print(split_sr3_alg)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop    nma direct indir. RoR z p-value
    Acu:MfT 0    0 0.7276      . 0.7276   . .       .
  Acu:PlaSh 1 1.00 0.7683 0.7683      .   . .       .
   Acu:rTMS 0    0 1.3171      . 1.3171   . .       .
  MfT:PlaSh 2 1.00 1.0559 1.0559      .   . .       .
   MfT:rTMS 0    0 1.8101      . 1.8101   . .       .
 rTMS:PlaSh 1 1.00 0.5833 0.5833      .   . .       .

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (OR) in network meta-analysis
 direct     - Estimated treatment effect (OR) derived from direct evidence
 indir.     - Estimated treatment effect (OR) derived from indirect evidence
 RoR        - Ratio of Ratios (direct versus indirect)
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr3_alg)

Forest plot of node-splitting for Subnet 3 (A | Lg)



Code 
# Heatmap
netheat(nma_sr3_alg)



Code 
# Funnel plot
funnel(nma_sr3_alg,
    order = "PlaSh",
)

Funnel plot for Subnet 3 (A | Lg)





Code 
# Read data
data_aim <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "A | Im")|>
    mutate(
        nRT1 = as.numeric(nRT1),
        nRT2 = as.numeric(nRT2),
        dp1 = as.numeric(dp1),
        dp2 = as.numeric(dp2)
    ) |>
    tidyr::drop_na() # excliniodo as linhas com NA


# Transform to contrast-based
pw_aim <- pairwise(
    treat = list(Treat1, Treat2),
    event = list(dp1, dp2), # observed events in each arm
    n = list(nRT1, nRT2), # total number of patients in each arm
    studlab = StudyID,
    data = data_aim,
    sm = "OR" # Medida de efeito (OR = Odds Ratio, pode ser "RR" ou "RD" se preferir)
)

# Check network connections
net_con <- netconnection(pw_aim)
net_con
Number of studies: k = 13
Number of pairwise comparisons: m = 13
Number of treatments: n = 8
Number of designs: d = 7
Number of networks: 1


There are three sub-networks:

Network:
- 13 studies
- 13 comparisons
- 8 treatments



Tip

The network is fully connected.

2.0.1 Network

Select the procedures performed

Important

The Network contains 13 studies, 13 comparisons and 8 treatments. This is the main analysis network for binary outcomes.

Code 
# Filter data for subnet 1
sr1_aim <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 1)

# Display first rows of comparison table
sr1_aim |> head()



Code 
# Unique treatments in subnet 1
unique_treat1_aim <- sr1_aim$treat1 |> unique()
unique_treat2_aim <- sr1_aim$treat2 |> unique()

# Combination of all unique treatments
trat_sr_aim <- unique(c(unique_treat1_aim, unique_treat2_aim))
print(trat_sr_aim)
[1] "Acu"   "rTMS"  "tDCS"  "McT"   "Elec"  "Bal"   "PlaSh" "WlNi"
Code 
# Total number of treatments
length(trat_sr_aim)
[1] 8



Code 
# Filter pairwise object only for comparisons within network
pw_sr_aim <- pw_aim %>%
    filter(treat1 %in% trat_sr_aim & treat2 %in% trat_sr_aim)

# Number of comparisons in network
nrow(pw_sr_aim)
[1] 25
Code 
# Number of unique studies
length(unique(pw_sr_aim$studlab))
[1] 25



Code 
# Fit NMA model for subnet 1
nma_sr_aim <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_sr_aim,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    ref = "WlNi" # Reference treatment (change if you want another control)
)
Comparisons not considered in network meta-analysis:
        studlab treat1 treat2 TE seTE
      Boyer2014   rTMS  PlaSh NA   NA
   Brietzke2019   tDCS  PlaSh NA   NA
    Buskila2001    Bal   WlNi NA   NA
   Curatolo2017   tDCS  PlaSh NA   NA
 Fioravanti2007    Bal   WlNi NA   NA
   Mendonça2011   tDCS  PlaSh NA   NA
    Neumann2001    Bal   WlNi NA   NA
    Passard2007   rTMS  PlaSh NA   NA
      Short2011   rTMS  PlaSh NA   NA
     Stival2013    Acu  PlaSh NA   NA
      Valle2009   tDCS  PlaSh NA   NA
     Forogh2021   rTMS   tDCS NA   NA
Code 
# Basic model summary
print(nma_sr_aim)
Number of studies: k = 13
Number of pairwise comparisons: m = 13
Number of observations: o = 658
Number of treatments: n = 8
Number of designs: d = 7

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'WlNi'):
          OR            95%-CI     z p-value
Acu   0.2076 [0.0066;  6.5694] -0.89  0.3725
Bal   4.5714 [0.4731; 44.1699]  1.31  0.1891
Elec  0.0459 [0.0006;  3.5298] -1.39  0.1643
McT   1.4655 [0.6439;  3.3355]  0.91  0.3624
PlaSh 0.8102 [0.0367; 17.8804] -0.13  0.8939
rTMS  0.7546 [0.0276; 20.6479] -0.17  0.8676
tDCS  1.0000 [0.0591; 16.9279]  0.00  1.0000
WlNi       .                 .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0% [0.0%; 70.8%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           1.21    6  0.9763
Within designs  1.21    6  0.9763
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q
Note

These three studies were excluded from the model because they reported a standard deviation of zero, which makes division by zero impossible.
- Boyer2014: rTMS vs PlaSh
- Brietzke2019: tDCS vs PlaSh
- Buskila2001: Bal vs WlNi
- Curatolo2017: tDCS vs PlaSh
- Fioravanti2007: Bal vs WlNi
- Mendonça2011: tDCS vs PlaSh
- Neumann2001: Bal vs WlNi
- Passard2007: rTMS vs PlaSh
- Short2011: rTMS vs PlaSh
- Stival2013: Acu vs PlaSh
- Valle2009: tDCS vs PlaSh
- Forogh2021: rTMS vs tDCS



Code 
# Network plot
netgraph(
    nma_sr_aim,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 1 (A | Im)



Code 
# Detailed model summary
summary(nma_sr_aim)
Original data:

              treat1 treat2      TE   seTE
Assefi2005       Acu  PlaSh -1.3614 0.7836
Cheng2019      PlaSh   rTMS  0.9985 1.6933
Fagerlund2015   tDCS   WlNi  0.0000 1.4434
Fregni2006     PlaSh   tDCS -0.3819 1.6758
Hamnes2012       McT   WlNi  0.3822 0.4196
Khedr2017      PlaSh   tDCS -0.0000 1.0541
Lauretti2013    Elec  PlaSh -2.8717 1.5552
Lee2012        PlaSh   rTMS -0.2231 1.0000
Mhalla2011     PlaSh   rTMS -0.0000 1.4510
Ozkurt2011       Bal   WlNi  1.5198 1.1573
Tekin2014      PlaSh   rTMS  1.2141 1.6565
Yagci2014      PlaSh   rTMS -0.6131 1.2885
deMelo2020     PlaSh   tDCS -0.3185 0.9170

Number of treatment arms (by study):
              narms
Assefi2005        2
Cheng2019         2
Fagerlund2015     2
Fregni2006        2
Hamnes2012        2
Khedr2017         2
Lauretti2013      2
Lee2012           2
Mhalla2011        2
Ozkurt2011        2
Tekin2014         2
Yagci2014         2
deMelo2020        2

Results (random effects model):

              treat1 treat2     OR            95%-CI
Assefi2005       Acu  PlaSh 0.2563 [0.0552;  1.1904]
Cheng2019      PlaSh   rTMS 1.0737 [0.3321;  3.4707]
Fagerlund2015   tDCS   WlNi 1.0000 [0.0591; 16.9279]
Fregni2006     PlaSh   tDCS 0.8102 [0.2313;  2.8374]
Hamnes2012       McT   WlNi 1.4655 [0.6439;  3.3355]
Khedr2017      PlaSh   tDCS 0.8102 [0.2313;  2.8374]
Lauretti2013    Elec  PlaSh 0.0566 [0.0027;  1.1930]
Lee2012        PlaSh   rTMS 1.0737 [0.3321;  3.4707]
Mhalla2011     PlaSh   rTMS 1.0737 [0.3321;  3.4707]
Ozkurt2011       Bal   WlNi 4.5714 [0.4731; 44.1699]
Tekin2014      PlaSh   rTMS 1.0737 [0.3321;  3.4707]
Yagci2014      PlaSh   rTMS 1.0737 [0.3321;  3.4707]
deMelo2020     PlaSh   tDCS 0.8102 [0.2313;  2.8374]

Number of studies: k = 13
Number of pairwise comparisons: m = 13
Number of observations: o = 658
Number of treatments: n = 8
Number of designs: d = 7

