Network Meta-Analysis

Abstract

A network meta-analysis of fibromyalgia treatments

# 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.

P | Im

# 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.

Subnet 1

Select the procedures performed

Important

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

Data preparation

# 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

---

Treatment exploration

# 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"

# Total number of treatments
length(trat_sr1)

[1] 4

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr1)

Forest plot of treatment effects for Subnet 1

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 1

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr1)

Forest plot of node-splitting for Subnet 1

---

Network heatmap

# Heatmap
netheat(nma_sr1)

---

Funnel plot

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

Funnel plot for Subnet 1 (P | Im)

---

Subnet 2

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.

Data preparation

# 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()

---

Treatment exploration

# Unique treatments in subnet 2
unique_treat1_sr2 <- sr2$treat1 |> unique()
print(unique_treat1_sr2)

[1] "Acu"  "CBT"  "rTMS" "tDCS" "PbT"  "Elec" "MfT" 

unique_treat2_sr2 <- sr2$treat2 |> unique()
print(unique_treat2_sr2)

[1] "PlaSh" "tDCS" 

# 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"

# Total number of treatments
length(trat_sr2)

[1] 8

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_pim_sr2$studlab))

[1] 28

---

Network Meta-Analysis model

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr2)

Forest plot of treatment effects for Subnet 2

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 2

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr2)

Forest plot of node-splitting for Subnet 2

---

Network heatmap

# Heatmap
netheat(nma_sr2)

Heatmap of contribution matrix for Subnet 2

---

Funnel plot

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

Funnel plot for Subnet 2 (P | Im)

---

P | Sh

# 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 = 23
Number of designs: d = 52
Number of networks: 1

There are network:

Network:
- 106 studies
- 120 comparisons
- 23 treatments

Tip

The network is fully connected.

1.0.1 Network

Select the procedures performed

Important

The network contain 106 studies, 120 comparisons and 24 treatments.

Data preparation

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


# Display comparison table
sr

---

Treatment exploration

# Unique treatments in network
unique_treat_sr1 <- sr$treat1 |> unique()
print(unique_treat_sr1)

 [1] "Mnt"  "McT"  "WBV"  "MfT"  "AqET" "CBT"  "ReET" "Bal"  "Acu"  "AeET"
[11] "FlET" "MiET" "MasT" "PBT"  "rTMS" "tDCS" "DryN" "Elec" "HtT"  "Cry" 

unique_treat_sr2 <- sr$treat2 |> unique()
print(unique_treat_sr2)

 [1] "WlNi"  "WBV"   "PlaSh" "Bal"   "FlET"  "AqET"  "ReET"  "Mnt"   "CBT"  
[10] "McT"   "MasT"  "Elec"  "MiET"  "Plt"   "HtT"  

# Combination of all unique treatments
trat_sr <- unique(c(unique_treat_sr1, unique_treat_sr2))
print(trat_sr)

 [1] "Mnt"   "McT"   "WBV"   "MfT"   "AqET"  "CBT"   "ReET"  "Bal"   "Acu"  
[10] "AeET"  "FlET"  "MiET"  "MasT"  "PBT"   "rTMS"  "tDCS"  "DryN"  "Elec" 
[19] "HtT"   "Cry"   "WlNi"  "PlaSh" "Plt"  

# Total number of treatments
length(trat_sr)

[1] 23

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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 = 23
Number of designs: d = 52

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
           MD             95%-CI     z  p-value
Acu   -1.7935 [-2.9294; -0.6575] -3.09   0.0020
AeET  -1.2998 [-2.1502; -0.4494] -3.00   0.0027
AqET  -1.9221 [-2.8393; -1.0048] -4.11 < 0.0001
Bal   -2.9171 [-4.3997; -1.4346] -3.86   0.0001
CBT   -0.7386 [-1.2727; -0.2046] -2.71   0.0067
Cry   -1.9000 [-4.2887;  0.4887] -1.56   0.1190
DryN  -3.7102 [-5.1748; -2.2456] -4.97 < 0.0001
Elec  -2.0429 [-3.4009; -0.6849] -2.95   0.0032
FlET  -0.4309 [-1.4536;  0.5918] -0.83   0.4089
HtT   -1.2789 [-3.5901;  1.0323] -1.08   0.2781
MasT  -2.1060 [-3.1744; -1.0376] -3.86   0.0001
McT   -1.2493 [-1.9228; -0.5758] -3.64   0.0003
MfT   -2.3029 [-3.7612; -0.8446] -3.10   0.0020
MiET  -0.8438 [-1.5902; -0.0974] -2.22   0.0267
Mnt   -1.8719 [-3.0491; -0.6946] -3.12   0.0018
PBT   -3.5668 [-5.5915; -1.5422] -3.45   0.0006
PlaSh -0.6100 [-1.5885;  0.3684] -1.22   0.2217
Plt   -2.2228 [-3.6227; -0.8228] -3.11   0.0019
ReET  -1.2728 [-2.3172; -0.2285] -2.39   0.0169
rTMS  -1.8852 [-3.2900; -0.4805] -2.63   0.0085
tDCS  -2.0028 [-3.4352; -0.5704] -2.74   0.0061
WBV   -1.7234 [-3.2959; -0.1509] -2.15   0.0317
WlNi        .                  .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 1.1758; tau = 1.0843; I^2 = 83.7% [80.6%; 86.4%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           559.52   91 < 0.0001
Within designs  287.35   54 < 0.0001
Between designs 272.16   37 < 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