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'WlNi'):
          OR            95%-CI     z p-value
Acu   0.2076 [0.0066;  6.5694] -0.89  0.3725
Bal   4.5714 [0.4731; 44.1699]  1.31  0.1891
Elec  0.0459 [0.0006;  3.5298] -1.39  0.1643
McT   1.4655 [0.6439;  3.3355]  0.91  0.3624
PlaSh 0.8102 [0.0367; 17.8804] -0.13  0.8939
rTMS  0.7546 [0.0276; 20.6479] -0.17  0.8676
tDCS  1.0000 [0.0591; 16.9279]  0.00  1.0000
WlNi       .                 .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0% [0.0%; 70.8%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           1.21    6  0.9763
Within designs  1.21    6  0.9763
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr_aim)

Forest plot of treatment effects for Subnet 1 (A | Im)



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr_aim, ci = TRUE)
League table (random effects model):
                                                         
                         Acu                            .
 0.0454 [0.0007;     2.8313]                          Bal
 4.5278 [0.1491;   137.4731] 99.6828 [0.7423; 13386.5505]
 0.1417 [0.0041;     4.9371]  3.1193 [0.2794;    34.8246]
 0.2563 [0.0552;     1.1904]  5.6424 [0.1217;   261.6026]
 0.2752 [0.0398;     1.9008]  6.0580 [0.1096;   334.7204]
 0.2076 [0.0286;     1.5074]  4.5714 [0.1217;   171.7126]
 0.2076 [0.0066;     6.5694]  4.5714 [0.4731;    44.1699]
                                                        
                           .                           .
                           .                           .
                        Elec                           .
 0.0313 [0.0004;     2.6018]                         McT
 0.0566 [0.0027;     1.1930] 1.8089 [0.0736;    44.4478]
 0.0608 [0.0023;     1.5929] 1.9421 [0.0642;    58.7682]
 0.0459 [0.0017;     1.2382] 1.4655 [0.0770;    27.8905]
 0.0459 [0.0006;     3.5298] 1.4655 [0.6439;     3.3355]
                                                        
   0.2563 [0.0552;   1.1904]                           .
                           .                           .
   0.0566 [0.0027;   1.1930]                           .
                           .                           .
                       PlaSh   1.0737 [0.3321;   3.4707]
 1.0737 [0.3321;     3.4707]                        rTMS
 0.8102 [0.2313;     2.8374] 0.7546 [0.1356;     4.2009]
 0.8102 [0.0367;    17.8804] 0.7546 [0.0276;    20.6479]
                                                      
                           .                         .
                           . 4.5714 [0.4731;  44.1699]
                           .                         .
                           . 1.4655 [0.6439;   3.3355]
   0.8102 [0.2313;   2.8374]                         .
                           .                         .
                        tDCS 1.0000 [0.0591;  16.9279]
 1.0000 [0.0591;    16.9279]                      WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr_aim <- netrank(nma_sr_aim, small.values = "good")
print(ranking_sr_aim)
      P-score
Elec   0.9311
Acu    0.7998
WlNi   0.4819
rTMS   0.4772
PlaSh  0.4517
tDCS   0.3904
McT    0.3308
Bal    0.1371



Code 
# Rankogram
ran_sr_aim <- rankogram(nma_sr_aim)
plot(ran_sr_aim)

Rankogram of treatments for Subnet 1 (A | Im)



Code 
# Design decomposition
decomp_sr_aim <- decomp.design(nma_sr_aim)
print(decomp_sr_aim)
Q statistics to assess homogeneity / consistency

                   Q df p-value
Total           1.21  6  0.9763
Within designs  1.21  6  0.9763
Between designs 0.00  0      --

Design-specific decomposition of within-designs Q statistic

     Design    Q df p-value
 PlaSh:rTMS 1.15  4  0.8867
 PlaSh:tDCS 0.06  2  0.9684

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                   Q df p-value tau.within tau2.within
Between designs 0.00  0      --          0           0



Code 
# Node-splitting analysis to detect inconsistency
split_sr_aim <- netsplit(nma_sr_aim, show = "all")
print(split_sr_aim)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison k prop     nma direct  indir. RoR z p-value
    Acu:Bal 0    0  0.0454      .  0.0454   . .       .
   Acu:Elec 0    0  4.5278      .  4.5278   . .       .
    Acu:McT 0    0  0.1417      .  0.1417   . .       .
  Acu:PlaSh 1 1.00  0.2563 0.2563       .   . .       .
   Acu:rTMS 0    0  0.2752      .  0.2752   . .       .
   Acu:tDCS 0    0  0.2076      .  0.2076   . .       .
   Acu:WlNi 0    0  0.2076      .  0.2076   . .       .
   Bal:Elec 0    0 99.6828      . 99.6828   . .       .
    Bal:McT 0    0  3.1193      .  3.1193   . .       .
  Bal:PlaSh 0    0  5.6424      .  5.6424   . .       .
   Bal:rTMS 0    0  6.0580      .  6.0580   . .       .
   Bal:tDCS 0    0  4.5714      .  4.5714   . .       .
   Bal:WlNi 1 1.00  4.5714 4.5714       .   . .       .
   Elec:McT 0    0  0.0313      .  0.0313   . .       .
 Elec:PlaSh 1 1.00  0.0566 0.0566       .   . .       .
  Elec:rTMS 0    0  0.0608      .  0.0608   . .       .
  Elec:tDCS 0    0  0.0459      .  0.0459   . .       .
  Elec:WlNi 0    0  0.0459      .  0.0459   . .       .
  McT:PlaSh 0    0  1.8089      .  1.8089   . .       .
   McT:rTMS 0    0  1.9421      .  1.9421   . .       .
   McT:tDCS 0    0  1.4655      .  1.4655   . .       .
   McT:WlNi 1 1.00  1.4655 1.4655       .   . .       .
 PlaSh:rTMS 5 1.00  1.0737 1.0737       .   . .       .
 PlaSh:tDCS 3 1.00  0.8102 0.8102       .   . .       .
 PlaSh:WlNi 0    0  0.8102      .  0.8102   . .       .
  rTMS:tDCS 0    0  0.7546      .  0.7546   . .       .
  rTMS:WlNi 0    0  0.7546      .  0.7546   . .       .
  tDCS:WlNi 1 1.00  1.0000 1.0000       .   . .       .

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (OR) in network meta-analysis
 direct     - Estimated treatment effect (OR) derived from direct evidence
 indir.     - Estimated treatment effect (OR) derived from indirect evidence
 RoR        - Ratio of Ratios (direct versus indirect)
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr_aim)

Forest plot of node-splitting for Subnet 1 (A | Im)



Code 
# Heatmap
netheat(nma_sr_aim)



Code 
# Funnel plot
funnel(nma_sr_aim,
    order = "WlNi",
)

Funnel plot for Network (A | Im)





Code 
# Read data
data_ash <- read_excel("data/Banco de Dados_Rstudio (1).xlsx", sheet = "A | Sh")|>
    mutate(
        nRT1 = as.numeric(nRT1),
        nRT2 = as.numeric(nRT2),
        dp1 = as.numeric(dp1),
        dp2 = as.numeric(dp2)
    ) 


# Transform to contrast-based
pw_ash <- pairwise(
    treat = list(Treat1, Treat2, Treat3),
    event = list(dp1, dp2, dp3), # observed events in each arm
    n = list(nRT1, nRT2, nRT3), # total number of patients in each arm
    studlab = StudyID,
    data = data_ash,
    sm = "OR" # Medida de efeito (OR = Odds Ratio, pode ser "RR" ou "RD" se preferir)
)

# Check network connections
net_con <- netconnection(pw_ash)
net_con
Number of studies: k = 92
Number of pairwise comparisons: m = 100
Number of treatments: n = 22
Number of designs: d = 40
Number of networks: 1


There are three sub-networks:

Network:
- 92 studies
- 100 comparisons
- 22 treatments



Tip

The network is fully connected.

2.0.2 Network

Select the procedures performed

Important

The Network contains 92 studies, 100 comparisons and 22 treatments. This is the main analysis network for binary outcomes.