---

Network visualization

# 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)

---

Detailed results

# 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   1.2573     2         
Alentorn-Geli2008          McT    WBV  1.8100 0.7468   1.5847     3        *
Alentorn-Geli2008          McT   WlNi -1.2900 0.7892   1.6412     3        *
Alentorn-Geli2008          WBV   WlNi -3.1000 0.8292   1.7036     3        *
Alfano2001                 MfT  PlaSh -0.6200 0.5434   1.2128     2         
Alptug2023                 Mnt   WlNi -3.4000 0.6919   1.2863     2         
Altan2004                 AqET    Bal  0.1800 0.6504   1.2644     2         
Ang2010                    CBT   WlNi  0.1000 0.6426   1.2604     2         
Arakaki2021               FlET   ReET  2.1800 0.8189   1.3588     2         
Ardic2007                  Bal   WlNi -4.2500 0.6931   1.2869     2         
Assefi2005                 Acu  PlaSh  0.6100 0.5069   1.1969     2         
Assis2006                 AeET   AqET  0.5000 0.5320   1.2078     2         
Assumpçao2018             FlET   ReET  0.2000 1.0224   1.8254     3        *
Assumpçao2018             FlET   WlNi -1.8000 1.0018   1.7920     3        *
Assumpçao2018             ReET   WlNi -2.0000 1.0408   1.8574     3        *
Atan2020                  MiET   WlNi -3.6000 0.4812   1.1863     2         
Audoux2023                MasT    Mnt -1.8000 0.8445   1.3744     2         
Baelz2022                  Acu  PlaSh -0.7000 0.8905   1.4031     2         
Barranengoa-Cuadra2021     CBT   WlNi -2.6000 0.3939   1.1536     2         
Bircan2008                AeET   ReET -0.4600 0.6518   1.2651     2         
Boggiss2022                CBT    PBT  4.0000 1.1997   1.6171     2         
Bongi2010                  CBT   WlNi -2.8300 0.5312   1.2074     2         
Bongi2012                  CBT    McT  0.6500 0.3294   1.1333     2         
Bourgault2015              McT   WlNi -0.1300 0.5563   1.2187     2         
Boyer2014                PlaSh   rTMS -1.2000 0.8003   1.3477     2         
Bressan2008               AeET   FlET  0.4700 1.1193   1.5584     2         
Brietzke2019             PlaSh   tDCS  2.4800 0.3776   1.1482     2         
Calandre2009              AqET   WlNi  0.0000 0.5134   1.1997     2         
Cao2020                    Acu   MasT -0.2200 0.3452   1.1380     2         
Carretero2009            PlaSh   rTMS -1.2000 0.8010   1.3481     2         
Carson2010                 McT   WlNi -1.0200 0.5934   1.2361     2         
Casanueva2014             DryN   WlNi -1.5000 0.3493   1.1392     2         
Castro-Sanchez2019        DryN   MasT -2.9300 0.4500   1.1740     2         
Castro-Sanchez2020        DryN   Elec -2.6800 0.4366   1.1689     2         
Caumo2023                PlaSh   tDCS  1.6600 0.1140   1.0903     2         
Ceballos-Laita2020         McT   MiET -2.1600 0.8359   1.3691     2         
Colbert1999                MfT  PlaSh -1.8100 0.8309   1.3661     2         
Collado-Mateo2017         MiET   WlNi -1.3300 0.4507   1.1742     2         
Coste2021                  Mnt  PlaSh -0.2900 0.6548   1.2667     2         
Da Costa2005              MiET   WlNi -0.9400 0.6066   1.2425     2         
Dailey2019                Elec  PlaSh -1.3000 0.3488   1.1390     2         
daSilva2008               AqET   Elec  3.2000 1.1908   1.6105     2         
deMedeiros2020            AqET    Plt -0.6000 0.6063   1.2423     2         
Ekici2008                 MasT    Plt  0.4200 0.4772   1.1847     2         
Ekici2017                 MasT    Plt  0.3800 0.5255   1.2050     2         
Espi-Lopes2016            MiET   WlNi -0.2800 0.9255   1.4256     2         
Evcik2002                  Bal   WlNi -3.4000 1.7701   2.0758     2         
Fernandes2016             AeET   AqET  0.5000 0.6362   1.2572     2         
Fitzgibbon2018           PlaSh   rTMS  0.4800 0.8369   1.3697     2         
Franco2023                AeET    Plt  1.2000 0.5585   1.2197     2         
Friedberg2019              CBT   WlNi -0.5500 0.3803   1.1491     2         
Giannotti2014              McT   WlNi -0.2500 0.8210   1.3601     2         
Goldway2019                CBT  PlaSh  0.8200 0.7901   1.3417     2         
Gomez-Hernandez2019       AeET   MiET  1.0100 0.1025   1.0892     2         
Gowans1999                 McT   WlNi -0.3000 0.6841   1.2821     2         
Gunther1994                Bal    CBT -1.1200 1.1934   1.6125     2         
Hargrove2012             PlaSh   tDCS  1.4000 0.6895   1.2850     2         
Harris2005                 Acu  PlaSh -0.3100 0.6954   1.2881     2         
Harte2013                  Acu  PlaSh  0.5800 0.5773   1.2284     2         
Hsu2010                    CBT   WlNi -0.5800 0.6751   1.2773     2         
Izquierdo-Alventosa2020   MiET   WlNi -0.1200 0.7797   1.3356     2         
Jamison2021               Elec  PlaSh -0.6200 0.2762   1.1190     2         
Jensen2012                 CBT   WlNi -1.0900 0.8702   1.3903     2         
Jones2002                  McT   ReET  0.5300 0.5654   1.2229     2         
Jones2012                  CBT    McT  1.1000 0.5460   1.2140     2         
Karatay2018                Acu  PlaSh -2.5200 0.5807   1.2300     2         
Kayo2012                  AeET   ReET -0.9700 0.7347   1.6187     3        *
Kayo2012                  AeET   WlNi -1.6000 0.7111   1.5858     3        *
Kayo2012                  ReET   WlNi -0.6300 0.6963   1.5666     3        *
Lami2018                   CBT   WlNi -0.0800 0.3222   1.1312     2         
Lauche2016                MasT  PlaSh -0.9200 0.4103   1.1594     2         
Lee2024                    CBT    McT -0.5000 0.3579   1.1419     2         
Lopes-Rodrigues2012       AqET   FlET -2.5300 0.5685   1.2243     2         
Lopes-Rodrigues2013       AqET   FlET -2.1600 0.4565   1.1765     2         
Luciano2014                CBT   WlNi -1.7700 0.2840   1.1209     2         
Lynch2012                  McT   WlNi -1.5700 0.3863   1.1511     2         
Maestu2013               PlaSh   rTMS  2.0000 0.6998   1.2905     2         
McCrae2019                 CBT   WlNi -0.4900 0.6214   1.2498     2         
Menzies2014                CBT   WlNi -0.5000 0.5384   1.2106     2         
Mhalla2011               PlaSh   rTMS  2.1200 0.3835   1.1501     2         
Mingorance2021.2           WBV   WlNi -0.5100 0.1736   1.0981     2         
Mist2018                   Acu    CBT -1.6000 0.1918   1.1012     2         
Nadal-Nicolas2020         MasT  PlaSh -2.9000 0.9876   1.4667     2         
Norrengaard1997           AeET    HtT  1.0000 1.1510   2.0702     3        *
Norrengaard1997           AeET   MiET  1.0000 1.1426   2.0438     3        *
Norrengaard1997            HtT   MiET  0.0000 0.5714   1.3515     3        *
Oka2019                    MfT  PlaSh -0.5500 0.6779   1.2788     2         
Paolucci2016               MfT  PlaSh -2.5000 0.4369   1.1691     2         
Paolucci2022               CBT   MiET -1.5000 0.9648   1.4514     2         
Park2021                  FlET   ReET -0.0400 0.6996   1.2904     2         
Parra-Delgado2013          CBT   WlNi -0.0600 0.1291   1.0920     2         
Redondo2004                CBT   MiET  0.4000 0.8083   1.3525     2         
Rivera2018                 Cry   WlNi -1.9000 0.5565   1.2188     2         
Rodriguez-Mansilla2021     McT   MiET -0.6300 0.5229   1.4745     3        *
Rodriguez-Mansilla2021    MiET   WlNi -0.5200 0.4364   1.3959     3        *
Rodriguez-Mansilla2021     McT   WlNi -1.1500 0.5830   1.5481     3        *
Ruaro2014                  PBT  PlaSh -2.3000 0.5385   1.2107     2         
Samartin-Veiga2022       PlaSh   tDCS  0.3100 0.7259   1.3049     2         
Sarmento2020               McT  PlaSh -3.7000 0.8544   1.3805     2         
Schachter2003             AeET   WlNi -1.2600 0.5078   1.1973     2         
Schulze2023               FlET   MasT  2.4500 0.2841   1.3739     3        *
Schulze2023               MasT   WlNi -2.6800 0.2735   1.3675     3        *
Schulze2023               FlET   WlNi -0.2300 0.2841   1.3739     3        *
Sencan2004                AeET  PlaSh -2.1500 0.4530   1.1751     2         
Sevimli2015               AeET   AqET  0.0200 0.2773   1.3584     3        *
Sevimli2015               AeET   MiET -2.4200 0.3318   1.3938     3        *
Sevimli2015               AqET   MiET -2.4400 0.3388   1.3991     3        *
Silva2019                  CBT   ReET  1.0400 0.5562   1.2187     2         
Sutbeyaz2009               MfT  PlaSh -2.7600 0.4486   1.1735     2         
Tanwar2020               PlaSh   rTMS  3.9000 0.2989   1.1248     2         
To2017                   PlaSh   tDCS  0.8100 0.4671   1.1807     2         
Tomas-Carus2007b&c        AqET   WlNi -2.0000 0.7472   1.3168     2         
Torres2015                 CBT    Mnt  1.6700 0.5133   1.1997     2         
Udina-Cortés2020          Elec  PlaSh -1.9000 0.5940   1.2364     2         
Ugurlu2017                 Acu  PlaSh -2.8900 0.4682   1.1811     2         
Valim2003                 AeET   FlET  0.3000 0.6728   1.2761     2         
Vas2016                    Acu  PlaSh -1.4800 0.3803   1.1491     2         
Verkaik2013                CBT   WlNi  0.0400 0.5154   1.2006     2         
Wicksell2013               CBT   WlNi -0.4000 0.3706   1.1459     2         
Wong2018                   McT   WlNi -1.7000 0.5833   1.2313     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 -1.8719 [-3.0491; -0.6946]
Alentorn-Geli2008          McT    WBV  0.4742 [-1.1680;  2.1163]
Alentorn-Geli2008          McT   WlNi -1.2493 [-1.9228; -0.5758]
Alentorn-Geli2008          WBV   WlNi -1.7234 [-3.2959; -0.1509]
Alfano2001                 MfT  PlaSh -1.6929 [-2.7743; -0.6115]
Alptug2023                 Mnt   WlNi -1.8719 [-3.0491; -0.6946]
Altan2004                 AqET    Bal  0.9950 [-0.5688;  2.5589]
Ang2010                    CBT   WlNi -0.7386 [-1.2727; -0.2046]
Arakaki2021               FlET   ReET  0.8419 [-0.2870;  1.9709]
Ardic2007                  Bal   WlNi -2.9171 [-4.3997; -1.4346]
Assefi2005                 Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Assis2006                 AeET   AqET  0.6223 [-0.3101;  1.5546]
Assumpçao2018             FlET   ReET  0.8419 [-0.2870;  1.9709]
Assumpçao2018             FlET   WlNi -0.4309 [-1.4536;  0.5918]
Assumpçao2018             ReET   WlNi -1.2728 [-2.3172; -0.2285]
Atan2020                  MiET   WlNi -0.8438 [-1.5902; -0.0974]
Audoux2023                MasT    Mnt -0.2342 [-1.6107;  1.1424]
Baelz2022                  Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Barranengoa-Cuadra2021     CBT   WlNi -0.7386 [-1.2727; -0.2046]
Bircan2008                AeET   ReET -0.0270 [-1.1374;  1.0834]
Boggiss2022                CBT    PBT  2.8282 [ 0.8258;  4.8306]
Bongi2010                  CBT   WlNi -0.7386 [-1.2727; -0.2046]
Bongi2012                  CBT    McT  0.5106 [-0.2391;  1.2603]
Bourgault2015              McT   WlNi -1.2493 [-1.9228; -0.5758]
Boyer2014                PlaSh   rTMS  1.2752 [ 0.2672;  2.2832]
Bressan2008               AeET   FlET -0.8689 [-1.9152;  0.1774]
Brietzke2019             PlaSh   tDCS  1.3927 [ 0.3466;  2.4389]
Calandre2009              AqET   WlNi -1.9221 [-2.8393; -1.0048]
Cao2020                    Acu   MasT  0.3125 [-0.8661;  1.4912]
Carretero2009            PlaSh   rTMS  1.2752 [ 0.2672;  2.2832]
Carson2010                 McT   WlNi -1.2493 [-1.9228; -0.5758]
Casanueva2014             DryN   WlNi -3.7102 [-5.1748; -2.2456]
Castro-Sanchez2019        DryN   MasT -1.6042 [-3.0988; -0.1096]
Castro-Sanchez2020        DryN   Elec -1.6673 [-3.2392; -0.0954]
Caumo2023                PlaSh   tDCS  1.3927 [ 0.3466;  2.4389]
Ceballos-Laita2020         McT   MiET -0.4055 [-1.3201;  0.5092]
Colbert1999                MfT  PlaSh -1.6929 [-2.7743; -0.6115]
Collado-Mateo2017         MiET   WlNi -0.8438 [-1.5902; -0.0974]
Coste2021                  Mnt  PlaSh -1.2618 [-2.5760;  0.0523]
Da Costa2005              MiET   WlNi -0.8438 [-1.5902; -0.0974]
Dailey2019                Elec  PlaSh -1.4329 [-2.5750; -0.2907]
daSilva2008               AqET   Elec  0.1208 [-1.3509;  1.5925]
deMedeiros2020            AqET    Plt  0.3007 [-1.1116;  1.7130]
Ekici2008                 MasT    Plt  0.1168 [-1.1896;  1.4231]
Ekici2017                 MasT    Plt  0.1168 [-1.1896;  1.4231]
Espi-Lopes2016            MiET   WlNi -0.8438 [-1.5902; -0.0974]
Evcik2002                  Bal   WlNi -2.9171 [-4.3997; -1.4346]
Fernandes2016             AeET   AqET  0.6223 [-0.3101;  1.5546]
Fitzgibbon2018           PlaSh   rTMS  1.2752 [ 0.2672;  2.2832]
Franco2023                AeET    Plt  0.9230 [-0.4658;  2.3118]
Friedberg2019              CBT   WlNi -0.7386 [-1.2727; -0.2046]
Giannotti2014              McT   WlNi -1.2493 [-1.9228; -0.5758]
Goldway2019                CBT  PlaSh -0.1286 [-1.1172;  0.8600]
Gomez-Hernandez2019       AeET   MiET -0.4560 [-1.3945;  0.4825]
Gowans1999                 McT   WlNi -1.2493 [-1.9228; -0.5758]
Gunther1994                Bal    CBT -2.1785 [-3.7036; -0.6534]
Hargrove2012             PlaSh   tDCS  1.3927 [ 0.3466;  2.4389]
Harris2005                 Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Harte2013                  Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Hsu2010                    CBT   WlNi -0.7386 [-1.2727; -0.2046]
Izquierdo-Alventosa2020   MiET   WlNi -0.8438 [-1.5902; -0.0974]
Jamison2021               Elec  PlaSh -1.4329 [-2.5750; -0.2907]
Jensen2012                 CBT   WlNi -0.7386 [-1.2727; -0.2046]
Jones2002                  McT   ReET  0.0236 [-1.1201;  1.1673]
Jones2012                  CBT    McT  0.5106 [-0.2391;  1.2603]
Karatay2018                Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Kayo2012                  AeET   ReET -0.0270 [-1.1374;  1.0834]
Kayo2012                  AeET   WlNi -1.2998 [-2.1502; -0.4494]
Kayo2012                  ReET   WlNi -1.2728 [-2.3172; -0.2285]
Lami2018                   CBT   WlNi -0.7386 [-1.2727; -0.2046]
Lauche2016                MasT  PlaSh -1.4960 [-2.5494; -0.4425]
Lee2024                    CBT    McT  0.5106 [-0.2391;  1.2603]
Lopes-Rodrigues2012       AqET   FlET -1.4912 [-2.5585; -0.4239]
Lopes-Rodrigues2013       AqET   FlET -1.4912 [-2.5585; -0.4239]
Luciano2014                CBT   WlNi -0.7386 [-1.2727; -0.2046]
Lynch2012                  McT   WlNi -1.2493 [-1.9228; -0.5758]
Maestu2013               PlaSh   rTMS  1.2752 [ 0.2672;  2.2832]
McCrae2019                 CBT   WlNi -0.7386 [-1.2727; -0.2046]
Menzies2014                CBT   WlNi -0.7386 [-1.2727; -0.2046]
Mhalla2011               PlaSh   rTMS  1.2752 [ 0.2672;  2.2832]
Mingorance2021.2           WBV   WlNi -1.7234 [-3.2959; -0.1509]
Mist2018                   Acu    CBT -1.0548 [-2.1863;  0.0767]
Nadal-Nicolas2020         MasT  PlaSh -1.4960 [-2.5494; -0.4425]
Norrengaard1997           AeET    HtT -0.0209 [-2.3345;  2.2927]
Norrengaard1997           AeET   MiET -0.4560 [-1.3945;  0.4825]
Norrengaard1997            HtT   MiET -0.4351 [-2.6708;  1.8006]
Oka2019                    MfT  PlaSh -1.6929 [-2.7743; -0.6115]
Paolucci2016               MfT  PlaSh -1.6929 [-2.7743; -0.6115]
Paolucci2022               CBT   MiET  0.1051 [-0.7381;  0.9483]
Park2021                  FlET   ReET  0.8419 [-0.2870;  1.9709]
Parra-Delgado2013          CBT   WlNi -0.7386 [-1.2727; -0.2046]
Redondo2004                CBT   MiET  0.1051 [-0.7381;  0.9483]
Rivera2018                 Cry   WlNi -1.9000 [-4.2887;  0.4887]
Rodriguez-Mansilla2021     McT   MiET -0.4055 [-1.3201;  0.5092]
Rodriguez-Mansilla2021    MiET   WlNi -0.8438 [-1.5902; -0.0974]
Rodriguez-Mansilla2021     McT   WlNi -1.2493 [-1.9228; -0.5758]
Ruaro2014                  PBT  PlaSh -2.9568 [-4.8892; -1.0244]
Samartin-Veiga2022       PlaSh   tDCS  1.3927 [ 0.3466;  2.4389]
Sarmento2020               McT  PlaSh -0.6392 [-1.7353;  0.4569]
Schachter2003             AeET   WlNi -1.2998 [-2.1502; -0.4494]
Schulze2023               FlET   MasT  1.6751 [ 0.3870;  2.9632]
Schulze2023               MasT   WlNi -2.1060 [-3.1744; -1.0376]
Schulze2023               FlET   WlNi -0.4309 [-1.4536;  0.5918]
Sencan2004                AeET  PlaSh -0.6898 [-1.8046;  0.4251]
Sevimli2015               AeET   AqET  0.6223 [-0.3101;  1.5546]
Sevimli2015               AeET   MiET -0.4560 [-1.3945;  0.4825]
Sevimli2015               AqET   MiET -1.0783 [-2.1307; -0.0259]
Silva2019                  CBT   ReET  0.5342 [-0.5593;  1.6276]
Sutbeyaz2009               MfT  PlaSh -1.6929 [-2.7743; -0.6115]
Tanwar2020               PlaSh   rTMS  1.2752 [ 0.2672;  2.2832]
To2017                   PlaSh   tDCS  1.3927 [ 0.3466;  2.4389]
Tomas-Carus2007b&c        AqET   WlNi -1.9221 [-2.8393; -1.0048]
Torres2015                 CBT    Mnt  1.1332 [-0.0743;  2.3407]
Udina-Cortés2020          Elec  PlaSh -1.4329 [-2.5750; -0.2907]
Ugurlu2017                 Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Valim2003                 AeET   FlET -0.8689 [-1.9152;  0.1774]
Vas2016                    Acu  PlaSh -1.1834 [-2.0005; -0.3663]
Verkaik2013                CBT   WlNi -0.7386 [-1.2727; -0.2046]
Wicksell2013               CBT   WlNi -0.7386 [-1.2727; -0.2046]
Wong2018                   McT   WlNi -1.2493 [-1.9228; -0.5758]

Number of studies: k = 106
Number of pairwise comparisons: m = 120
Number of observations: o = 6143
Number of treatments: n = 23
Number of designs: d = 52

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
           MD             95%-CI     z  p-value
Acu   -1.7935 [-2.9294; -0.6575] -3.09   0.0020
AeET  -1.2998 [-2.1502; -0.4494] -3.00   0.0027
AqET  -1.9221 [-2.8393; -1.0048] -4.11 < 0.0001
Bal   -2.9171 [-4.3997; -1.4346] -3.86   0.0001
CBT   -0.7386 [-1.2727; -0.2046] -2.71   0.0067
Cry   -1.9000 [-4.2887;  0.4887] -1.56   0.1190
DryN  -3.7102 [-5.1748; -2.2456] -4.97 < 0.0001
Elec  -2.0429 [-3.4009; -0.6849] -2.95   0.0032
FlET  -0.4309 [-1.4536;  0.5918] -0.83   0.4089
HtT   -1.2789 [-3.5901;  1.0323] -1.08   0.2781
MasT  -2.1060 [-3.1744; -1.0376] -3.86   0.0001
McT   -1.2493 [-1.9228; -0.5758] -3.64   0.0003
MfT   -2.3029 [-3.7612; -0.8446] -3.10   0.0020
MiET  -0.8438 [-1.5902; -0.0974] -2.22   0.0267
Mnt   -1.8719 [-3.0491; -0.6946] -3.12   0.0018
PBT   -3.5668 [-5.5915; -1.5422] -3.45   0.0006
PlaSh -0.6100 [-1.5885;  0.3684] -1.22   0.2217
Plt   -2.2228 [-3.6227; -0.8228] -3.11   0.0019
ReET  -1.2728 [-2.3172; -0.2285] -2.39   0.0169
rTMS  -1.8852 [-3.2900; -0.4805] -2.63   0.0085
tDCS  -2.0028 [-3.4352; -0.5704] -2.74   0.0061
WBV   -1.7234 [-3.2959; -0.1509] -2.15   0.0317
WlNi        .                  .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 1.1758; tau = 1.0843; I^2 = 83.7% [80.6%; 86.4%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           559.52   91 < 0.0001
Within designs  287.35   54 < 0.0001
Between designs 272.16   37 < 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