Code 
# Filter data for subnet 1
sr1_ash <- tibble(
    treat1 = net_con$treat1,
    treat2 = net_con$treat2,
    subnet = net_con$subnet
) |>
    filter(subnet == 1)

# Display first rows of comparison table
sr1_ash |> head()



Code 
# Unique treatments in subnet 1
unique_treat1_ash <- sr1_ash$treat1 |> unique()
unique_treat2_ash <- sr1_ash$treat2 |> unique()

# Combination of all unique treatments
trat_sr_ash <- unique(c(unique_treat1_ash, unique_treat2_ash))
print(trat_sr_aim)
[1] "Acu"   "rTMS"  "tDCS"  "McT"   "Elec"  "Bal"   "PlaSh" "WlNi"
Code 
# Total number of treatments
length(trat_sr_ash)
[1] 22



Code 
# Filter pairwise object only for comparisons within network
pw_sr_ash <- pw_ash %>%
    filter(treat1 %in% trat_sr_ash & treat2 %in% trat_sr_ash)

# Number of comparisons in network
nrow(pw_sr_ash)
[1] 131
Code 
# Number of unique studies
length(unique(pw_sr_ash$studlab))
[1] 119



Code 
# Fit NMA model for subnet 1
nma_sr_ash <- netmeta(
    TE, seTE, treat1, treat2, studlab,
    data = pw_sr_ash,
    n1 = n1,
    n2 = n2,
    random = TRUE,
    common = FALSE,
    ref = "WlNi" # Reference treatment (change if you want another control)
)
Comparisons not considered in network meta-analysis:
                 studlab treat1 treat2 TE seTE
             Bressan2008   AeET   FlET NA   NA
            Brietzke2019   tDCS  PlaSh NA   NA
      Castro-Sanchez2019   DryN   MasT NA   NA
      Castro-Sanchez2020   DryN   Elec NA   NA
             Colbert1999    MfT  PlaSh NA   NA
             daSilva2008   AqET   WlNi NA   NA
               Evcik2002    Bal   WlNi NA   NA
             Fonseca2019   AqET    CBT NA   NA
              Garcia2006    CBT   WlNi NA   NA
     Gomez-Hernandez2019   AeET   MiET NA   NA
              Gowans2001   AqET   WlNi NA   NA
              Harris2005    Acu  PlaSh NA   NA
               Harte2013    Acu  PlaSh NA   NA
                Kayo2012   AeET   ReET NA   NA
                Kayo2012   AeET   WlNi NA   NA
                Kayo2012   ReET   WlNi NA   NA
                King2002    CBT    McT NA   NA
              Mhalla2011   rTMS  PlaSh NA   NA
                 Oka2019    MfT  PlaSh NA   NA
           Schachter2003   AeET   WlNi NA   NA
              Sencan2004   AeET  PlaSh NA   NA
             Sevimli2015   AeET   AqET NA   NA
             Sevimli2015   AeET   MiET NA   NA
             Sevimli2015   AqET   MiET NA   NA
                  To2017   tDCS  PlaSh NA   NA
              Torres2015    MnT    CBT NA   NA
              Ugurlu2017    Acu  PlaSh NA   NA
               Valim2003   AeET   FlET NA   NA
             Vallejo2015    CBT   WlNi NA   NA
 Izquierdo-Alventosa2020   MiET   WlNi NA   NA
        Mingorance2021.2    WBV   WlNi NA   NA
Code 
# Basic model summary
print(nma_sr_ash)
Number of studies: k = 92
Number of pairwise comparisons: m = 100
Number of observations: o = 6562
Number of treatments: n = 22
Number of designs: d = 40

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'WlNi'):
          OR            95%-CI     z p-value
Acu   0.9064 [0.3001;  2.7381] -0.17  0.8617
AeET  1.5649 [0.7452;  3.2863]  1.18  0.2368
AqET  1.4451 [0.5955;  3.5068]  0.81  0.4157
Bal   1.0603 [0.3278;  3.4296]  0.10  0.9221
CBT   1.1774 [0.8906;  1.5566]  1.15  0.2517
Cry   2.3731 [0.0929; 60.6503]  0.52  0.6012
DryN  1.0000 [0.3828;  2.6122]  0.00  1.0000
Elec  1.2453 [0.4358;  3.5585]  0.41  0.6822
FlET  1.2249 [0.5146;  2.9155]  0.46  0.6467
HtT   0.2014 [0.0204;  1.9872] -1.37  0.1701
MasT  0.7564 [0.2386;  2.3975] -0.47  0.6352
McT   0.9869 [0.6857;  1.4203] -0.07  0.9433
MfT   0.8232 [0.2311;  2.9323] -0.30  0.7641
MiET  1.0008 [0.6534;  1.5329]  0.00  0.9971
MnT   0.5819 [0.1658;  2.0422] -0.85  0.3980
PlaSh 0.9915 [0.3883;  2.5320] -0.02  0.9858
Plt   2.7557 [0.6206; 12.2373]  1.33  0.1826
ReET  1.1212 [0.5497;  2.2869]  0.31  0.7531
rTMS  0.7426 [0.2192;  2.5163] -0.48  0.6327
tDCS  0.8650 [0.2536;  2.9511] -0.23  0.8169
WBV   1.1111 [0.2705;  4.5634]  0.15  0.8838
WlNi       .                 .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0% [0.0%; 27.5%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f. p-value
Total           64.44   75  0.8027
Within designs  48.63   52  0.6073
Between designs 15.81   23  0.8632

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q
Note

These three studies were excluded from the model because they reported a standard deviation of zero, which makes division by zero impossible.
- Bressan2008: AeET vs FlET
- Brietzke2019: tDCSvs PlaSh
- Castro-Sanchez2019: DryN vs MasT
- Castro-Sanchez2020: DryN vs Elec
- Colbert1999: MfT vs PlaSh
- daSilva2008: AqET vs WlNi
- Evcik2002: Bal vs WlNi
- Fonseca2019: AqET vs CBT
- Garcia2006: CBT vs WlNi
- Gomez-Hernandez2019: AeET vs MiET
- Gowans2001: AqET vs WlNi
- Harris2005: Acuvs PlaSh
- Harte2013: Acu vs PlaSh
- Kayo2012: AeET vs ReET
- Kayo2012: AeET vs WlNi
- Kayo2012: ReET vs WlNi
- King2002: CBT vs McT
- Mhalla2011: rTMSvs PlaSh
- Oka2019: MfT vs PlaSh
- Schachter2003: AeET vs WlNi
- Sencan2004: AeETvs PlaSh
- Sevimli2015: AeET vs AqET
- Sevimli2015: AeET vs MiET
- Sevimli2015: AqET vs MiET
- To2017: tDCSvs PlaSh
- Torres2015: MnT vs CBT
- Ugurlu2017: Acuvs PlaSh
- Valim2003: AeET vs FlET
- Vallejo2015: CBT vs WlNi
- Izquierdo-Alventosa2020: MiET vs WlNi
- Mingorance2021.2: WBV vs WlNi



Code 
# Network plot
netgraph(
    nma_sr_ash,
    seq = "optimal",
    number.of.studies = TRUE,
    cex.points = n.trts,
    labels = paste0(trts, "\n(n=", round(n.trts), ")")
)

Network plot of treatments for Subnet 1 (A | Sh)



Code 
# Detailed model summary
summary(nma_sr_ash)
Original data (with adjusted standard errors for multi-arm studies):

                        treat1 treat2      TE   seTE seTE.adj narms multiarm
Albers2018                 MnT   WlNi  0.2032 1.6625   1.6625     2         
Alentorn-Geli2008          McT    WBV -1.1820 1.6833   2.4493     3        *
Alentorn-Geli2008          McT   WlNi -1.7838 1.6048   1.9855     3        *
Alentorn-Geli2008          WBV   WlNi -0.6018 1.1175   1.1951     3        *
Alfano2001                 MfT  PlaSh -0.0174 0.5669   0.5669     2         
Altan2004                 AqET    Bal -1.1856 1.1918   1.1918     2         
Ang2010                    CBT   WlNi -0.1431 1.0694   1.0694     2         
Ardic2007                  Bal   WlNi -2.2203 1.5719   1.5719     2         
Assefi2005                 Acu  PlaSh -0.3533 0.6141   0.6141     2         
Assis2006                 AeET   AqET  1.1701 1.1853   1.1853     2         
Assumpçao2018             FlET   ReET  0.4212 0.8469   0.9695     3        *
Assumpçao2018             FlET   WlNi  0.6931 0.9449   1.1648     3        *
Assumpçao2018             ReET   WlNi  0.2719 0.9835   1.2927     3        *
Astin2003                  CBT    McT -0.0625 0.3536   0.3536     2         
Baumueller2017             CBT   WlNi  0.0000 1.4510   1.4510     2         
Bircan2008                AeET   ReET  0.0000 1.0742   1.0742     2         
Bongi2012                  CBT    McT  0.0000 0.7958   0.7958     2         
Bongi2010                  CBT   WlNi -2.0890 1.5432   1.5432     2         
Bourgault2015              McT   WlNi  1.1331 1.6540   1.6540     2         
Boyer2014                PlaSh   rTMS  0.9008 0.7996   0.7996     2         
Calandre2009              AqET   FlET  0.7538 0.6006   0.6006     2         
Carretero2009            PlaSh   rTMS  0.1671 1.4724   1.4724     2         
Carson2010                 McT   WlNi  0.5725 0.9577   0.9577     2         
Casanueva2014             DryN   WlNi  0.0000 0.4899   0.4899     2         
Collado-Mateo2017         MiET   WlNi -1.9500 1.1044   1.1044     2         
Da Costa2005              MiET   WlNi  0.2693 0.6517   0.6517     2         
Dailey2019                Elec  PlaSh  0.4692 0.2901   0.2901     2         
deMedeiros2020            AqET    Plt -0.4595 0.9703   0.9703     2         
Ekici2017                 MasT    Plt -2.1282 1.1318   1.1318     2         
Ekici2008                 MasT    Plt -0.5754 1.2565   1.2565     2         
Espi-Lopes2016            MiET   WlNi  1.2685 1.1426   1.1426     2         
Fernandes2016             AeET   AqET  0.0846 1.0278   1.0278     2         
Fitzgibbon2018           PlaSh   rTMS -0.6061 1.2939   1.2939     2         
Friedberg2019              CBT   WlNi  0.9555 0.9628   0.9628     2         
Garcia-Martinez2012       MiET   WlNi  0.7732 1.2885   1.2885     2         
Giannotti2014              McT   WlNi -1.6094 1.1673   1.1673     2         
Glasgow2017               ReET   WlNi  1.0217 1.6795   1.6795     2         
Goldway2019                CBT  PlaSh -0.3285 0.8069   0.8069     2         
Gowans1999                 McT   WlNi  1.1474 1.1962   1.1962     2         
Gunther1994                Bal    CBT  1.1756 1.6795   1.6795     2         
Hargrove2012             PlaSh   tDCS  0.3137 0.5862   0.5862     2         
Hsu2010                    CBT   WlNi  1.9459 1.5423   1.5423     2         
Jensen2012                 CBT   WlNi  0.4568 0.7870   0.7870     2         
Jones2002                  McT   ReET  0.0000 0.6362   0.6362     2         
Jones2012                  CBT    McT  2.0268 1.5252   1.5252     2         
Karatay2018                Acu  PlaSh  0.0000 1.2500   1.2500     2         
Kurt2016                   Bal   MiET -0.3151 0.7988   0.7988     2         
Lami2018                   CBT   WlNi  1.1517 0.4971   0.4971     2         
Lauche2016                MasT  PlaSh  0.1788 0.5132   0.5132     2         
Lopes-Rodrigues2012       AqET   FlET  0.1158 0.4815   0.4815     2         
Lopes-Rodrigues2013       AqET   FlET  0.1517 0.5513   0.5513     2         
Luciano2014                CBT   WlNi  0.5942 0.7583   0.7583     2         
Lynch2012                  McT   WlNi  1.5266 0.8100   0.8100     2         
Maestu2013               PlaSh   rTMS -0.1823 0.6619   0.6619     2         
McCrae2019                 CBT   WlNi  0.0364 0.4658   0.4658     2         
Menzies2014                CBT   WlNi  0.7885 0.7508   0.7508     2         
Mist2018                   Acu    CBT -1.0296 0.9599   0.9599     2         
Norrengaard1997           AeET    HtT  2.6391 1.2012   1.5648     3        *
Norrengaard1997           AeET   MiET  1.7047 0.8006   0.8546     3        *
Norrengaard1997            HtT   MiET -0.9343 1.2181   1.6681     3        *
Olivares2011               WBV   WlNi  0.4055 0.9718   0.9718     2         
Paolucci2016               MfT  PlaSh -0.6931 1.2780   1.2780     2         
Paolucci2015              MiET   WlNi  0.4055 0.9789   0.9789     2         
Parra-Delgado2013          CBT   WlNi  1.6720 1.5891   1.5891     2         
Pereira-Pernambuco2018     McT   WlNi -0.1967 0.6187   0.6187     2         
Perez-Aranda2019           CBT   WlNi -0.2933 0.3285   0.3285     2         
Picard2013                 CBT   WlNi -0.7270 1.2521   1.2521     2         
Redondo2004                CBT   MiET  0.1586 0.7610   0.7610     2         
Richards2002              AeET    McT -0.0357 0.4499   0.4499     2         
Rivera2018                 Cry   WlNi  0.8642 1.6536   1.6536     2         
Salaffi2015                McT   WlNi  0.0000 1.0274   1.0274     2         
Schmidt2011                CBT   WlNi  0.5320 0.4669   0.4669     2         
Silva2019                  CBT   ReET -0.1967 0.6282   0.6282     2         
Simister2018               CBT   WlNi  0.8313 0.7545   0.7545     2         
Soares2002                 CBT   WlNi -0.4626 0.8185   0.8185     2         
Sutbeyaz2009               MfT  PlaSh -0.3285 0.8155   0.8155     2         
Tomas-Carus2007b&c        AqET   WlNi  1.0986 1.6676   1.6676     2         
Vas2016                    Acu  PlaSh  1.4240 1.1292   1.1292     2         
Verkaik2013                CBT   WlNi -0.4349 0.6286   0.6286     2         
Wang2018                   McT   MiET -0.3430 0.3500   0.3500     2         
Wicksell2013               CBT   WlNi  0.8755 1.2024   1.2024     2         
Wong2018                   McT   WlNi -1.8036 1.1534   1.1534     2         
Arakaki2021               FlET   ReET  0.7673 0.9078   0.9078     2         
Atan2020                  MiET   WlNi -1.2098 0.9584   0.9584     2         
Barranengoa-Cuadra 2021    CBT   WlNi -0.4203 0.9290   0.9290     2         
Cao2020                    Acu   MasT  0.4418 0.9519   0.9519     2         
Ceballos-Laita2020         McT   MiET -1.2417 1.2153   1.2153     2         
Coste2021                  MnT  PlaSh -0.5960 0.4839   0.4839     2         
Jamison2021               Elec  PlaSh -0.4513 0.4853   0.4853     2         
Nadal-Nicolas2020         MasT  PlaSh -1.9459 1.1711   1.1711     2         
Rodriguez-Mansilla2021     McT   MiET -0.0000 0.4511   0.5643     3        *
Rodriguez-Mansilla2021    MiET   WlNi -0.3805 0.4379   0.5309     3        *
Rodriguez-Mansilla2021     McT   WlNi -0.3805 0.4379   0.5309     3        *
Sarmento2020               McT  PlaSh  0.0000 0.8367   0.8367     2         
Tanwar2020               PlaSh   rTMS  2.2892 1.5061   1.5061     2         
Udina-Cortés2020          Elec  PlaSh  0.2429 0.9706   0.9706     2         
Lacroix2022              PlaSh   rTMS  0.1082 1.0267   1.0267     2         
Paolucci2022               CBT   MiET  0.6931 1.2860   1.2860     2         
Park2021                  FlET   ReET -0.0000 0.7303   0.7303     2         
Samartin-Veiga2022       PlaSh   tDCS -0.0238 0.5576   0.5576     2         

Number of treatment arms (by study):
                        narms
Albers2018                  2
Alentorn-Geli2008           3
Alfano2001                  2
Altan2004                   2
Ang2010                     2
Ardic2007                   2
Assefi2005                  2
Assis2006                   2
Assumpçao2018               3
Astin2003                   2
Baumueller2017              2
Bircan2008                  2
Bongi2012                   2
Bongi2010                   2
Bourgault2015               2
Boyer2014                   2
Calandre2009                2
Carretero2009               2
Carson2010                  2
Casanueva2014               2
Collado-Mateo2017           2
Da Costa2005                2
Dailey2019                  2
deMedeiros2020              2
Ekici2017                   2
Ekici2008                   2
Espi-Lopes2016              2
Fernandes2016               2
Fitzgibbon2018              2
Friedberg2019               2
Garcia-Martinez2012         2
Giannotti2014               2
Glasgow2017                 2
Goldway2019                 2
Gowans1999                  2
Gunther1994                 2
Hargrove2012                2
Hsu2010                     2
Jensen2012                  2
Jones2002                   2
Jones2012                   2
Karatay2018                 2
Kurt2016                    2
Lami2018                    2
Lauche2016                  2
Lopes-Rodrigues2012         2
Lopes-Rodrigues2013         2
Luciano2014                 2
Lynch2012                   2
Maestu2013                  2
McCrae2019                  2
Menzies2014                 2
Mist2018                    2
Norrengaard1997             3
Olivares2011                2
Paolucci2016                2
Paolucci2015                2
Parra-Delgado2013           2
Pereira-Pernambuco2018      2
Perez-Aranda2019            2
Picard2013                  2
Redondo2004                 2
Richards2002                2
Rivera2018                  2
Salaffi2015                 2
Schmidt2011                 2
Silva2019                   2
Simister2018                2
Soares2002                  2
Sutbeyaz2009                2
Tomas-Carus2007b&c          2
Vas2016                     2
Verkaik2013                 2
Wang2018                    2
Wicksell2013                2
Wong2018                    2
Arakaki2021                 2
Atan2020                    2
Barranengoa-Cuadra 2021     2
Cao2020                     2
Ceballos-Laita2020          2
Coste2021                   2
Jamison2021                 2
Nadal-Nicolas2020           2
Rodriguez-Mansilla2021      3
Sarmento2020                2
Tanwar2020                  2
Udina-Cortés2020            2
Lacroix2022                 2
Paolucci2022                2
Park2021                    2
Samartin-Veiga2022          2