---

Forest plot

# Forest plot
forest(nma_sr)

Forest plot of treatment effects for Network

---

League table

# Pairwise comparison table with confidence intervals
netleague(nma_sr, ci = TRUE)

League table (random effects model):
                                                      
                        Acu                          .
 -0.4936 [-1.7647;  0.7774]                       AeET
  0.1286 [-1.2036;  1.4609]  0.6223 [-0.3101;  1.5546]
  1.1237 [-0.6946;  2.9419]  1.6173 [-0.0133;  3.2479]
 -1.0548 [-2.1863;  0.0767] -0.5612 [-1.4993;  0.3770]
  0.1065 [-2.5386;  2.7516]  0.6002 [-1.9354;  3.1358]
  1.9167 [ 0.2789;  3.5546]  2.4104 [ 0.8045;  4.0163]
  0.2494 [-1.1206;  1.6194]  0.7431 [-0.7172;  2.2034]
 -1.3626 [-2.7702;  0.0451] -0.8689 [-1.9152;  0.1774]
 -0.5146 [-3.0427;  2.0136] -0.0209 [-2.3345;  2.2927]
  0.3125 [-0.8661;  1.4912]  0.8062 [-0.3834;  1.9958]
 -0.5442 [-1.7883;  0.6999] -0.0506 [-1.0695;  0.9684]
  0.5095 [-0.8459;  1.8648]  1.0031 [-0.5500;  2.5563]
 -0.9497 [-2.2434;  0.3440] -0.4560 [-1.3945;  0.4825]
  0.0784 [-1.3748;  1.5316]  0.5720 [-0.8117;  1.9558]
  1.7734 [-0.2933;  3.8400]  2.2670 [ 0.1467;  4.3874]
 -1.1834 [-2.0005; -0.3663] -0.6898 [-1.8046;  0.4251]
  0.4293 [-1.1613;  2.0200]  0.9230 [-0.4658;  2.3118]
 -0.5206 [-1.9713;  0.9300] -0.0270 [-1.1374;  1.0834]
  0.0918 [-1.2058;  1.3894]  0.5854 [-0.9176;  2.0884]
  0.2093 [-1.1181;  1.5367]  0.7030 [-0.8259;  2.2318]
 -0.0700 [-1.9971;  1.8570]  0.4236 [-1.3543;  2.2015]
 -1.7935 [-2.9294; -0.6575] -1.2998 [-2.1502; -0.4494]
                                                      
                          .                          .
  0.3190 [-1.0283;  1.6662]                          .
                       AqET  0.1800 [-2.2983;  2.6583]
  0.9950 [-0.5688;  2.5589]                        Bal
 -1.1834 [-2.1901; -0.1768] -2.1785 [-3.7036; -0.6534]
 -0.0221 [-2.5809;  2.5367] -1.0171 [-3.8285;  1.7943]
  1.7881 [ 0.1549;  3.4213]  0.7931 [-1.2582;  2.8443]
  0.1208 [-1.3509;  1.5925] -0.8742 [-2.8289;  1.0804]
 -1.4912 [-2.5585; -0.4239] -2.4862 [-4.2081; -0.7644]
 -0.6432 [-3.0456;  1.7592] -1.6382 [-4.3536;  1.0771]
  0.1839 [-1.0522;  1.4200] -0.8111 [-2.5852;  0.9630]
 -0.6728 [-1.7615;  0.4159] -1.6679 [-3.2734; -0.0624]
  0.3808 [-1.2266;  1.9883] -0.6142 [-2.6487;  1.4203]
 -1.0783 [-2.1307; -0.0259] -2.0733 [-3.6948; -0.4519]
 -0.0502 [-1.4807;  1.3802] -1.0453 [-2.9103;  0.8197]
  1.6448 [-0.5125;  3.8020]  0.6497 [-1.8245;  3.1240]
 -1.3121 [-2.5014; -0.1227] -2.3071 [-4.0304; -0.5837]
  0.3007 [-1.1116;  1.7130] -0.6943 [-2.6572;  1.2685]
 -0.6493 [-1.8750;  0.5765] -1.6443 [-3.4065;  0.1180]
 -0.0369 [-1.5959;  1.5222] -1.0319 [-3.0284;  0.9646]
  0.0807 [-1.5033;  1.6647] -0.9143 [-2.9304;  1.1017]
 -0.1987 [-2.0115;  1.6141] -1.1937 [-3.3505;  0.9631]
 -1.9221 [-2.8393; -1.0048] -2.9171 [-4.3997; -1.4346]
                                                      
 -1.6000 [-3.7582;  0.5582]                          .
                          .                          .
                          .                          .
 -1.1200 [-4.2804;  2.0404]                          .
                        CBT                          .
  1.1614 [-1.2864;  3.6091]                        Cry
  2.9716 [ 1.4552;  4.4879]  1.8102 [-0.9918;  4.6122]
  1.3042 [-0.0782;  2.6867]  0.1429 [-2.6049;  2.8907]
 -0.3078 [-1.4067;  0.7912] -1.4691 [-4.0676;  1.1294]
  0.5402 [-1.8042;  2.8847] -0.6211 [-3.9449;  2.7027]
  1.3674 [ 0.2515;  2.4832]  0.2060 [-2.4108;  2.8228]
  0.5106 [-0.2391;  1.2603] -0.6507 [-3.1326;  1.8311]
  1.5643 [ 0.0991;  3.0295]  0.4029 [-2.3958;  3.2016]
  0.1051 [-0.7381;  0.9483] -1.0562 [-3.5589;  1.4464]
  1.1332 [-0.0743;  2.3407] -0.0281 [-2.6912;  2.6349]
  2.8282 [ 0.8258;  4.8306]  1.6668 [-1.4645;  4.7982]
 -0.1286 [-1.1172;  0.8600] -1.2900 [-3.8713;  1.2914]
  1.4841 [ 0.0374;  2.9308]  0.3228 [-2.4460;  3.0915]
  0.5342 [-0.5593;  1.6276] -0.6272 [-3.2342;  1.9799]
  1.1466 [-0.2653;  2.5585] -0.0148 [-2.7860;  2.7564]
  1.2641 [-0.1753;  2.7035]  0.1028 [-2.6825;  2.8881]
  0.9848 [-0.6624;  2.6319] -0.1766 [-3.0365;  2.6833]
 -0.7386 [-1.2727; -0.2046] -1.9000 [-4.2887;  0.4887]
                                                      
                          .                          .
                          .                          .
                          .  3.2000 [ 0.0434;  6.3566]
                          .                          .
                          .                          .
                          .                          .
                       DryN -2.6800 [-4.9711; -0.3889]
 -1.6673 [-3.2392; -0.0954]                       Elec
 -3.2793 [-4.9789; -1.5798] -1.6120 [-3.1909; -0.0331]
 -2.4313 [-5.1369;  0.2743] -0.7640 [-3.3965;  1.8685]
 -1.6042 [-3.0988; -0.1096]  0.0631 [-1.3667;  1.4929]
 -2.4609 [-4.0408; -0.8811] -0.7936 [-2.2507;  0.6635]
 -1.4073 [-3.2668;  0.4523]  0.2600 [-1.3128;  1.8329]
 -2.8664 [-4.4750; -1.2578] -1.1991 [-2.6895;  0.2913]
 -1.8383 [-3.6150; -0.0617] -0.1710 [-1.8194;  1.4773]
 -0.1434 [-2.5257;  2.2390]  1.5240 [-0.6909;  3.7388]
 -3.1002 [-4.6129; -1.5874] -1.4329 [-2.5750; -0.2907]
 -1.4874 [-3.3355;  0.3607]  0.1799 [-1.5774;  1.9372]
 -2.4374 [-4.1806; -0.6942] -0.7701 [-2.3983;  0.8581]
 -1.8250 [-3.6428; -0.0071] -0.1577 [-1.6810;  1.3657]
 -1.7074 [-3.5467;  0.1318] -0.0401 [-1.5890;  1.5087]
 -1.9868 [-4.1296;  0.1560] -0.3195 [-2.3865;  1.7476]
 -3.7102 [-5.1748; -2.2456] -2.0429 [-3.4009; -0.6849]
                                                      
                          .                          .
  0.3682 [-1.5669;  2.3034]  1.0000 [-2.0994;  4.0994]
 -2.3376 [-4.0003; -0.6750]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                       FlET                          .
  0.8480 [-1.6065;  3.3025]                        HtT
  1.6751 [ 0.3870;  2.9632]  0.8271 [-1.6689;  3.3231]
  0.8184 [-0.3495;  1.9863] -0.0296 [-2.4028;  2.3435]
  1.8720 [ 0.1971;  3.5469]  1.0240 [-1.6611;  3.7092]
  0.4129 [-0.7586;  1.5844] -0.4351 [-2.6708;  1.8006]
  1.4410 [-0.0555;  2.9374]  0.5930 [-1.9766;  3.1625]
  3.1360 [ 0.9302;  5.3417]  2.2880 [-0.7499;  5.3258]
  0.1792 [-1.0999;  1.4582] -0.6688 [-3.1266;  1.7889]
  1.7919 [ 0.2462;  3.3376]  0.9439 [-1.6824;  3.5701]
  0.8419 [-0.2870;  1.9709] -0.0061 [-2.4783;  2.4662]
  1.4543 [-0.1742;  3.0828]  0.6063 [-2.0501;  3.2628]
  1.5719 [-0.0805;  3.2243]  0.7239 [-1.9473;  3.3950]
  1.2925 [-0.5741;  3.1592]  0.4445 [-2.3435;  3.2326]
 -0.4309 [-1.4536;  0.5918] -1.2789 [-3.5901;  1.0323]
                                                      
 -0.2200 [-2.4504;  2.0104]                          .
                          .                          .
                          .                          .
                          .                          .
                          .  0.3907 [-0.9235;  1.7049]
                          .                          .
 -2.9300 [-5.2310; -0.6290]                          .
                          .                          .
  2.4500 [ 0.2530;  4.6470]                          .
                          .                          .
                       MasT                          .
 -0.8568 [-2.0635;  0.3500]                        McT
  0.1969 [-1.3128;  1.7066]  1.0537 [-0.4860;  2.5934]
 -1.2622 [-2.4987; -0.0258] -0.4055 [-1.3201;  0.5092]
 -0.2342 [-1.6107;  1.1424]  0.6226 [-0.6941;  1.9393]
  1.4608 [-0.6703;  3.5920]  2.3176 [ 0.2307;  4.4045]
 -1.4960 [-2.5494; -0.4425] -0.6392 [-1.7353;  0.4569]
  0.1168 [-1.1896;  1.4231]  0.9735 [-0.5370;  2.4840]
 -0.8332 [-2.2165;  0.5502]  0.0236 [-1.1201;  1.1673]
 -0.2208 [-1.6788;  1.2372]  0.6360 [-0.8531;  2.1251]
 -0.1032 [-1.5879;  1.3814]  0.7535 [-0.7617;  2.2687]
 -0.3826 [-2.2744;  1.5092]  0.4742 [-1.1680;  2.1163]
 -2.1060 [-3.1744; -1.0376] -1.2493 [-1.9228; -0.5758]
                                                      
                          .                          .
                          . -0.3101 [-1.6879;  1.0676]
                          . -2.4400 [-4.6666; -0.2134]
                          .                          .
                          . -0.4831 [-2.4224;  1.4563]
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .  0.0000 [-2.4023;  2.4023]
                          .                          .
                          . -1.2971 [-3.0690;  0.4748]
                        MfT                          .
 -1.4591 [-3.0408;  0.1225]                       MiET
 -0.4311 [-2.1329;  1.2708]  1.0281 [-0.3312;  2.3873]
  1.2639 [-0.9505;  3.4783]  2.7231 [ 0.6035;  4.8426]
 -1.6929 [-2.7743; -0.6115] -0.2337 [-1.3880;  0.9205]
 -0.0802 [-1.9180;  1.7577]  1.3790 [-0.1249;  2.8829]
 -1.0301 [-2.7419;  0.6817]  0.4290 [-0.7703;  1.6284]
 -0.4177 [-1.8960;  1.0606]  1.0414 [-0.4910;  2.5739]
 -0.3002 [-1.8047;  1.2044]  1.1590 [-0.3988;  2.7168]
 -0.5795 [-2.7117;  1.5527]  0.8796 [-0.8483;  2.6076]
 -2.3029 [-3.7612; -0.8446] -0.8438 [-1.5902; -0.0974]
                                                      
                          .                          .
                          .                          .
                          .                          .
                          .                          .
  1.6700 [-0.6814;  4.0214]  4.0000 [ 0.8305;  7.1695]
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
 -1.8000 [-4.4938;  0.8938]                          .
                          .                          .
                          .                          .
                          .                          .
                        Mnt                          .
  1.6950 [-0.5441;  3.9341]                        PBT
 -1.2618 [-2.5760;  0.0523] -2.9568 [-4.8892; -1.0244]
  0.3509 [-1.3605;  2.0624] -1.3441 [-3.7000;  1.0118]
 -0.5990 [-2.1233;  0.9253] -2.2940 [-4.5169; -0.0712]
  0.0134 [-1.6428;  1.6696] -1.6816 [-3.8612;  0.4979]
  0.1309 [-1.5488;  1.8106] -1.5641 [-3.7615;  0.6334]
 -0.1484 [-2.1060;  1.8091] -1.8434 [-4.3972;  0.7103]
 -1.8719 [-3.0491; -0.6946] -3.5668 [-5.5915; -1.5422]
                                                      