Results (random effects model):

                        treat1 treat2     OR            95%-CI
Albers2018                 MnT   WlNi 0.5819 [0.1658;  2.0422]
Alentorn-Geli2008          McT    WBV 0.8882 [0.2081;  3.7905]
Alentorn-Geli2008          McT   WlNi 0.9869 [0.6857;  1.4203]
Alentorn-Geli2008          WBV   WlNi 1.1111 [0.2705;  4.5634]
Alfano2001                 MfT  PlaSh 0.8303 [0.3523;  1.9565]
Altan2004                 AqET    Bal 1.3629 [0.3654;  5.0835]
Ang2010                    CBT   WlNi 1.1774 [0.8906;  1.5566]
Ardic2007                  Bal   WlNi 1.0603 [0.3278;  3.4296]
Assefi2005                 Acu  PlaSh 0.9142 [0.4044;  2.0664]
Assis2006                 AeET   AqET 1.0829 [0.4187;  2.8008]
Assumpçao2018             FlET   ReET 1.0925 [0.4980;  2.3966]
Assumpçao2018             FlET   WlNi 1.2249 [0.5146;  2.9155]
Assumpçao2018             ReET   WlNi 1.1212 [0.5497;  2.2869]
Astin2003                  CBT    McT 1.1930 [0.8139;  1.7487]
Baumueller2017             CBT   WlNi 1.1774 [0.8906;  1.5566]
Bircan2008                AeET   ReET 1.3957 [0.5806;  3.3549]
Bongi2012                  CBT    McT 1.1930 [0.8139;  1.7487]
Bongi2010                  CBT   WlNi 1.1774 [0.8906;  1.5566]
Bourgault2015              McT   WlNi 0.9869 [0.6857;  1.4203]
Boyer2014                PlaSh   rTMS 1.3352 [0.6113;  2.9162]
Calandre2009              AqET   FlET 1.1798 [0.6684;  2.0824]
Carretero2009            PlaSh   rTMS 1.3352 [0.6113;  2.9162]
Carson2010                 McT   WlNi 0.9869 [0.6857;  1.4203]
Casanueva2014             DryN   WlNi 1.0000 [0.3828;  2.6122]
Collado-Mateo2017         MiET   WlNi 1.0008 [0.6534;  1.5329]
Da Costa2005              MiET   WlNi 1.0008 [0.6534;  1.5329]
Dailey2019                Elec  PlaSh 1.2559 [0.7828;  2.0149]
deMedeiros2020            AqET    Plt 0.5244 [0.1223;  2.2479]
Ekici2017                 MasT    Plt 0.2745 [0.0699;  1.0779]
Ekici2008                 MasT    Plt 0.2745 [0.0699;  1.0779]
Espi-Lopes2016            MiET   WlNi 1.0008 [0.6534;  1.5329]
Fernandes2016             AeET   AqET 1.0829 [0.4187;  2.8008]
Fitzgibbon2018           PlaSh   rTMS 1.3352 [0.6113;  2.9162]
Friedberg2019              CBT   WlNi 1.1774 [0.8906;  1.5566]
Garcia-Martinez2012       MiET   WlNi 1.0008 [0.6534;  1.5329]
Giannotti2014              McT   WlNi 0.9869 [0.6857;  1.4203]
Glasgow2017               ReET   WlNi 1.1212 [0.5497;  2.2869]
Goldway2019                CBT  PlaSh 1.1874 [0.4723;  2.9856]
Gowans1999                 McT   WlNi 0.9869 [0.6857;  1.4203]
Gunther1994                Bal    CBT 0.9006 [0.2761;  2.9373]
Hargrove2012             PlaSh   tDCS 1.1462 [0.5193;  2.5302]
Hsu2010                    CBT   WlNi 1.1774 [0.8906;  1.5566]
Jensen2012                 CBT   WlNi 1.1774 [0.8906;  1.5566]
Jones2002                  McT   ReET 0.8802 [0.4337;  1.7862]
Jones2012                  CBT    McT 1.1930 [0.8139;  1.7487]
Karatay2018                Acu  PlaSh 0.9142 [0.4044;  2.0664]
Kurt2016                   Bal   MiET 1.0595 [0.3329;  3.3715]
Lami2018                   CBT   WlNi 1.1774 [0.8906;  1.5566]
Lauche2016                MasT  PlaSh 0.7628 [0.3395;  1.7142]
Lopes-Rodrigues2012       AqET   FlET 1.1798 [0.6684;  2.0824]
Lopes-Rodrigues2013       AqET   FlET 1.1798 [0.6684;  2.0824]
Luciano2014                CBT   WlNi 1.1774 [0.8906;  1.5566]
Lynch2012                  McT   WlNi 0.9869 [0.6857;  1.4203]
Maestu2013               PlaSh   rTMS 1.3352 [0.6113;  2.9162]
McCrae2019                 CBT   WlNi 1.1774 [0.8906;  1.5566]
Menzies2014                CBT   WlNi 1.1774 [0.8906;  1.5566]
Mist2018                   Acu    CBT 0.7699 [0.2592;  2.2868]
Norrengaard1997           AeET    HtT 7.7705 [0.8074; 74.7823]
Norrengaard1997           AeET   MiET 1.5636 [0.7378;  3.3138]
Norrengaard1997            HtT   MiET 0.2012 [0.0207;  1.9520]
Olivares2011               WBV   WlNi 1.1111 [0.2705;  4.5634]
Paolucci2016               MfT  PlaSh 0.8303 [0.3523;  1.9565]
Paolucci2015              MiET   WlNi 1.0008 [0.6534;  1.5329]
Parra-Delgado2013          CBT   WlNi 1.1774 [0.8906;  1.5566]
Pereira-Pernambuco2018     McT   WlNi 0.9869 [0.6857;  1.4203]
Perez-Aranda2019           CBT   WlNi 1.1774 [0.8906;  1.5566]
Picard2013                 CBT   WlNi 1.1774 [0.8906;  1.5566]
Redondo2004                CBT   MiET 1.1764 [0.7425;  1.8641]
Richards2002              AeET    McT 1.5857 [0.7954;  3.1612]
Rivera2018                 Cry   WlNi 2.3731 [0.0929; 60.6503]
Salaffi2015                McT   WlNi 0.9869 [0.6857;  1.4203]
Schmidt2011                CBT   WlNi 1.1774 [0.8906;  1.5566]
Silva2019                  CBT   ReET 1.0501 [0.5158;  2.1378]
Simister2018               CBT   WlNi 1.1774 [0.8906;  1.5566]
Soares2002                 CBT   WlNi 1.1774 [0.8906;  1.5566]
Sutbeyaz2009               MfT  PlaSh 0.8303 [0.3523;  1.9565]
Tomas-Carus2007b&c        AqET   WlNi 1.4451 [0.5955;  3.5068]
Vas2016                    Acu  PlaSh 0.9142 [0.4044;  2.0664]
Verkaik2013                CBT   WlNi 1.1774 [0.8906;  1.5566]
Wang2018                   McT   MiET 0.9861 [0.6481;  1.5004]
Wicksell2013               CBT   WlNi 1.1774 [0.8906;  1.5566]
Wong2018                   McT   WlNi 0.9869 [0.6857;  1.4203]
Arakaki2021               FlET   ReET 1.0925 [0.4980;  2.3966]
Atan2020                  MiET   WlNi 1.0008 [0.6534;  1.5329]
Barranengoa-Cuadra 2021    CBT   WlNi 1.1774 [0.8906;  1.5566]
Cao2020                    Acu   MasT 1.1984 [0.4291;  3.3471]
Ceballos-Laita2020         McT   MiET 0.9861 [0.6481;  1.5004]
Coste2021                  MnT  PlaSh 0.5869 [0.2354;  1.4632]
Jamison2021               Elec  PlaSh 1.2559 [0.7828;  2.0149]
Nadal-Nicolas2020         MasT  PlaSh 0.7628 [0.3395;  1.7142]
Rodriguez-Mansilla2021     McT   MiET 0.9861 [0.6481;  1.5004]
Rodriguez-Mansilla2021    MiET   WlNi 1.0008 [0.6534;  1.5329]
Rodriguez-Mansilla2021     McT   WlNi 0.9869 [0.6857;  1.4203]
Sarmento2020               McT  PlaSh 0.9953 [0.3890;  2.5470]
Tanwar2020               PlaSh   rTMS 1.3352 [0.6113;  2.9162]
Udina-Cortés2020          Elec  PlaSh 1.2559 [0.7828;  2.0149]
Lacroix2022              PlaSh   rTMS 1.3352 [0.6113;  2.9162]
Paolucci2022               CBT   MiET 1.1764 [0.7425;  1.8641]
Park2021                  FlET   ReET 1.0925 [0.4980;  2.3966]
Samartin-Veiga2022       PlaSh   tDCS 1.1462 [0.5193;  2.5302]