 -0.9965 [-1.9097; -0.0833]                          .
 -2.1500 [-4.4532;  0.1532]  1.2000 [-1.1905;  3.5905]
                          . -0.6000 [-3.0349;  1.8349]
                          .                          .
  0.8200 [-1.8096;  3.4496]                          .
                          .                          .
                          .                          .
 -1.2323 [-2.5466;  0.0821]                          .
                          .                          .
                          .                          .
 -1.6814 [-3.4641;  0.1012]  0.4003 [-1.2554;  2.0561]
 -3.7000 [-6.4057; -0.9943]                          .
 -1.6929 [-2.7743; -0.6115]                          .
                          .                          .
 -0.2900 [-2.7726;  2.1926]                          .
 -2.3000 [-4.6729;  0.0729]                          .
                      PlaSh                          .
  1.6127 [ 0.1267;  3.0988]                        Plt
  0.6628 [-0.6642;  1.9898] -0.9499 [-2.5750;  0.6751]
  1.2752 [ 0.2672;  2.2832] -0.3375 [-2.1332;  1.4581]
  1.3927 [ 0.3466;  2.4389] -0.2200 [-2.0374;  1.5974]
  1.1134 [-0.7243;  2.9510] -0.4994 [-2.5968;  1.5981]
 -0.6100 [-1.5885;  0.3684] -2.2228 [-3.6227; -0.8228]
                                                      
                          .                          .
 -0.7062 [-2.4897;  1.0773]                          .
                          .                          .
                          .                          .
  1.0400 [-1.3485;  3.4285]                          .
                          .                          .
                          .                          .
                          .                          .
  0.7829 [-0.7703;  2.3361]                          .
                          .                          .
                          .                          .
  0.5300 [-1.8668;  2.9268]                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .  1.2752 [ 0.2672;  2.2832]
                          .                          .
                       ReET                          .
  0.6124 [-1.0540;  2.2788]                       rTMS
  0.7299 [-0.9598;  2.4197]  0.1175 [-1.3352;  1.5703]
  0.4506 [-1.4212;  2.3224] -0.1618 [-2.2578;  1.9341]
 -1.2728 [-2.3172; -0.2285] -1.8852 [-3.2900; -0.4805]
                                                      
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .                          .
                          .  1.8100 [-0.7705;  4.3905]
                          .                          .
                          .                          .
                          .                          .
                          .                          .
  1.3927 [ 0.3466;  2.4389]                          .
                          .                          .
                          .                          .
                          .                          .
                       tDCS                          .
 -0.2794 [-2.3939;  1.8352]                        WBV
 -2.0028 [-3.4352; -0.5704] -1.7234 [-3.2959; -0.1509]
                           
                          .
 -1.4165 [-3.1406;  0.3077]
 -0.9072 [-2.6454;  0.8310]
 -4.0140 [-6.1578; -1.8702]
 -0.8331 [-1.4811; -0.1851]
 -1.9000 [-4.2887;  0.4887]
 -1.5000 [-3.7328;  0.7328]
                          .
 -0.8041 [-2.5539;  0.9456]
                          .
 -2.6800 [-4.8718; -0.4882]
 -0.9507 [-1.8180; -0.0834]
                          .
 -1.2195 [-2.2160; -0.2229]
 -2.7301 [-4.4923; -0.9679]
                          .
                          .
                          .
 -1.2104 [-3.1278;  0.7070]
                          .
                          .
 -1.5276 [-3.2046;  0.1494]
                       WlNi

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

---

Treatment ranking

# Treatment ranking
ranking_sr <- netrank(nma_sr, small.values = "good")
print(ranking_sr)

      P-score
DryN   0.9486
PBT    0.9097
Bal    0.8337
MfT    0.7021
Plt    0.6782
MasT   0.6544
Elec   0.6235
tDCS   0.6091
AqET   0.5970
Mnt    0.5715
rTMS   0.5702
Cry    0.5548
Acu    0.5418
WBV    0.5187
HtT    0.3959
AeET   0.3718
ReET   0.3692
McT    0.3562
MiET   0.2185
CBT    0.1807
PlaSh  0.1507
FlET   0.1179
WlNi   0.0259

---

Rankogram

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

Rankogram of treatments network

---

Inconsistency assessment

# Design decomposition
decomp_sr <- decomp.design(nma_sr)
print(decomp_sr)

Q statistics to assess homogeneity / consistency

                     Q df  p-value
Total           559.52 91 < 0.0001
Within designs  287.35 54 < 0.0001
Between designs 272.16 37 < 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
   WlNi:Mnt  1.94  1   0.1635
  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 181.20 35 < 0.0001
       AeET:MiET 187.64 36 < 0.0001
       WlNi:DryN 228.09 36 < 0.0001
       DryN:MasT 250.05 36 < 0.0001
      AeET:PlaSh 253.33 36 < 0.0001
  WlNi:FlET:MasT 255.40 35 < 0.0001
       McT:PlaSh 258.44 36 < 0.0001
        WlNi:WBV 259.69 36 < 0.0001
    WlNi:McT:WBV 259.65 35 < 0.0001
        McT:MiET 262.34 36 < 0.0001
       AqET:Elec 262.48 36 < 0.0001
       WlNi:AqET 263.96 36 < 0.0001
       Acu:PlaSh 264.55 36 < 0.0001
       DryN:Elec 264.55 36 < 0.0001
        WlNi:Bal 264.85 36 < 0.0001
   WlNi:McT:MiET 264.25 35 < 0.0001
       AeET:FlET 266.78 36 < 0.0001
        WlNi:Mnt 266.82 36 < 0.0001
        MasT:Mnt 267.03 36 < 0.0001
        CBT:MiET 267.29 36 < 0.0001
         Acu:CBT 267.97 36 < 0.0001
       Mnt:PlaSh 268.20 36 < 0.0001
        AqET:Bal 268.24 36 < 0.0001
       AqET:FlET 268.50 36 < 0.0001
        AqET:Plt 269.32 36 < 0.0001
         CBT:McT 269.61 36 < 0.0001
         CBT:PBT 270.26 36 < 0.0001
       PBT:PlaSh 270.26 36 < 0.0001
        MasT:Plt 270.43 36 < 0.0001
        McT:ReET 270.66 36 < 0.0001
      Elec:PlaSh 270.70 36 < 0.0001
       CBT:PlaSh 270.74 36 < 0.0001
       WlNi:MiET 270.75 36 < 0.0001
        CBT:ReET 270.82 36 < 0.0001
  WlNi:FlET:ReET 268.60 35 < 0.0001
         Bal:CBT 270.97 36 < 0.0001
       AeET:AqET 271.10 36 < 0.0001
       AeET:ReET 271.10 36 < 0.0001
       WlNi:AeET 271.42 36 < 0.0001
         CBT:Mnt 271.51 36 < 0.0001
      MasT:PlaSh 271.57 36 < 0.0001
        Acu:MasT 271.62 36 < 0.0001
  WlNi:AeET:ReET 269.42 35 < 0.0001
        WlNi:CBT 271.95 36 < 0.0001
       FlET:ReET 272.06 36 < 0.0001
        WlNi:McT 272.12 36 < 0.0001
        AeET:Plt 272.16 36 < 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 48.28 37  0.1014     0.9823      0.9650

---

Node-splitting

# 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 0.27 -1.0548 -1.6000 -0.8481 -0.7519 -0.58  0.5610
   Acu:MasT  1 0.28  0.3125 -0.2200  0.5189 -0.7389 -0.55  0.5815
  Acu:PlaSh  7 0.80 -1.1834 -0.9965 -1.9338  0.9373  0.90  0.3690
  AeET:AqET  3 0.48  0.6223  0.3190  0.9011 -0.5821 -0.61  0.5410
  AeET:FlET  2 0.29 -0.8689  0.3682 -1.3800  1.7483  1.49  0.1363
   AeET:HtT  1 0.56 -0.0209  1.0000 -1.3057  2.3057  0.97  0.3319
  AeET:MiET  3 0.46 -0.4560 -0.3101 -0.5823  0.2722  0.28  0.7768
 AeET:PlaSh  1 0.23 -0.6898 -2.1500 -0.2430 -1.9070 -1.42  0.1556
   AeET:Plt  1 0.34  0.9230  1.2000  0.7818  0.4182  0.28  0.7802
  AeET:ReET  2 0.39 -0.0270 -0.7062  0.4029 -1.1091 -0.95  0.3402
  AeET:WlNi  2 0.24 -1.2998 -1.4165 -1.2623 -0.1542 -0.15  0.8788
   AqET:Bal  1 0.40  0.9950  0.1800  1.5343 -1.3543 -0.83  0.4060
  AqET:Elec  1 0.22  0.1208  3.2000 -0.7344  3.9344  2.16  0.0307
  AqET:FlET  2 0.41 -1.4912 -2.3376 -0.8980 -1.4396 -1.30  0.1932
  AqET:MiET  1 0.22 -1.0783 -2.4400 -0.6866 -1.7534 -1.36  0.1738
   AqET:Plt  1 0.34  0.3007 -0.6000  0.7573 -1.3573 -0.89  0.3735
  AqET:WlNi  2 0.28 -1.9221 -0.9072 -2.3138  1.4066  1.35  0.1779
    Bal:CBT  1 0.23 -2.1785 -1.1200 -2.4998  1.3798  0.75  0.4536
   Bal:WlNi  2 0.48 -2.9171 -4.0140 -1.9116 -2.1024 -1.39  0.1650
    CBT:McT  3 0.33  0.5106  0.3907  0.5685 -0.1777 -0.22  0.8277
   CBT:MiET  2 0.19  0.1051 -0.4831  0.2423 -0.7253 -0.66  0.5092
    CBT:Mnt  1 0.26  1.1332  1.6700  0.9409  0.7291  0.52  0.6021
    CBT:PBT  1 0.40  2.8282  4.0000  2.0498  1.9502  0.93  0.3499
  CBT:PlaSh  1 0.14 -0.1286  0.8200 -0.2848  1.1048  0.76  0.4455
   CBT:ReET  1 0.21  0.5342  1.0400  0.4001  0.6399  0.47  0.6406
   CBT:WlNi 13 0.68 -0.7386 -0.8331 -0.5388 -0.2943 -0.50  0.6142
  DryN:Elec  1 0.47 -1.6673 -2.6800 -0.7665 -1.9135 -1.19  0.2337
  DryN:MasT  1 0.42 -1.6042 -2.9300 -0.6366 -2.2934 -1.49  0.1375
  DryN:WlNi  1 0.43 -3.7102 -1.5000 -5.3793  3.8793  2.57  0.0102
 Elec:PlaSh  3 0.76 -1.4329 -1.2323 -2.0515  0.8193  0.60  0.5455
  FlET:MasT  1 0.34  1.6751  2.4500  1.2692  1.1808  0.85  0.3935
  FlET:ReET  3 0.53  0.8419  0.7829  0.9081 -0.1251 -0.11  0.9136
  FlET:WlNi  2 0.34 -0.4309 -0.8041 -0.2372 -0.5669 -0.52  0.6063
   HtT:MiET  1 0.87 -0.4351  0.0000 -3.2501  3.2501  0.97  0.3319
   MasT:Mnt  1 0.26 -0.2342 -1.8000  0.3192 -2.1192 -1.33  0.1850
 MasT:PlaSh  2 0.35 -1.4960 -1.6814 -1.3965 -0.2850 -0.25  0.8005
   MasT:Plt  2 0.62  0.1168  0.4003 -0.3508  0.7511  0.55  0.5848
  MasT:WlNi  1 0.24 -2.1060 -2.6800 -1.9271 -0.7529 -0.59  0.5566
   McT:MiET  2 0.27 -0.4055 -1.2971 -0.0816 -1.2155 -1.15  0.2495
  McT:PlaSh  1 0.16 -0.6392 -3.7000 -0.0383 -3.6617 -2.43  0.0153
   McT:ReET  1 0.23  0.0236  0.5300 -0.1257  0.6557  0.47  0.6375
    McT:WBV  1 0.40  0.4742  1.8100 -0.4349  2.2449  1.32  0.1884
   McT:WlNi  8 0.60 -1.2493 -0.9507 -1.7028  0.7521  1.07  0.2842
  MiET:WlNi  6 0.56 -0.8438 -1.2195 -0.3638 -0.8557 -1.12  0.2648
  Mnt:PlaSh  1 0.28 -1.2618 -0.2900 -1.6401  1.3501  0.90  0.3658
   Mnt:WlNi  2 0.45 -1.8719 -2.7301 -1.1801 -1.5500 -1.28  0.1996
  PBT:PlaSh  1 0.66 -2.9568 -2.3000 -4.2502  1.9502  0.93  0.3499
  ReET:WlNi  2 0.30 -1.2728 -1.2104 -1.2992  0.0887  0.08  0.9394
   WBV:WlNi  2 0.88 -1.7234 -1.5276 -3.1493  1.6217  0.66  0.5102

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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr)

Forest plot of node-splitting for Network

---

Network heatmap

# Heatmap
netheat(nma_sr)

Heatmap of contribution matrix for Network

---

Funnel plot

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

Funnel plot for Network (P | Sh)

---

P | Lg

# 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 = 14
Number of designs: d = 16
Number of networks: 3

Details on subnetworks: 
 subnetwork  k  m n
          1 20 24 8
          2  1  1 2
          3  4  4 4

There are three sub-networks:

Subnet 1:
- 20 studies
- 24 comparisons
- 8 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.

Subnet 1

Select the procedures performed

Important

the first subnet contains 20 studies, 24 comparisons and 8 treatments.

Data preparation

# 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

---

Treatment exploration

# 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"

# Total number of treatments
length(trat_sr1)

[1] 8

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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 = 8
Number of designs: d = 12

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
          MD             95%-CI     z p-value
AeET -1.2747 [-2.0171; -0.5324] -3.37  0.0008
AqET -1.4358 [-2.2325; -0.6392] -3.53  0.0004
CBT  -0.5002 [-1.7042;  0.7037] -0.81  0.4155
FlET  0.4708 [-1.2013;  2.1429]  0.55  0.5810
McT  -0.5893 [-1.8902;  0.7117] -0.89  0.3747
MiET -1.2404 [-2.4820;  0.0011] -1.96  0.0502
ReET -2.4288 [-3.9852; -0.8723] -3.06  0.0022
WlNi       .                  .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.6247; tau = 0.7904; I^2 = 66.4% [43.2%; 80.2%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f.  p-value
Total           44.69   15 < 0.0001
Within designs  31.37    8   0.0001
Between designs 13.33    7   0.0646

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

---

Network visualization

# 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)

---

Detailed results

# 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   0.9132     2         
Andrade2019              AqET   WlNi -1.0000 0.6137   1.0007     2         
Assis2006                AeET   AqET  0.0000 0.5601   0.9688     2         
Baptista2012             AeET   WlNi -2.9000 0.3860   0.8796     2         
Hakkinen2001             ReET   WlNi -3.9200 1.1181   1.3693     2         
Kayo2012                 AeET   ReET  0.3700 0.7979   1.4239     3        *
Kayo2012                 AeET   WlNi -1.3700 0.7203   1.2855     3        *
Kayo2012                 ReET   WlNi -1.7400 0.7288   1.2982     3        *
Larsson2015               McT   MiET  1.6100 0.4798   0.9246     2         
Letieri2013              AqET   WlNi -2.0800 0.3616   0.8692     2         
Mannerkorpi2000           McT   WlNi -0.5000 0.6372   1.0152     2         
Mengshoel1992            AeET   WlNi -0.6500 0.8641   1.1711     2         
Munguia-Izquierdo 2007   AqET   WlNi -0.9700 0.5334   0.9535     2         
Rooks2007                 CBT    McT  1.0000 0.5752   1.2444     3        *
Rooks2007                 CBT   MiET  0.9000 0.5016   1.1331     3        *
Rooks2007                 McT   MiET -0.1000 0.4732   1.1008     3        *
Sanudo2015               MiET   WlNi -0.3000 0.7371   1.0808     2         
Schachter2003            AeET   WlNi -0.0400 0.4272   0.8985     2         
Tomas-Carus2008          AqET   WlNi -1.3000 0.5888   0.9856     2         
Valim2003                AeET   FlET -1.1800 0.6042   0.9949     2         
Valkeinen2008            MiET   WlNi -1.7100 1.4134   1.6194     2         
Williams2010              CBT   WlNi -0.6000 0.2855   0.8404     2         
Hernando-Garijo2021      AeET   WlNi -1.5400 0.6724   1.0377     2         
Saranya2022               CBT   FlET -1.8700 0.9740   1.2543     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  0.1611 [-0.7411;  1.0633]
Andrade2019              AqET   WlNi -1.4358 [-2.2325; -0.6392]
Assis2006                AeET   AqET  0.1611 [-0.7411;  1.0633]
Baptista2012             AeET   WlNi -1.2747 [-2.0171; -0.5324]
Hakkinen2001             ReET   WlNi -2.4288 [-3.9852; -0.8723]
Kayo2012                 AeET   ReET  1.1540 [-0.4701;  2.7782]
Kayo2012                 AeET   WlNi -1.2747 [-2.0171; -0.5324]
Kayo2012                 ReET   WlNi -2.4288 [-3.9852; -0.8723]
Larsson2015               McT   MiET  0.6512 [-0.5014;  1.8037]
Letieri2013              AqET   WlNi -1.4358 [-2.2325; -0.6392]
Mannerkorpi2000           McT   WlNi -0.5893 [-1.8902;  0.7117]
Mengshoel1992            AeET   WlNi -1.2747 [-2.0171; -0.5324]
Munguia-Izquierdo 2007   AqET   WlNi -1.4358 [-2.2325; -0.6392]
Rooks2007                 CBT    McT  0.0891 [-1.3245;  1.5027]
Rooks2007                 CBT   MiET  0.7402 [-0.6233;  2.1038]
Rooks2007                 McT   MiET  0.6512 [-0.5014;  1.8037]
Sanudo2015               MiET   WlNi -1.2404 [-2.4820;  0.0011]
Schachter2003            AeET   WlNi -1.2747 [-2.0171; -0.5324]
Tomas-Carus2008          AqET   WlNi -1.4358 [-2.2325; -0.6392]
Valim2003                AeET   FlET -1.7455 [-3.3606; -0.1305]
Valkeinen2008            MiET   WlNi -1.2404 [-2.4820;  0.0011]
Williams2010              CBT   WlNi -0.5002 [-1.7042;  0.7037]
Hernando-Garijo2021      AeET   WlNi -1.2747 [-2.0171; -0.5324]
Saranya2022               CBT   FlET -0.9710 [-2.7109;  0.7688]

Number of studies: k = 20
Number of pairwise comparisons: m = 24
Number of observations: o = 1270
Number of treatments: n = 8
Number of designs: d = 12

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
          MD             95%-CI     z p-value
AeET -1.2747 [-2.0171; -0.5324] -3.37  0.0008
AqET -1.4358 [-2.2325; -0.6392] -3.53  0.0004
CBT  -0.5002 [-1.7042;  0.7037] -0.81  0.4155
FlET  0.4708 [-1.2013;  2.1429]  0.55  0.5810
McT  -0.5893 [-1.8902;  0.7117] -0.89  0.3747
MiET -1.2404 [-2.4820;  0.0011] -1.96  0.0502
ReET -2.4288 [-3.9852; -0.8723] -3.06  0.0022
WlNi       .                  .     .       .

Quantifying heterogeneity / inconsistency:
tau^2 = 0.6247; tau = 0.7904; I^2 = 66.4% [43.2%; 80.2%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                    Q d.f.  p-value
Total           44.69   15 < 0.0001
Within designs  31.37    8   0.0001
Between designs 13.33    7   0.0646

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

---

Forest plot

# Forest plot
forest(nma_sr1)

Forest plot of treatment effects for Subnet 1

---

League table

# Pairwise comparison table with confidence intervals
netleague(nma_sr1, ci = TRUE)

League table (random effects model):
                                                      
                       AeET  0.2648 [-1.0377;  1.5672]
  0.1611 [-0.7411;  1.0633]                       AqET
 -0.7745 [-2.1309;  0.5818] -0.9356 [-2.3604;  0.4891]
 -1.7455 [-3.3606; -0.1305] -1.9066 [-3.6903; -0.1230]
 -0.6855 [-2.1619;  0.7910] -0.8466 [-2.3650;  0.6719]
 -0.0343 [-1.4589;  1.3904] -0.1954 [-1.6633;  1.2725]
  1.1540 [-0.4701;  2.7782]  0.9929 [-0.7229;  2.7087]
 -1.2747 [-2.0171; -0.5324] -1.4358 [-2.2325; -0.6392]
                                                      
                          . -1.1800 [-3.1299;  0.7699]
                          .                          .
                        CBT -1.8700 [-4.3284;  0.5884]
 -0.9710 [-2.7109;  0.7688]                       FlET
  0.0891 [-1.3245;  1.5027]  1.0601 [-0.9418;  3.0620]
  0.7402 [-0.6233;  2.1038]  1.7113 [-0.2539;  3.6764]
  1.9285 [-0.0267;  3.8838]  2.8996 [ 0.6650;  5.1342]
 -0.5002 [-1.7042;  0.7037]  0.4708 [-1.2013;  2.1429]
                                                      
                          .                          .
                          .                          .
  1.0000 [-0.9159;  2.9159]  0.9000 [-0.9348;  2.7348]
                          .                          .
                        McT  0.7519 [-0.5272;  2.0309]
  0.6512 [-0.5014;  1.8037]                       MiET
  1.8395 [-0.1843;  3.8632]  1.1883 [-0.7978;  3.1744]
 -0.5893 [-1.8902;  0.7117] -1.2404 [-2.4820;  0.0011]
                                                      
  0.3700 [-1.8312;  2.5712] -1.3626 [-2.2337; -0.4916]
                          . -1.3831 [-2.3121; -0.4541]
                          . -0.6000 [-2.2472;  1.0472]
                          .                          .
                          . -0.5000 [-2.4898;  1.4898]
                          . -0.7345 [-2.4964;  1.0274]
                       ReET -2.5714 [-4.2288; -0.9141]
 -2.4288 [-3.9852; -0.8723]                       WlNi

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

---

Treatment ranking

# Treatment ranking
ranking_sr1 <- netrank(nma_sr1, small.values = "good")
print(ranking_sr1)

     P-score
ReET  0.9427
AqET  0.7305
MiET  0.6646
AeET  0.6619
McT   0.3860
CBT   0.3581
WlNi  0.1616
FlET  0.0945

---

Rankogram

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

Rankogram of treatments for Subnet 1

---

Inconsistency assessment

# Design decomposition
decomp_sr1 <- decomp.design(nma_sr1)
print(decomp_sr1)

Q statistics to assess homogeneity / consistency

                    Q df  p-value
Total           44.69 15 < 0.0001
Within designs  31.37  8   0.0001
Between designs 13.33  7   0.0646

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 0.0646)

 Detached design     Q df p-value
        McT:MiET  7.02  6  0.3195
    CBT:McT:MiET  6.86  5  0.2309
       WlNi:ReET 10.56  6  0.1029
        CBT:FlET 11.32  6  0.0789
       AeET:FlET 11.32  6  0.0789
       WlNi:MiET 11.66  6  0.0699
  WlNi:AeET:ReET 10.56  5  0.0608
       WlNi:AeET 12.79  6  0.0466
       AeET:AqET 13.11  6  0.0413
       WlNi:AqET 13.11  6  0.0413
        WlNi:CBT 13.15  6  0.0406
        WlNi:McT 13.29  6  0.0386

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 4.17  7  0.7597     0.9355      0.8752

---

Node-splitting

# 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 0.48  0.1611  0.2648  0.0655  0.1993  0.22  0.8288
   AeET:CBT 0    0 -0.7745       . -0.7745       .     .       .
  AeET:FlET 1 0.69 -1.7455 -1.1800 -2.9810  1.8010  1.01  0.3104
   AeET:McT 0    0 -0.6855       . -0.6855       .     .       .
  AeET:MiET 0    0 -0.0343       . -0.0343       .     .       .
  AeET:ReET 1 0.54  1.1540  0.3700  2.0909 -1.7209 -1.03  0.3010
  AeET:WlNi 5 0.73 -1.2747 -1.3626 -1.0414 -0.3212 -0.38  0.7053
   AqET:CBT 0    0 -0.9356       . -0.9356       .     .       .
  AqET:FlET 0    0 -1.9066       . -1.9066       .     .       .
   AqET:McT 0    0 -0.8466       . -0.8466       .     .       .
  AqET:MiET 0    0 -0.1954       . -0.1954       .     .       .
  AqET:ReET 0    0  0.9929       .  0.9929       .     .       .
  AqET:WlNi 4 0.74 -1.4358 -1.3831 -1.5824  0.1993  0.22  0.8288
   CBT:FlET 1 0.50 -0.9710 -1.8700 -0.0690 -1.8010 -1.01  0.3104
    CBT:McT 1 0.54  0.0891  1.0000 -0.9993  1.9993  1.38  0.1674
   CBT:MiET 1 0.55  0.7402  0.9000  0.5432  0.3568  0.26  0.7987
   CBT:ReET 0    0  1.9285       .  1.9285       .     .       .
   CBT:WlNi 1 0.53 -0.5002 -0.6000 -0.3857 -0.2143 -0.17  0.8619
   FlET:McT 0    0  1.0601       .  1.0601       .     .       .
  FlET:MiET 0    0  1.7113       .  1.7113       .     .       .
  FlET:ReET 0    0  2.8996       .  2.8996       .     .       .
  FlET:WlNi 0    0  0.4708       .  0.4708       .     .       .
   McT:MiET 2 0.81  0.6512  0.7519  0.2165  0.5354  0.36  0.7220
   McT:ReET 0    0  1.8395       .  1.8395       .     .       .
   McT:WlNi 1 0.43 -0.5893 -0.5000 -0.6559  0.1559  0.12  0.9075
  MiET:ReET 0    0  1.1883       .  1.1883       .     .       .
  MiET:WlNi 2 0.50 -1.2404 -0.7345 -1.7394  1.0049  0.79  0.4277
  ReET:WlNi 2 0.88 -2.4288 -2.5714 -1.3636 -1.2079 -0.49  0.6235

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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr1)

Forest plot of node-splitting for Subnet 1

---

Network heatmap

# Heatmap
netheat(nma_sr1)

Heatmap of contribution matrix for Subnet 1

---

Funnel plot

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

Funnel plot for Subnet 1 (P | Lg)

---

Subnet 2

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.

Data preparation

# 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()

---

Treatment exploration

# Unique treatments in subnet 2
unique_treat1_sr2 <- sr2$treat1 |> unique()
print(unique_treat1_sr2)

[1] "DryN"

unique_treat2_sr2 <- sr2$treat2 |> unique()
print(unique_treat2_sr2)

[1] "MasT"

# Combination of all unique treatments
trat_sr2 <- unique(c(unique_treat1_sr2, unique_treat2_sr2))
print(trat_sr2)

[1] "DryN" "MasT"

# Total number of treatments
length(trat_sr2)

[1] 2

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_plg_sr2$studlab))

[1] 1

---

Network Meta-Analysis model

# 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

---

Network visualization

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

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

---

Detailed results

# 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

---

Subnet 3

Select the procedures performed

Important

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

Data preparation

# 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()

---

Treatment exploration

# Unique treatments in subnet 3
unique_treat1_sr3 <- sr3$treat1 |> unique()
print(unique_treat1_sr3)

[1] "MfT"  "Acu"  "rTMS"

unique_treat2_sr3 <- sr3$treat2 |> unique()
print(unique_treat2_sr3)

[1] "PlaSh"

# Combination of all unique treatments
trat_sr3 <- unique(c(unique_treat1_sr3, unique_treat2_sr3))
print(trat_sr3)

[1] "MfT"   "Acu"   "rTMS"  "PlaSh"

# Total number of treatments
length(trat_sr3)

[1] 4

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_plg_sr3$studlab))

[1] 4

---

Network Meta-Analysis model

# 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

---

Network visualization

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

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

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr3)

Forest plot of treatment effects for Subnet 3

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 2

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr3)

Forest plot of node-splitting for Subnet 3

---

Network heatmap

# Heatmap
netheat(nma_sr3)

---

Funnel plot

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

Funnel plot for Subnet 3 (P | Lg)

---

Q | Im

# 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.

Data preparation

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


# Display comparison table
sr

---

Treatment exploration

# Unique treatments in network
unique_treat_sr1 <- sr$treat1 |> unique()
print(unique_treat_sr1)

[1] "Mnt"  "PbT"  "CBT"  "rTMS" "tDCS" "HtT"  "Bal"  "McT"  "Cry" 

unique_treat_sr2 <- sr$treat2 |> unique()
print(unique_treat_sr2)

[1] "WlNi"  "PlaSh"

# 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"

# Total number of treatments
length(trat_sr)

[1] 11

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr)

Forest plot of treatment effects for network

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments network

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr)

Forest plot of node-splitting for Network

---

Network heatmap

# Heatmap
netheat(nma_sr)

---

Funnel plot

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

Funnel plot for Network (Q | Im)

---

Q | Sh

# 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 = 21
Number of designs: d = 47
Number of networks: 1

There are network:

Network:
- 99 studies
- 115 comparisons
- 21 treatments

Tip

The network is fully connected.