Number of studies: k = 92
Number of pairwise comparisons: m = 100
Number of observations: o = 6562
Number of treatments: n = 22
Number of designs: d = 40

Random effects model

Treatment estimate (sm = 'OR', comparison: other treatments vs 'WlNi'):
          OR            95%-CI     z p-value
Acu   0.9064 [0.3001;  2.7381] -0.17  0.8617
AeET  1.5649 [0.7452;  3.2863]  1.18  0.2368
AqET  1.4451 [0.5955;  3.5068]  0.81  0.4157
Bal   1.0603 [0.3278;  3.4296]  0.10  0.9221
CBT   1.1774 [0.8906;  1.5566]  1.15  0.2517
Cry   2.3731 [0.0929; 60.6503]  0.52  0.6012
DryN  1.0000 [0.3828;  2.6122]  0.00  1.0000
Elec  1.2453 [0.4358;  3.5585]  0.41  0.6822
FlET  1.2249 [0.5146;  2.9155]  0.46  0.6467
HtT   0.2014 [0.0204;  1.9872] -1.37  0.1701
MasT  0.7564 [0.2386;  2.3975] -0.47  0.6352
McT   0.9869 [0.6857;  1.4203] -0.07  0.9433
MfT   0.8232 [0.2311;  2.9323] -0.30  0.7641
MiET  1.0008 [0.6534;  1.5329]  0.00  0.9971
MnT   0.5819 [0.1658;  2.0422] -0.85  0.3980
PlaSh 0.9915 [0.3883;  2.5320] -0.02  0.9858
Plt   2.7557 [0.6206; 12.2373]  1.33  0.1826
ReET  1.1212 [0.5497;  2.2869]  0.31  0.7531
rTMS  0.7426 [0.2192;  2.5163] -0.48  0.6327
tDCS  0.8650 [0.2536;  2.9511] -0.23  0.8169
WBV   1.1111 [0.2705;  4.5634]  0.15  0.8838
WlNi       .                 .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0% [0.0%; 27.5%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f. p-value
Total           64.44   75  0.8027
Within designs  48.63   52  0.6073
Between designs 15.81   23  0.8632

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q



Code 
# Forest plot
forest(nma_sr_ash)

Forest plot of treatment effects for Subnet 1 (A | Sh)



Code 
# Pairwise comparison table with confidence intervals
netleague(nma_sr_ash, ci = TRUE)
League table (random effects model):
                                                                              
                       Acu                         .                         .
 0.5792 [0.1611;   2.0830]                      AeET 1.7341 [0.3785;   7.9442]
 0.6272 [0.1660;   2.3701] 1.0829 [0.4187;   2.8008]                      AqET
 0.8549 [0.1763;   4.1451] 1.4759 [0.3956;   5.5061] 1.3629 [0.3654;   5.0835]
 0.7699 [0.2592;   2.2868] 1.3291 [0.6267;   2.8188] 1.2274 [0.5023;   2.9991]
 0.3819 [0.0124;  11.7261] 0.6594 [0.0237;  18.3266] 0.6089 [0.0212;  17.5302]
 0.9064 [0.2096;   3.9198] 1.5649 [0.4650;   5.2659] 1.4451 [0.3911;   5.3389]
 0.7279 [0.2836;   1.8683] 1.2566 [0.3679;   4.2922] 1.1604 [0.3227;   4.1725]
 0.7400 [0.1955;   2.8017] 1.2776 [0.4872;   3.3499] 1.1798 [0.6684;   2.0824]
 4.5008 [0.3617;  56.0073] 7.7705 [0.8074;  74.7823] 7.1755 [0.6532;  78.8241]
 1.1984 [0.4291;   3.3471] 2.0690 [0.5593;   7.6530] 1.9106 [0.5109;   7.1441]
 0.9185 [0.3019;   2.7938] 1.5857 [0.7954;   3.1612] 1.4643 [0.6039;   3.5502]
 1.1011 [0.3373;   3.5946] 1.9009 [0.4589;   7.8749] 1.7554 [0.4052;   7.6037]
 0.9057 [0.2859;   2.8695] 1.5636 [0.7378;   3.3138] 1.4439 [0.5727;   3.6406]
 1.5576 [0.4625;   5.2459] 2.6891 [0.6552;  11.0373] 2.4833 [0.5768;  10.6907]
 0.9142 [0.4044;   2.0664] 1.5783 [0.5079;   4.9042] 1.4574 [0.4437;   4.7869]
 0.3289 [0.0680;   1.5915] 0.5679 [0.1172;   2.7511] 0.5244 [0.1223;   2.2479]
 0.8084 [0.2291;   2.8532] 1.3957 [0.5806;   3.3549] 1.2889 [0.5406;   3.0725]
 1.2206 [0.3945;   3.7759] 2.1072 [0.5318;   8.3498] 1.9459 [0.4690;   8.0734]
 1.0478 [0.3362;   3.2656] 1.8090 [0.4538;   7.2117] 1.6705 [0.4003;   6.9717]
 0.8158 [0.1361;   4.8915] 1.4084 [0.2872;   6.9074] 1.3006 [0.2462;   6.8705]
 0.9064 [0.3001;   2.7381] 1.5649 [0.7452;   3.2863] 1.4451 [0.5955;   3.5068]
                                                                               
                         . 0.3571 [0.0544;   2.3438]                          .
                         .                         .                          .
 0.3056 [0.0296;   3.1592]                         .                          .
                       Bal 3.2400 [0.1205;  87.1251]                          .
 0.9006 [0.2761;   2.9373]                       CBT                          .
 0.4468 [0.0142;  14.0314] 0.4961 [0.0192;  12.8328]                        Cry
 1.0603 [0.2327;   4.8313] 1.1774 [0.4332;   3.2003]  2.3731 [0.0808;  69.7118]
 0.8514 [0.1827;   3.9679] 0.9455 [0.3355;   2.6645]  1.9057 [0.0632;  57.4888]
 0.8656 [0.2274;   3.2956] 0.9612 [0.4012;   2.3030]  1.9375 [0.0676;  55.4961]
 5.2650 [0.4185;  66.2399] 5.8464 [0.5897;  57.9656] 11.7839 [0.2229; 623.0541]
 1.4019 [0.2824;   6.9585] 1.5567 [0.4967;   4.8781]  3.1376 [0.1006;  97.8653]
 1.0744 [0.3290;   3.5084] 1.1930 [0.8139;   1.7487]  2.4047 [0.0922;  62.7226]
 1.2880 [0.2360;   7.0298] 1.4302 [0.4061;   5.0366]  2.8827 [0.0887;  93.6650]
 1.0595 [0.3329;   3.3715] 1.1764 [0.7425;   1.8641]  2.3712 [0.0902;  62.3182]
 1.8221 [0.3367;   9.8604] 2.0233 [0.5813;   7.0425]  4.0781 [0.1262; 131.7906]
 1.0694 [0.2472;   4.6262] 1.1874 [0.4723;   2.9856]  2.3934 [0.0820;  69.8617]
 0.3848 [0.0620;   2.3891] 0.4272 [0.0965;   1.8910]  0.8612 [0.0243;  30.5045]
 0.9457 [0.2565;   3.4869] 1.0501 [0.5158;   2.1378]  2.1166 [0.0766;  58.4504]
 1.4278 [0.2715;   7.5091] 1.5854 [0.4735;   5.3085]  3.1956 [0.1001; 101.9865]
 1.2257 [0.2319;   6.4789] 1.3611 [0.4037;   4.5888]  2.7434 [0.0858;  87.7657]
 0.9543 [0.1524;   5.9742] 1.0597 [0.2515;   4.4643]  2.1359 [0.0623;  73.2838]
 1.0603 [0.3278;   3.4296] 1.1774 [0.8906;   1.5566]  2.3731 [0.0929;  60.6503]
                                                                              
                         .                         .                         .
                         .                         .                         .
                         .                         . 1.3467 [0.7329;   2.4746]
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                      DryN                         .                         .
 0.8030 [0.1936;   3.3315]                      Elec                         .
 0.8164 [0.2239;   2.9773] 1.0167 [0.2820;   3.6658]                      FlET
 4.9655 [0.4148;  59.4414] 6.1836 [0.5097;  75.0217] 6.0821 [0.5533;  66.8546]
 1.3221 [0.2947;   5.9312] 1.6464 [0.6447;   4.2047] 1.6194 [0.4270;   6.1418]
 1.0133 [0.3629;   2.8295] 1.2618 [0.4408;   3.6125] 1.2412 [0.5204;   2.9600]
 1.2147 [0.2471;   5.9710] 1.5127 [0.5684;   4.0261] 1.4879 [0.3427;   6.4608]
 0.9992 [0.3495;   2.8570] 1.2443 [0.4151;   3.7296] 1.2239 [0.4917;   3.0467]
 1.7184 [0.3538;   8.3475] 2.1400 [0.7651;   5.9856] 2.1049 [0.4883;   9.0739]
 1.0085 [0.2636;   3.8593] 1.2559 [0.7828;   2.0149] 1.2353 [0.3750;   4.0697]
 0.3629 [0.0616;   2.1373] 0.4519 [0.0982;   2.0793] 0.4445 [0.0982;   2.0110]
 0.8919 [0.2698;   2.9489] 1.1107 [0.3309;   3.7278] 1.0925 [0.4980;   2.3966]
 1.3466 [0.2850;   6.3622] 1.6769 [0.6729;   4.1788] 1.6494 [0.3965;   6.8604]
 1.1560 [0.2434;   5.4913] 1.4396 [0.5725;   3.6203] 1.4160 [0.3385;   5.9241]
 0.9000 [0.1631;   4.9671] 1.1208 [0.1934;   6.4953] 1.1024 [0.2108;   5.7651]
 1.0000 [0.3828;   2.6122] 1.2453 [0.4358;   3.5585] 1.2249 [0.5146;   2.9155]
                                                                               
                          . 1.5556 [0.2408;  10.0492]                         .
 14.0000 [1.3295; 147.4289]                         . 0.9649 [0.3995;   2.3304]
                          .                         .                         .
                          .                         .                         .
                          .                         . 1.0378 [0.5585;   1.9285]
                          .                         .                         .
                          .                         .                         .
                          .                         .                         .
                          .                         .                         .
                        HtT                         .                         .
  0.2663 [0.0210;   3.3703]                      MasT                         .
  0.2041 [0.0209;   1.9951] 0.7664 [0.2412;   2.4351]                       McT
  0.2446 [0.0182;   3.2815] 0.9188 [0.2826;   2.9875] 1.1988 [0.3360;   4.2767]
  0.2012 [0.0207;   1.9520] 0.7558 [0.2285;   2.5000] 0.9861 [0.6481;   1.5004]
  0.3461 [0.0259;   4.6166] 1.2997 [0.3860;   4.3769] 1.6959 [0.4806;   5.9847]
  0.2031 [0.0175;   2.3554] 0.7628 [0.3395;   1.7142] 0.9953 [0.3890;   2.5470]
  0.0731 [0.0049;   1.0830] 0.2745 [0.0699;   1.0779] 0.3581 [0.0806;   1.5915]
  0.1796 [0.0170;   1.8947] 0.6746 [0.1862;   2.4440] 0.8802 [0.4337;   1.7862]
  0.2712 [0.0207;   3.5511] 1.0185 [0.3306;   3.1375] 1.3289 [0.3916;   4.5100]
  0.2328 [0.0177;   3.0585] 0.8744 [0.2817;   2.7135] 1.1409 [0.3339;   3.8983]
  0.1813 [0.0123;   2.6629] 0.6807 [0.1102;   4.2054] 0.8882 [0.2081;   3.7905]
  0.2014 [0.0204;   1.9872] 0.7564 [0.2386;   2.3975] 0.9869 [0.6857;   1.4203]
                                                                              
                         .                         .                         .
                         . 5.5000 [1.1453;  26.4124]                         .
                         .                         .                         .
                         . 0.7297 [0.1525;   3.4925]                         .
                         . 1.3461 [0.3729;   4.8594]                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         . 0.3929 [0.0361;   4.2764]                         .
                         .                         .                         .
                         . 0.7675 [0.4524;   1.3019]                         .
                       MfT                         .                         .
 0.8226 [0.2219;   3.0489]                      MiET                         .
 1.4147 [0.4042;   4.9511] 1.7198 [0.4696;   6.2983]                       MnT
 0.8303 [0.3523;   1.9565] 1.0094 [0.3748;   2.7184] 0.5869 [0.2354;   1.4632]
 0.2987 [0.0554;   1.6118] 0.3632 [0.0795;   1.6600] 0.2112 [0.0387;   1.1529]
 0.7342 [0.1799;   2.9961] 0.8926 [0.4125;   1.9314] 0.5190 [0.1284;   2.0981]
 1.1085 [0.3476;   3.5354] 1.3477 [0.3816;   4.7591] 0.7836 [0.2355;   2.6069]
 0.9517 [0.2963;   3.0569] 1.1570 [0.3255;   4.1127] 0.6727 [0.2008;   2.2535]
 0.7409 [0.1112;   4.9388] 0.9008 [0.2068;   3.9240] 0.5238 [0.0793;   3.4575]
 0.8232 [0.2311;   2.9323] 1.0008 [0.6534;   1.5329] 0.5819 [0.1658;   2.0422]
                                                                              
 1.0451 [0.3959;   2.7591]                         .                         .
                         .                         . 1.0000 [0.1218;   8.2099]
                         . 0.6316 [0.0943;   4.2302]                         .
                         .                         .                         .
 0.7200 [0.1481;   3.5009]                         . 0.8214 [0.2398;   2.8140]
                         .                         .                         .
                         .                         .                         .
 1.2559 [0.7828;   2.0149]                         .                         .
                         .                         . 1.4031 [0.5560;   3.5411]
                         .                         .                         .
 0.8492 [0.3380;   2.1336] 0.2387 [0.0459;   1.2405]                         .
 1.0000 [0.1940;   5.1543]                         . 1.0000 [0.2874;   3.4797]
 0.8303 [0.3523;   1.9565]                         .                         .
                         .                         .                         .
 0.5510 [0.2135;   1.4224]                         .                         .
                     PlaSh                         .                         .
 0.3598 [0.0843;   1.5359]                       Plt                         .
 0.8843 [0.2901;   2.6962] 2.4578 [0.5229;  11.5532]                      ReET
 1.3352 [0.6113;   2.9162] 3.7108 [0.7140;  19.2874] 1.5098 [0.3870;   5.8898]
 1.1462 [0.5193;   2.5302] 3.1857 [0.6098;  16.6420] 1.2961 [0.3302;   5.0873]
 0.8924 [0.1643;   4.8473] 2.4803 [0.3189;  19.2880] 1.0091 [0.2082;   4.8922]
 0.9915 [0.3883;   2.5320] 2.7557 [0.6206;  12.2373] 1.1212 [0.5497;   2.2869]
                                                                              
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
                         .                         . 0.3067 [0.0113;   8.3086]
                         .                         .                         .
                         .                         .                         .
                         .                         .                         .
 1.3352 [0.6113;   2.9162] 1.1462 [0.5193;   2.5302]                         .
                         .                         .                         .
                         .                         .                         .
                      rTMS                         .                         .
 0.8585 [0.2823;   2.6110]                      tDCS                         .
 0.6684 [0.1036;   4.3101] 0.7786 [0.1202;   5.0431]                       WBV
 0.7426 [0.2192;   2.5163] 0.8650 [0.2536;   2.9511] 1.1111 [0.2705;   4.5634]
                          
                         .
                         .
 3.0000 [0.1142;  78.8136]
 0.1086 [0.0050;   2.3645]
 1.2413 [0.9090;   1.6951]
 2.3731 [0.0929;  60.6503]
 1.0000 [0.3828;   2.6122]
                         .
 2.0000 [0.3138;  12.7450]
                         .
                         .
 0.8968 [0.5343;   1.5051]
                         .
 0.8168 [0.4627;   1.4421]
 1.2254 [0.0471;  31.8681]
                         .
                         .
 1.5894 [0.3012;   8.3878]
                         .
                         .
 0.9721 [0.2310;   4.0920]
                      WlNi

Lower triangle: results from network meta-analysis (column vs row)
Upper triangle: results from direct comparisons (row vs column)



Code 
# Treatment ranking
ranking_sr_ash <- netrank(nma_sr_ash, small.values = "good")
print(ranking_sr_ash)
      P-score
HtT    0.8996
MnT    0.7745
rTMS   0.6707
MasT   0.6675
MfT    0.6121
tDCS   0.5881
Acu    0.5665
McT    0.5474
WlNi   0.5389
MiET   0.5321
DryN   0.5183
PlaSh  0.5123
Bal    0.4880
WBV    0.4671
ReET   0.4539
FlET   0.4066
CBT    0.3930
Elec   0.3646
Cry    0.3123
AqET   0.3047
AeET   0.2530
Plt    0.1286