1.0.3 Network

Select the procedures performed

Important

The network contain 99 studies, 115 comparisons and 22 treatments.

Data preparation

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


# Display comparison table
sr

---

Treatment exploration

# Unique treatments in network
unique_treat_sr1 <- sr$treat1 |> unique()
print(unique_treat_sr1)

 [1] "Mnt"  "McT"  "WBV"  "MfT"  "AqET" "Bal"  "AeET" "FlET" "ReET" "CBT" 
[11] "rTMS" "DryN" "MiET" "Elec" "MasT" "tDCS" "Acu"  "PbT" 

unique_treat_sr2 <- sr$treat2 |> unique()
print(unique_treat_sr2)

 [1] "WlNi"  "WBV"   "PlaSh" "Bal"   "AqET"  "ReET"  "McT"   "FlET"  "MasT" 
[10] "Plt"   "CBT"   "MiET"  "Mnt"  

# 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"  "ReET" 
[10] "CBT"   "rTMS"  "DryN"  "MiET"  "Elec"  "MasT"  "tDCS"  "Acu"   "PbT"  
[19] "WlNi"  "PlaSh" "Plt"  

# Total number of treatments
length(trat_sr)

[1] 21

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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 = 21
Number of designs: d = 47

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD               95%-CI     z  p-value
Acu   -23.7569 [-35.9372; -11.5766] -3.82   0.0001
AeET  -13.4354 [-20.0894;  -6.7814] -3.96 < 0.0001
AqET  -14.8091 [-21.9496;  -7.6686] -4.06 < 0.0001
Bal   -16.1977 [-26.8461;  -5.5493] -2.98   0.0029
CBT    -7.7135 [-11.9020;  -3.5249] -3.61   0.0003
DryN  -24.7308 [-39.0871; -10.3745] -3.38   0.0007
Elec  -19.6014 [-36.0315;  -3.1714] -2.34   0.0194
FlET   -6.5412 [-14.6940;   1.6117] -1.57   0.1158
MasT  -17.1916 [-27.1616;  -7.2217] -3.38   0.0007
McT   -12.9538 [-17.6261;  -8.2815] -5.43 < 0.0001
MfT   -23.9171 [-38.9107;  -8.9236] -3.13   0.0018
MiET  -10.7914 [-16.0339;  -5.5489] -4.03 < 0.0001
Mnt   -11.9810 [-23.1959;  -0.7661] -2.09   0.0363
PbT   -20.5345 [-42.2167;   1.1478] -1.86   0.0634
PlaSh  -7.9345 [-18.1090;   2.2401] -1.53   0.1264
Plt   -21.2186 [-33.7539;  -8.6833] -3.32   0.0009
ReET  -20.3620 [-28.6709; -12.0532] -4.80 < 0.0001
rTMS  -15.8801 [-30.1998;  -1.5603] -2.17   0.0297
tDCS  -12.2882 [-27.4754;   2.8989] -1.59   0.1128
WBV   -12.5886 [-22.1624;  -3.0148] -2.58   0.0100
WlNi         .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 80.2482; tau = 8.9581; I^2 = 84.4% [81.3%; 87.0%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           557.76   87 < 0.0001
Within designs  298.03   53 < 0.0001
Between designs 259.74   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

---

Network visualization

# 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)

---

Detailed results

# 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  10.5720     2         
Alentorn-Geli2008          McT    WBV   6.4100  6.4532  13.0119     3        *
Alentorn-Geli2008          McT   WlNi  -9.4400  7.3279  14.1541     3        *
Alentorn-Geli2008          WBV   WlNi -15.8500  7.9606  15.3257     3        *
Alfano2001                 MfT  PlaSh  -4.6400  3.5345   9.6302     2         
Altan2004                 AqET    Bal  -1.8800  4.7088  10.1203     2         
Ardic2007                  Bal   WlNi  -8.6800  4.3832   9.9730     2         
Assis2006                 AeET   AqET   3.0000  5.0248  10.2712     2         
Assumpçao2018             FlET   ReET   9.1000  9.5318  17.0101     3        *
Assumpçao2018             FlET   WlNi -14.8000  8.1936  14.4632     3        *
Assumpçao2018             ReET   WlNi -23.9000  8.2018  14.4746     3        *
Astin2003                  CBT    McT   1.3000  4.1904   9.8898     2         
Baumueller2017             CBT   WlNi   2.3700  6.6855  11.1778     2         
Bongi2012                  CBT    McT  10.0900  6.8643  11.2857     2         
Bongi2010                  CBT   WlNi -13.9000  5.6413  10.5864     2         
Bourgault2015              McT   WlNi  -1.5700  4.9106  10.2158     2         
Boyer2014                PlaSh   rTMS  11.6000  4.3853   9.9739     2         
Calandre2009              AqET   FlET  -4.7200  4.2444   9.9128     2         
Carson2010                 McT   WlNi -13.2000  5.0135  10.2656     2         
Casanueva2014             DryN   WlNi  -9.7000  3.3866   9.5769     2         
Castro-Sanchez2019        DryN   MasT -23.8200  4.3700   9.9672     2         
Collado-Mateo2017         MiET  PlaSh  -6.9300  3.3233   9.5547     2         
daCosta2005               MiET   WlNi  -7.3000  4.2695   9.9236     2         
Dailey2019                Elec  PlaSh -56.0600 23.1621  24.8341     2         
deMedeiros2020            AqET    Plt   7.0000  5.0943  10.3054     2         
Ekici2017                 MasT    Plt   6.5600  3.3208   9.5538     2         
Espi-Lopes2016            MiET   WlNi   1.7600  7.0148  11.3779     2         
Evcik2002                  Bal   WlNi -33.8000 10.9424  14.1416     2         
Fernandes2016             AeET   AqET   3.4800  4.1605   9.8772     2         
Fitzgibbon2018           PlaSh   rTMS   3.0700  7.9323  11.9654     2         
Fonseca2019               AqET    CBT  13.6000  4.3355   9.9521     2         
Garcia2006                 CBT   WlNi -13.8800  9.9308  13.3742     2         
Garcia-Martinez2012       MiET   WlNi -18.2100  7.4089  11.6249     2         
Giannotti2014              McT   WlNi   4.5300  5.6870  10.6109     2         
Glasgow2017               ReET   WlNi -30.0000  7.0456  11.3969     2         
Gomez-Hernandez2019       AeET   MiET  10.6200  0.8775   9.0010     2         
Gowans2001                AqET   WlNi  -6.7300  5.8527  10.7006     2         
Hargrove2012             PlaSh   tDCS   9.9000  4.5112  10.0299     2         
Jones2002                  McT   ReET   5.5500  4.8917  10.2067     2         
Jones2012                  CBT    McT  13.4000  6.5801  11.1151     2         
Karatay2018                Acu  PlaSh -17.1100  4.8992  10.2103     2         
Kayo2012                  AeET   ReET  -9.7400  5.4131  12.8701     3        *
Kayo2012                  AeET   WlNi -16.1300  5.3516  12.7912     3        *
Kayo2012                  ReET   WlNi  -6.3900  5.2328  12.6452     3        *
King2002                   CBT    McT  11.6000  4.8603  10.1917     2         
Kurt2016                   Bal   MiET  -7.1000  2.5883   9.3246     2         
Lami2018                   CBT   WlNi   1.4400  3.3937   9.5794     2         
Lauche2016                MasT  PlaSh  -6.6000  2.8655   9.4053     2         
Lopes-Rodrigues2012       AqET   FlET -17.0700  4.6996  10.1160     2         
Lopes-Rodrigues2013       AqET   FlET -14.7900  4.2189   9.9019     2         
Luciano2014                CBT   WlNi -18.9800  1.5949   9.0990     2         
Lynch2012                  McT   WlNi -17.5200  3.2954   9.5451     2         
Mhalla2011               PlaSh   rTMS  10.7000  4.4529  10.0038     2         
Mist2018                   Acu    CBT -22.4000  5.0071  10.2625     2         
Olivares2011               WBV   WlNi  -3.7300  3.6133   9.6594     2         
Paolucci2016               MfT  PlaSh -22.3000  4.2735   9.9253     2         
Paolucci2015              MiET   WlNi  -9.7000  3.6907   9.6886     2         
Parra-Delgado2013          CBT   WlNi  -4.4300  5.5637  10.5453     2         
Pereira-Pernambuco2018     McT   WlNi -37.5900  3.2725   9.5372     2         
Perez-Aranda2019           CBT   WlNi  -6.8600  2.9360   9.4270     2         
Picard2013                 CBT   WlNi  -1.3500  4.6479  10.0921     2         
Redondo2004                CBT   MiET   4.3600  5.5606  10.5436     2         
Richards2002              AeET    McT   0.3000  2.6343   9.3374     2         
Rivera2018                 WBV   WlNi -22.0000  4.7523  10.1407     2         
Ruaro2014                  PbT  PlaSh -12.6000  3.8967   9.7689     2         
Salaffi2015                McT   WlNi  -8.2400  2.1713   9.2175     2         
Schachter2003             AeET   WlNi -10.1900  3.3527   9.5650     2         
Schmidt2011                CBT   WlNi  -3.0300  2.4137   9.2776     2         
Sevimli2015               AeET   AqET   1.7000  4.6428  12.3735     3        *
Sevimli2015               AeET   MiET -26.3000  4.4976  12.2139     3        *
Sevimli2015               AqET   MiET -28.0000  4.6973  12.4363     3        *
Silva2019                  CBT   ReET  25.7400  4.1233   9.8615     2         
Simister2018               CBT   WlNi -16.2300  3.2949   9.5449     2         
Soares2002                 CBT   WlNi  -1.8400  1.6938   9.1169     2         
Sutbeyaz2009               MfT  PlaSh -21.4000  3.5877   9.6499     2         
Tomas-Carus2007b&c        AqET   WlNi  -8.0000  6.1835  10.8850     2         
Ugurlu2017                 Acu  PlaSh -26.0300  3.5736   9.6446     2         
Valim2003                 AeET   FlET  -3.3100  4.8020  10.1640     2         
Vallejo2015                CBT   WlNi  -2.7600  4.8915  10.2066     2         
Vas2016                    Acu  PlaSh  -8.5000  2.5814   9.3227     2         
Verkaik2013                CBT   WlNi  -3.8000  3.3368   9.5594     2         
Wang2018                   McT   MiET  -6.8800  2.9934   9.4450     2         
Wicksell2013               CBT   WlNi  -4.8000  3.6440   9.6709     2         
Arakaki2021               FlET   ReET  15.7100  5.6273  10.5790     2         
Atan2020                  MiET   WlNi -31.0800  4.3638   9.9645     2         
Barranengoa-Cuadra2021     CBT   WlNi -24.1000  3.0388   9.4595     2         
Ceballos-Laita2020         McT   MiET  -0.3500  7.7076  11.8176     2         
Coste2021                  Mnt  PlaSh  -0.8000  4.0600   9.8352     2         
Izquierdo-Alventosa2020   MiET   WlNi  -5.5800  5.9339  10.7452     2         
Jamison2021               Elec  PlaSh  -7.4700  2.4770   9.2943     2         
Mingorance2021.2           WBV   WlNi  -8.2000  2.5870   9.3242     2         
Rodriguez-Mansilla2021     McT   MiET  -0.0800  4.2198  12.5348     3        *
Rodriguez-Mansilla2021    MiET   WlNi -11.6600  3.2126  11.5197     3        *
Rodriguez-Mansilla2021     McT   WlNi -11.7400  2.9326  11.3193     3        *
Sarmento2020               McT  PlaSh -18.0000  9.1302  12.7909     2         
Udina-Cortés2020          Elec  PlaSh  -9.3000  4.5740  10.0583     2         
Lacroix2022              PlaSh   rTMS   5.1500  3.5083   9.6206     2         
Paolucci2022               CBT   MiET  -8.5000  6.9387  11.3311     2         
Park2021                  FlET   ReET  11.3000  6.5679  11.1079     2         
Samartin-Veiga2022       PlaSh   tDCS   1.3400  5.3236  10.4206     2         
Alptug2023                 Mnt   WlNi -24.1000  5.9968  10.7801     2         
Audoux2023                MasT    Mnt -10.3000  7.1849  11.4835     2         
Baelz2022                  Acu  PlaSh  -2.6000  7.3763  11.6042     2         
Caumo2023                PlaSh   tDCS   1.8800  3.1792   9.5056     2         
Franco2023                AeET    Plt   4.5000  4.2791   9.9277     2         
Rodríguez-Mansilla2023    AeET    McT   0.0900  3.2027  11.8078     3        *
Rodríguez-Mansilla2023    AeET   WlNi -10.4800  2.6296  11.3628     3        *
Rodríguez-Mansilla2023     McT   WlNi -10.5700  2.6113  11.3508     3        *
Patru2021                  McT   MiET  11.8000  4.6757  12.5027     3        *
Patru2021                  McT   WlNi  -8.1000  4.5444  12.3481     3        *
Patru2021                 MiET   WlNi -19.9000  4.1244  11.9154     3        *
Lee2024                    CBT    McT   0.1000  2.6946   9.3546     2         
Schulze2023               FlET   MasT  17.4400  2.1681  11.2974     3        *
Schulze2023               MasT   WlNi -33.6200  2.0780  11.2466     3        *
Schulze2023               FlET   WlNi -16.1800  2.1603  11.2929     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 -11.9810 [-23.1959;  -0.7661]
Alentorn-Geli2008          McT    WBV  -0.3651 [-10.7268;   9.9965]
Alentorn-Geli2008          McT   WlNi -12.9538 [-17.6261;  -8.2815]
Alentorn-Geli2008          WBV   WlNi -12.5886 [-22.1624;  -3.0148]
Alfano2001                 MfT  PlaSh -15.9827 [-26.9957;  -4.9697]
Altan2004                 AqET    Bal   1.3886 [-10.1255;  12.9027]
Ardic2007                  Bal   WlNi -16.1977 [-26.8461;  -5.5493]
Assis2006                 AeET   AqET   1.3737 [ -6.2522;   8.9996]
Assumpçao2018             FlET   ReET  13.8209 [  4.4199;  23.2218]
Assumpçao2018             FlET   WlNi  -6.5412 [-14.6940;   1.6117]
Assumpçao2018             ReET   WlNi -20.3620 [-28.6709; -12.0532]
Astin2003                  CBT    McT   5.2403 [ -0.1262;  10.6068]
Baumueller2017             CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Bongi2012                  CBT    McT   5.2403 [ -0.1262;  10.6068]
Bongi2010                  CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Bourgault2015              McT   WlNi -12.9538 [-17.6261;  -8.2815]
Boyer2014                PlaSh   rTMS   7.9456 [ -2.1309;  18.0221]
Calandre2009              AqET   FlET  -8.2679 [-16.4622;  -0.0736]
Carson2010                 McT   WlNi -12.9538 [-17.6261;  -8.2815]
Casanueva2014             DryN   WlNi -24.7308 [-39.0871; -10.3745]
Castro-Sanchez2019        DryN   MasT  -7.5392 [-22.0330;   6.9547]
Collado-Mateo2017         MiET  PlaSh  -2.8569 [-13.3836;   7.6698]
daCosta2005               MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Dailey2019                Elec  PlaSh -11.6670 [-24.5676;   1.2336]
deMedeiros2020            AqET    Plt   6.4095 [ -6.0784;  18.8974]
Ekici2017                 MasT    Plt   4.0270 [ -9.0700;  17.1239]
Espi-Lopes2016            MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Evcik2002                  Bal   WlNi -16.1977 [-26.8461;  -5.5493]
Fernandes2016             AeET   AqET   1.3737 [ -6.2522;   8.9996]
Fitzgibbon2018           PlaSh   rTMS   7.9456 [ -2.1309;  18.0221]
Fonseca2019               AqET    CBT  -7.0956 [-14.8641;   0.6728]
Garcia2006                 CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Garcia-Martinez2012       MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Giannotti2014              McT   WlNi -12.9538 [-17.6261;  -8.2815]
Glasgow2017               ReET   WlNi -20.3620 [-28.6709; -12.0532]
Gomez-Hernandez2019       AeET   MiET  -2.6440 [-10.0565;   4.7685]
Gowans2001                AqET   WlNi -14.8091 [-21.9496;  -7.6686]
Hargrove2012             PlaSh   tDCS   4.3538 [ -6.9214;  15.6289]
Jones2002                  McT   ReET   7.4083 [ -1.4691;  16.2857]
Jones2012                  CBT    McT   5.2403 [ -0.1262;  10.6068]
Karatay2018                Acu  PlaSh -15.8224 [-24.9286;  -6.7162]
Kayo2012                  AeET   ReET   6.9266 [ -2.6708;  16.5241]
Kayo2012                  AeET   WlNi -13.4354 [-20.0894;  -6.7814]
Kayo2012                  ReET   WlNi -20.3620 [-28.6709; -12.0532]
King2002                   CBT    McT   5.2403 [ -0.1262;  10.6068]
Kurt2016                   Bal   MiET  -5.4063 [-16.3489;   5.5363]
Lami2018                   CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Lauche2016                MasT  PlaSh  -9.2572 [-20.9331;   2.4187]
Lopes-Rodrigues2012       AqET   FlET  -8.2679 [-16.4622;  -0.0736]
Lopes-Rodrigues2013       AqET   FlET  -8.2679 [-16.4622;  -0.0736]
Luciano2014                CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Lynch2012                  McT   WlNi -12.9538 [-17.6261;  -8.2815]
Mhalla2011               PlaSh   rTMS   7.9456 [ -2.1309;  18.0221]
Mist2018                   Acu    CBT -16.0434 [-28.2856;  -3.8012]
Olivares2011               WBV   WlNi -12.5886 [-22.1624;  -3.0148]
Paolucci2016               MfT  PlaSh -15.9827 [-26.9957;  -4.9697]
Paolucci2015              MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Parra-Delgado2013          CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Pereira-Pernambuco2018     McT   WlNi -12.9538 [-17.6261;  -8.2815]
Perez-Aranda2019           CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Picard2013                 CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Redondo2004                CBT   MiET   3.0779 [ -3.0300;   9.1858]
Richards2002              AeET    McT  -0.4816 [ -7.7410;   6.7777]
Rivera2018                 WBV   WlNi -12.5886 [-22.1624;  -3.0148]
Ruaro2014                  PbT  PlaSh -12.6000 [-31.7468;   6.5468]
Salaffi2015                McT   WlNi -12.9538 [-17.6261;  -8.2815]
Schachter2003             AeET   WlNi -13.4354 [-20.0894;  -6.7814]
Schmidt2011                CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Sevimli2015               AeET   AqET   1.3737 [ -6.2522;   8.9996]
Sevimli2015               AeET   MiET  -2.6440 [-10.0565;   4.7685]
Sevimli2015               AqET   MiET  -4.0177 [-12.0560;   4.0206]
Silva2019                  CBT   ReET  12.6486 [  3.8907;  21.4065]
Simister2018               CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Soares2002                 CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Sutbeyaz2009               MfT  PlaSh -15.9827 [-26.9957;  -4.9697]
Tomas-Carus2007b&c        AqET   WlNi -14.8091 [-21.9496;  -7.6686]
Ugurlu2017                 Acu  PlaSh -15.8224 [-24.9286;  -6.7162]
Valim2003                 AeET   FlET  -6.8942 [-15.7839;   1.9955]
Vallejo2015                CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Vas2016                    Acu  PlaSh -15.8224 [-24.9286;  -6.7162]
Verkaik2013                CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Wang2018                   McT   MiET  -2.1624 [ -8.2277;   3.9029]
Wicksell2013               CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Arakaki2021               FlET   ReET  13.8209 [  4.4199;  23.2218]
Atan2020                  MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Barranengoa-Cuadra2021     CBT   WlNi  -7.7135 [-11.9020;  -3.5249]
Ceballos-Laita2020         McT   MiET  -2.1624 [ -8.2277;   3.9029]
Coste2021                  Mnt  PlaSh  -4.0465 [-16.4852;   8.3922]
Izquierdo-Alventosa2020   MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Jamison2021               Elec  PlaSh -11.6670 [-24.5676;   1.2336]
Mingorance2021.2           WBV   WlNi -12.5886 [-22.1624;  -3.0148]
Rodriguez-Mansilla2021     McT   MiET  -2.1624 [ -8.2277;   3.9029]
Rodriguez-Mansilla2021    MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Rodriguez-Mansilla2021     McT   WlNi -12.9538 [-17.6261;  -8.2815]
Sarmento2020               McT  PlaSh  -5.0193 [-15.5979;   5.5593]
Udina-Cortés2020          Elec  PlaSh -11.6670 [-24.5676;   1.2336]
Lacroix2022              PlaSh   rTMS   7.9456 [ -2.1309;  18.0221]
Paolucci2022               CBT   MiET   3.0779 [ -3.0300;   9.1858]
Park2021                  FlET   ReET  13.8209 [  4.4199;  23.2218]
Samartin-Veiga2022       PlaSh   tDCS   4.3538 [ -6.9214;  15.6289]
Alptug2023                 Mnt   WlNi -11.9810 [-23.1959;  -0.7661]
Audoux2023                MasT    Mnt  -5.2106 [-17.9883;   7.5670]
Baelz2022                  Acu  PlaSh -15.8224 [-24.9286;  -6.7162]
Caumo2023                PlaSh   tDCS   4.3538 [ -6.9214;  15.6289]
Franco2023                AeET    Plt   7.7832 [ -4.6090;  20.1754]
Rodríguez-Mansilla2023    AeET    McT  -0.4816 [ -7.7410;   6.7777]
Rodríguez-Mansilla2023    AeET   WlNi -13.4354 [-20.0894;  -6.7814]
Rodríguez-Mansilla2023     McT   WlNi -12.9538 [-17.6261;  -8.2815]
Patru2021                  McT   MiET  -2.1624 [ -8.2277;   3.9029]
Patru2021                  McT   WlNi -12.9538 [-17.6261;  -8.2815]
Patru2021                 MiET   WlNi -10.7914 [-16.0339;  -5.5489]
Lee2024                    CBT    McT   5.2403 [ -0.1262;  10.6068]
Schulze2023               FlET   MasT  10.6505 [ -0.8340;  22.1349]
Schulze2023               MasT   WlNi -17.1916 [-27.1616;  -7.2217]
Schulze2023               FlET   WlNi  -6.5412 [-14.6940;   1.6117]

Number of studies: k = 99
Number of pairwise comparisons: m = 115
Number of observations: o = 6658
Number of treatments: n = 21
Number of designs: d = 47

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
            MD               95%-CI     z  p-value
Acu   -23.7569 [-35.9372; -11.5766] -3.82   0.0001
AeET  -13.4354 [-20.0894;  -6.7814] -3.96 < 0.0001
AqET  -14.8091 [-21.9496;  -7.6686] -4.06 < 0.0001
Bal   -16.1977 [-26.8461;  -5.5493] -2.98   0.0029
CBT    -7.7135 [-11.9020;  -3.5249] -3.61   0.0003
DryN  -24.7308 [-39.0871; -10.3745] -3.38   0.0007
Elec  -19.6014 [-36.0315;  -3.1714] -2.34   0.0194
FlET   -6.5412 [-14.6940;   1.6117] -1.57   0.1158
MasT  -17.1916 [-27.1616;  -7.2217] -3.38   0.0007
McT   -12.9538 [-17.6261;  -8.2815] -5.43 < 0.0001
MfT   -23.9171 [-38.9107;  -8.9236] -3.13   0.0018
MiET  -10.7914 [-16.0339;  -5.5489] -4.03 < 0.0001
Mnt   -11.9810 [-23.1959;  -0.7661] -2.09   0.0363
PbT   -20.5345 [-42.2167;   1.1478] -1.86   0.0634
PlaSh  -7.9345 [-18.1090;   2.2401] -1.53   0.1264
Plt   -21.2186 [-33.7539;  -8.6833] -3.32   0.0009
ReET  -20.3620 [-28.6709; -12.0532] -4.80 < 0.0001
rTMS  -15.8801 [-30.1998;  -1.5603] -2.17   0.0297
tDCS  -12.2882 [-27.4754;   2.8989] -1.59   0.1128
WBV   -12.5886 [-22.1624;  -3.0148] -2.58   0.0100
WlNi         .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 80.2482; tau = 8.9581; I^2 = 84.4% [81.3%; 87.0%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           557.76   87 < 0.0001
Within designs  298.03   53 < 0.0001
Between designs 259.74   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

---

Forest plot

# Forest plot
forest(nma_sr)

Forest plot of treatment effects for network

---

League table

# Pairwise comparison table with confidence intervals
netleague(nma_sr, ci = TRUE)

League table (random effects model):
                                                            
                           Acu                             .
 -10.3215 [-23.7606;   3.1177]                          AeET
  -8.9478 [-22.6198;   4.7242]   1.3737 [ -6.2522;   8.9996]
  -7.5592 [-23.4584;   8.3400]   2.7623 [ -9.1694;  14.6940]
 -16.0434 [-28.2856;  -3.8012]  -5.7219 [-13.1542;   1.7103]
   0.9739 [-17.1418;  19.0897]  11.2954 [ -4.2314;  26.8222]
  -4.1554 [-19.9462;  11.6354]   6.1660 [-11.1799;  23.5120]
 -17.2157 [-31.3905;  -3.0409]  -6.8942 [-15.7839;   1.9955]
  -6.5652 [-20.4581;   7.3276]   3.7562 [ -7.3930;  14.9055]
 -10.8031 [-23.3452;   1.7390]  -0.4816 [ -7.7410;   6.7777]
   0.1603 [-14.1299;  14.4504]  10.4817 [ -5.5102;  26.4736]
 -12.9655 [-25.5384;  -0.3926]  -2.6440 [-10.0565;   4.7685]
 -11.7759 [-26.3770;   2.8252]  -1.4544 [-14.1832;  11.2744]
  -3.2224 [-24.4243;  17.9795]   7.0991 [-15.2852;  29.4833]
 -15.8224 [-24.9286;  -6.7162]  -5.5009 [-17.0964;   6.0946]
  -2.5383 [-19.2119;  14.1353]   7.7832 [ -4.6090;  20.1754]
  -3.3948 [-17.7989;  11.0092]   6.9266 [ -2.6708;  16.5241]
  -7.8768 [-21.4584;   5.7047]   2.4447 [-12.9173;  17.8066]
 -11.4686 [-25.9618;   3.0246]  -1.1472 [-17.3207;  15.0264]
 -11.1682 [-26.6023;   4.2658]  -0.8468 [-12.4249;  10.7314]
 -23.7569 [-35.9372; -11.5766] -13.4354 [-20.0894;  -6.7814]
                                                            