Code 
# Rankogram
ran_sr_ash <- rankogram(nma_sr_ash)
plot(ran_sr_ash)

Rankogram of treatments for Subnet 1 (A | Sh)



Code 
# Design decomposition
decomp_sr_ash <- decomp.design(nma_sr_ash)
print(decomp_sr_ash)
Q statistics to assess homogeneity / consistency

                    Q df p-value
Total           64.44 75  0.8027
Within designs  48.63 52  0.6073
Between designs 15.81 23  0.8632

Design-specific decomposition of within-designs Q statistic

     Design     Q df p-value
 MasT:PlaSh  2.76  1  0.0966
   WlNi:McT  9.60  7  0.2122
  WlNi:MiET  6.62  5  0.2505
 Elec:PlaSh  2.65  2  0.2657
   MasT:Plt  0.84  1  0.3585
  Acu:PlaSh  1.91  2  0.3842
    CBT:McT  1.78  2  0.4100
   McT:MiET  0.50  1  0.4773
  AeET:AqET  0.48  1  0.4890
  FlET:ReET  0.43  1  0.5102
   WlNi:CBT 16.29 18  0.5721
 PlaSh:rTMS  3.37  5  0.6427
  AqET:FlET  0.79  2  0.6738
 PlaSh:tDCS  0.17  1  0.6766
   CBT:MiET  0.13  1  0.7206
  MfT:PlaSh  0.28  2  0.8709

Between-designs Q statistic after detaching of single designs
(influential designs have p-value markedly different from 0.8632)

 Detached design     Q df p-value
        AeET:McT 12.67 22  0.9420
        WlNi:Bal 13.35 22  0.9228
        McT:MiET 13.46 22  0.9195
        AqET:Bal 13.51 22  0.9181
       AqET:FlET 14.39 22  0.8870
         Acu:CBT 14.85 22  0.8686
         Bal:CBT 15.15 22  0.8559
    WlNi:McT:WBV 14.37 21  0.8532
       AeET:AqET 15.21 22  0.8530
       CBT:PlaSh 15.23 22  0.8521
        WlNi:CBT 15.25 22  0.8512
        Bal:MiET 15.33 22  0.8476
   WlNi:McT:MiET 14.55 21  0.8449
         CBT:McT 15.50 22  0.8399
       WlNi:ReET 15.51 22  0.8396
       FlET:ReET 15.53 22  0.8383
        WlNi:McT 15.56 22  0.8369
       Acu:PlaSh 15.56 22  0.8369
       MnT:PlaSh 15.58 22  0.8363
        WlNi:MnT 15.58 22  0.8363
        CBT:ReET 15.58 22  0.8360
      MasT:PlaSh 15.58 22  0.8360
        WlNi:WBV 15.60 22  0.8352
       WlNi:AqET 15.61 22  0.8349
       AeET:ReET 15.70 22  0.8307
        Acu:MasT 15.71 22  0.8302
        MasT:Plt 15.72 22  0.8293
        AqET:Plt 15.72 22  0.8293
        McT:ReET 15.75 22  0.8279
        CBT:MiET 15.76 22  0.8274
       WlNi:MiET 15.77 22  0.8270
       McT:PlaSh 15.81 22  0.8251
  WlNi:FlET:ReET 15.40 21  0.8024

Q statistic to assess consistency under the assumption of
a full design-by-treatment interaction random effects model

                    Q df p-value tau.within tau2.within
Between designs 15.81 23  0.8632          0           0



Code 
# Node-splitting analysis to detect inconsistency
split_sr_ash <- netsplit(nma_sr_ash) # , show = "all")
print(split_sr_ash)
Separate indirect from direct evidence (SIDE) using back-calculation method

Random effects model: 

 comparison  k prop    nma  direct  indir.       RoR     z p-value
    Acu:CBT  1 0.33 0.7699  0.3571  1.1333    0.3151 -0.98  0.3265
   Acu:MasT  1 0.30 1.1984  1.5556  1.0699    1.4540  0.33  0.7427
  Acu:PlaSh  3 0.71 0.9142  1.0451  0.6631    1.5762  0.50  0.6183
  AeET:AqET  2 0.39 1.0829  1.7341  0.8016    2.1633  0.78  0.4376
   AeET:HtT  1 0.92 7.7705 14.0000  0.0055 2558.3630  1.79  0.0736
   AeET:McT  1 0.61 1.5857  0.9649  3.4739    0.2778 -1.77  0.0762
  AeET:MiET  1 0.23 1.5636  5.5000  1.0759    5.1119  1.79  0.0736
  AeET:ReET  1 0.17 1.3957  1.0000  1.4969    0.6680 -0.34  0.7328
   AqET:Bal  1 0.32 1.3629  0.3056  2.7331    0.1118 -1.52  0.1288
  AqET:FlET  3 0.87 1.1798  1.3467  0.4784    2.8150  1.19  0.2332
   AqET:Plt  1 0.59 0.5244  0.6316  0.4031    1.5668  0.30  0.7658
  AqET:WlNi  1 0.07 1.4451  3.0000  1.3636    2.2000  0.46  0.6490
    Bal:CBT  1 0.13 0.9006  3.2400  0.7450    4.3489  0.82  0.4140
   Bal:MiET  1 0.55 1.0595  0.7297  1.6608    0.4394 -0.69  0.4882
   Bal:WlNi  1 0.15 1.0603  0.1086  1.5614    0.0695 -1.57  0.1169
    CBT:McT  3 0.38 1.1930  1.0378  1.2998    0.7984 -0.56  0.5753
   CBT:MiET  2 0.13 1.1764  1.3461  1.1533    1.1672  0.22  0.8256
  CBT:PlaSh  1 0.34 1.1874  0.7200  1.5363    0.4687 -0.76  0.4454
   CBT:ReET  1 0.33 1.0501  0.8214  1.1873    0.6918 -0.48  0.6321
   CBT:WlNi 19 0.80 1.1774  1.2413  0.9492    1.3077  0.75  0.4538
  FlET:ReET  3 0.72 1.0925  1.4031  0.5737    2.4457  1.00  0.3165
  FlET:WlNi  1 0.22 1.2249  2.0000  1.0673    1.8739  0.59  0.5570
   HtT:MiET  1 0.91 0.2012  0.3929  0.0003 1213.4924  1.79  0.0736
 MasT:PlaSh  2 0.77 0.7628  0.8492  0.5301    1.6020  0.48  0.6324
   MasT:Plt  2 0.69 0.2745  0.2387  0.3740    0.6382 -0.30  0.7658
   McT:MiET  3 0.63 0.9861  0.7675  1.5132    0.5072 -1.53  0.1261
  McT:PlaSh  1 0.33 0.9953  1.0000  0.9930    1.0070  0.01  0.9945
   McT:ReET  1 0.32 0.8802  1.0000  0.8284    1.2071  0.24  0.8075
    McT:WBV  1 0.19 0.8882  0.3067  1.1463    0.2675 -0.70  0.4818
   McT:WlNi 10 0.49 0.9869  0.8968  1.0837    0.8275 -0.51  0.6103
  MiET:WlNi  7 0.56 1.0008  0.8168  1.2996    0.6285 -1.06  0.2895
  MnT:PlaSh  1 0.93 0.5869  0.5510  1.3211    0.4171 -0.49  0.6274
   MnT:WlNi  1 0.15 0.5819  1.2254  0.5111    2.3976  0.49  0.6274
  ReET:WlNi  2 0.18 1.1212  1.5894  1.0366    1.5334  0.46  0.6490
   WBV:WlNi  2 0.97 1.1111  0.9721 50.3217    0.0193 -0.99  0.3221

Legend:
 comparison - Treatment comparison
 k          - Number of studies providing direct evidence
 prop       - Direct evidence proportion
 nma        - Estimated treatment effect (OR) in network meta-analysis
 direct     - Estimated treatment effect (OR) derived from direct evidence
 indir.     - Estimated treatment effect (OR) derived from indirect evidence
 RoR        - Ratio of Ratios (direct versus indirect)
 z          - z-value of test for disagreement (direct versus indirect)
 p-value    - p-value of test for disagreement (direct versus indirect)



Code 
# Forest plot of node-splitting
forest(split_sr_ash)

Forest plot of node-splitting for Subnet 1 (A | Sh)



Code 
# Heatmap
netheat(nma_sr_ash)

Heatmap of contribution matrix for Subnet 1 (A | Sh)



Code 
# Funnel plot
funnel(nma_sr_ash,
    order = "WlNi",
)

Funnel plot for Network (A | Sh)