                             .                             .
   2.7344 [ -8.6669;  14.1357]                             .
                          AqET  -1.8800 [-21.7155;  17.9555]
   1.3886 [-10.1255;  12.9027]                           Bal
  -7.0956 [-14.8641;   0.6728]  -8.4842 [-19.7220;   2.7536]
   9.9217 [ -5.7593;  25.6026]   8.5331 [ -9.2133;  26.2795]
   4.7923 [-12.7429;  22.3276]   3.4038 [-15.9179;  22.7254]
  -8.2679 [-16.4622;  -0.0736]  -9.6565 [-22.4282;   3.1152]
   2.3825 [ -8.8896;  13.6547]   0.9940 [-13.2642;  15.2521]
  -1.8553 [ -9.8614;   6.1507]  -3.2439 [-14.5977;   8.1099]
   9.1080 [ -7.0891;  25.3051]   7.7194 [-10.3965;  25.8354]
  -4.0177 [-12.0560;   4.0206]  -5.4063 [-16.3489;   5.5363]
  -2.8281 [-15.7840;  10.1278]  -4.2167 [-19.5208;  11.0875]
   5.7254 [-16.8059;  28.2566]   4.3368 [-19.6111;  28.2846]
  -6.8746 [-18.7515;   5.0022]  -8.2632 [-22.6472;   6.1208]
   6.4095 [ -6.0784;  18.8974]   5.0209 [-10.8604;  20.9023]
   5.5529 [ -4.3556;  15.4614]   4.1644 [ -9.0295;  17.3582]
   1.0710 [-14.5045;  16.6464]  -0.3176 [-17.8800;  17.2447]
  -2.5209 [-18.8973;  13.8556]  -3.9094 [-22.1859;  14.3670]
  -2.2205 [-14.1125;   9.6716]  -3.6090 [-17.8976;  10.6795]
 -14.8091 [-21.9496;  -7.6686] -16.1977 [-26.8461;  -5.5493]
                                                            
 -22.4000 [-42.5142;  -2.2858]                             .
                             .                             .
  13.6000 [ -5.9058;  33.1058]                             .
                             .                             .
                           CBT                             .
  17.0173 [  2.1550;  31.8796]                          DryN
  11.8880 [ -4.7273;  28.5032]  -5.1294 [-26.2026;  15.9439]
  -1.1723 [ -9.9533;   7.6088] -18.1896 [-34.1978;  -2.1814]
   9.4782 [ -1.0668;  20.0231]  -7.5392 [-22.0330;   6.9547]
   5.2403 [ -0.1262;  10.6068] -11.7770 [-26.7590;   3.2049]
  16.2037 [  1.0074;  31.3999]  -0.8137 [-20.7872;  19.1599]
   3.0779 [ -3.0300;   9.1858] -13.9394 [-29.0623;   1.1835]
   4.2675 [ -7.5121;  16.0472] -12.7498 [-30.1326;   4.6330]
  12.8210 [ -9.0019;  34.6439]  -4.1963 [-29.5785;  21.1858]
   0.2210 [-10.2499;  10.6919] -16.7963 [-33.4593;  -0.1333]
  13.5051 [  0.5474;  26.4629]  -3.5122 [-21.4686;  14.4442]
  12.6486 [  3.8907;  21.4065]  -4.3688 [-20.7455;  12.0080]
   8.1666 [ -6.3653;  22.6985]  -8.8507 [-28.3236;  10.6221]
   4.5748 [-10.8125;  19.9621] -12.4426 [-32.5618;   7.6767]
   4.8752 [ -5.5036;  15.2539] -12.1422 [-29.3838;   5.0994]
  -7.7135 [-11.9020;  -3.5249] -24.7308 [-39.0871; -10.3745]
                                                            
                             .                             .
                             .  -3.3100 [-23.2312;  16.6112]
                             . -12.1298 [-23.4179;  -0.8417]
                             .                             .
                             .                             .
                             .                             .
                          Elec                             .
 -13.0602 [-30.9717;   4.8512]                          FlET
  -2.4098 [-19.8096;  14.9900]  10.6505 [ -0.8340;  22.1349]
  -6.6477 [-23.3310;  10.0356]   6.4126 [ -2.5136;  15.3388]
   4.3157 [-12.6464;  21.2778]  17.3759 [  0.7723;  33.9796]
  -8.8100 [-25.4605;   7.8404]   4.2502 [ -4.9038;  13.4042]
  -7.6204 [-25.5410;  10.3002]   5.4398 [ -7.9928;  18.8724]
   0.9330 [-22.1543;  24.0204]  13.9933 [ -8.8320;  36.8186]
 -11.6670 [-24.5676;   1.2336]   1.3933 [-11.0323;  13.8188]
   1.6172 [-18.2471;  21.4814]  14.6774 [  1.0635;  28.2913]
   0.7606 [-17.3793;  18.9005]  13.8209 [  4.4199;  23.2218]
  -3.7214 [-20.0909;  12.6481]   9.3389 [ -6.6589;  25.3367]
  -7.3132 [-24.4467;   9.8203]   5.7471 [-11.0316;  22.5257]
  -7.0128 [-25.9791;  11.9535]   6.0474 [ -6.4792;  18.5741]
 -19.6014 [-36.0315;  -3.1714]  -6.5412 [-14.6940;   1.6117]
                                                            
                             .                             .
                             .   0.1970 [-12.8641;  13.2580]
                             .                             .
                             .                             .
                             .   6.6447 [ -2.3744;  15.6639]
 -23.8200 [-43.3554;  -4.2846]                             .
                             .                             .
  17.4400 [ -0.6246;  35.5046]                             .
                          MasT                             .
  -4.2379 [-14.9146;   6.4389]                           McT
   6.7255 [ -9.3248;  22.7758]  10.9634 [ -4.3073;  26.2340]
  -6.4002 [-17.2034;   4.4029]  -2.1624 [ -8.2277;   3.9029]
  -5.2106 [-17.9883;   7.5670]  -0.9728 [-12.8950;  10.9494]
   3.3428 [-19.0832;  25.7688]   7.5807 [-14.2941;  29.4555]
  -9.2572 [-20.9331;   2.4187]  -5.0193 [-15.5979;   5.5593]
   4.0270 [ -9.0700;  17.1239]   8.2648 [ -4.7436;  21.2732]
   3.1704 [ -9.2383;  15.5791]   7.4083 [ -1.4691;  16.2857]
  -1.3116 [-16.7344;  14.1112]   2.9263 [-11.6834;  17.5359]
  -4.9034 [-21.1347;  11.3279]  -0.6655 [-16.1263;  14.7953]
  -4.6030 [-18.3886;   9.1826]  -0.3651 [-10.7268;   9.9965]
 -17.1916 [-27.1616;  -7.2217] -12.9538 [-17.6261;  -8.2815]
                                                            
                             .                             .
                             .  -5.8609 [-18.9871;   7.2653]
                             . -28.0000 [-47.8250;  -8.1750]
                             .  -7.1000 [-25.3758;  11.1758]
                             .  -1.6076 [-16.7364;  13.5211]
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .   0.9154 [ -9.0914;  10.9223]
                           MfT                             .
 -13.1257 [-28.3605;   2.1090]                          MiET
 -11.9361 [-28.5496;   4.6774]   1.1896 [-10.8602;  13.2394]
  -3.3827 [-25.4708;  18.7055]   9.7431 [-12.1066;  31.5928]
 -15.9827 [-26.9957;  -4.9697]  -2.8569 [-13.3836;   7.6698]
  -2.6985 [-21.3921;  15.9951]  10.4272 [ -2.6533;  23.5077]
  -3.5551 [-20.4049;  13.2947]   9.5707 [  0.1525;  18.9888]
  -8.0371 [-22.9643;   6.8901]   5.0887 [ -9.4835;  19.6608]
 -11.6289 [-27.3901;   4.1323]   1.4968 [-13.9285;  16.9222]
 -11.3285 [-29.0649;   6.4079]   1.7972 [ -9.0372;  12.6317]
 -23.9171 [-38.9107;  -8.9236] -10.7914 [-16.0339;  -5.5489]
                                                            
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
 -10.3000 [-32.8073;  12.2073]                             .
                             .                             .
                             .                             .
                             .                             .
                           Mnt                             .
   8.5535 [-14.2790;  31.3859]                           PbT
  -4.0465 [-16.4852;   8.3922] -12.6000 [-31.7468;   6.5468]
   9.2376 [ -6.7395;  25.2147]   0.6841 [-23.7036;  25.0719]
   8.3811 [ -5.3604;  22.1225]  -0.1724 [-23.1774;  22.8325]
   3.8991 [-12.1090;  19.9071]  -4.6544 [-26.2908;  16.9820]
   0.3073 [-16.4812;  17.0957]  -8.2462 [-30.4662;  13.9738]
   0.6076 [-14.1119;  15.3272]  -7.9458 [-31.6079;  15.7162]
 -11.9810 [-23.1959;  -0.7661] -20.5345 [-42.2167;   1.1478]
                                                            
 -14.2857 [-24.1755;  -4.3958]                             .
                             .   4.5000 [-14.9579;  23.9579]
                             .   7.0000 [-13.1981;  27.1981]
                             .                             .
                             .                             .
                             .                             .
 -11.6670 [-24.5676;   1.2336]                             .
                             .                             .
  -6.6000 [-25.0340;  11.8340]   6.5600 [-12.1652;  25.2852]
 -18.0000 [-43.0698;   7.0698]                             .
 -15.9827 [-26.9957;  -4.9697]                             .
  -6.9300 [-25.6569;  11.7969]                             .
  -0.8000 [-20.0767;  18.4767]                             .
 -12.6000 [-31.7468;   6.5468]                             .
                         PlaSh                             .
  13.2841 [ -1.8210;  28.3892]                           Plt
  12.4276 [ -0.3250;  25.1802]  -0.8565 [-15.2507;  13.5376]
   7.9456 [ -2.1309;  18.0221]  -5.3385 [-23.4962;  12.8191]
   4.3538 [ -6.9214;  15.6289]  -8.9304 [-27.7796;   9.9189]
   4.6542 [ -9.2488;  18.5571]  -8.6300 [-24.3597;   7.0998]
  -7.9345 [-18.1090;   2.2401] -21.2186 [-33.7539;  -8.6833]
                                                            
                             .                             .
  -9.7400 [-30.2542;  10.7742]                             .
                             .                             .
                             .                             .
  25.7400 [  6.4117;  45.0683]                             .
                             .                             .
                             .                             .
  12.4601 [ -0.4961;  25.4162]                             .
                             .                             .
   5.5500 [-14.4548;  25.5548]                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .   7.9456 [ -2.1309;  18.0221]
                             .                             .
                          ReET                             .
  -4.4820 [-20.7351;  11.7711]                          rTMS
  -8.0738 [-25.0961;   8.9485]  -3.5918 [-18.7135;  11.5299]
  -7.7734 [-20.3831;   4.8362]  -3.2914 [-20.4620;  13.8791]
 -20.3620 [-28.6709; -12.0532] -15.8801 [-30.1998;  -1.5603]
                                                            
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .                             .
                             .   6.4100 [-15.2289;  28.0489]
                             .                             .
                             .                             .
                             .                             .
                             .                             .
   4.3538 [ -6.9214;  15.6289]                             .
                             .                             .
                             .                             .
                             .                             .
                          tDCS                             .
   0.3004 [-17.6000;  18.2007]                           WBV
 -12.2882 [-27.4754;   2.8989] -12.5886 [-22.1624;  -3.0148]
                              
                             .
 -12.0224 [-23.0503;  -0.9944]
  -7.3542 [-22.3103;   7.6020]
 -17.0236 [-32.9975;  -1.0496]
  -7.5411 [-12.5586;  -2.5237]
  -9.7000 [-28.4704;   9.0704]
                             .
 -15.6756 [-30.0616;  -1.2895]
 -33.6200 [-51.6438; -15.5962]
 -11.8545 [-17.9972;  -5.7119]
                             .
 -13.0721 [-20.1822;  -5.9619]
 -16.0919 [-30.8857;  -1.2980]
                             .
                             .
                             .
 -19.0313 [-31.7442;  -6.3184]
                             .
                             .
 -11.7869 [-21.7234;  -1.8504]
                          WlNi

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

---

Treatment ranking

# Treatment ranking
ranking_sr <- netrank(nma_sr, small.values = "good")
print(ranking_sr)

      P-score
Acu    0.8318
DryN   0.8308
MfT    0.8172
Plt    0.7486
ReET   0.7423
Elec   0.6733
PbT    0.6732
MasT   0.6101
Bal    0.5687
rTMS   0.5437
AqET   0.5160
AeET   0.4482
McT    0.4268
WBV    0.4133
tDCS   0.4014
Mnt    0.3847
MiET   0.3145
PlaSh  0.2023
CBT    0.1792
FlET   0.1610
WlNi   0.0130

---

Rankogram

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

Rankogram of treatments network

---

Inconsistency assessment

# Design decomposition
decomp_sr <- decomp.design(nma_sr)
print(decomp_sr)

Q statistics to assess homogeneity / consistency

                     Q df  p-value
Total           557.76 87 < 0.0001
Within designs  298.03 53 < 0.0001
Between designs 259.74 34 < 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
      WlNi:Mnt   3.66  1   0.0558
       CBT:McT   7.78  4   0.0999
     AqET:FlET   4.54  2   0.1033
    Elec:PlaSh   4.41  2   0.1101
 WlNi:McT:MiET   3.92  2   0.1407
      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 192.66 32 < 0.0001
       AeET:MiET 196.12 33 < 0.0001
  WlNi:FlET:MasT 194.55 32 < 0.0001
       DryN:MasT 211.60 33 < 0.0001
       WlNi:DryN 211.60 33 < 0.0001
        AqET:CBT 236.76 33 < 0.0001
  WlNi:AeET:ReET 236.44 32 < 0.0001
        CBT:ReET 244.83 33 < 0.0001
        McT:MiET 248.90 33 < 0.0001
        MasT:Plt 251.17 33 < 0.0001
        AeET:Plt 251.27 33 < 0.0001
       AqET:FlET 252.35 33 < 0.0001
        Bal:MiET 252.84 33 < 0.0001
       McT:PlaSh 255.78 33 < 0.0001
        AeET:McT 255.85 33 < 0.0001
       WlNi:AqET 256.15 33 < 0.0001
        WlNi:Bal 256.47 33 < 0.0001
        CBT:MiET 256.93 33 < 0.0001
      MiET:PlaSh 257.13 33 < 0.0001
      MasT:PlaSh 257.20 33 < 0.0001
       WlNi:MiET 257.42 33 < 0.0001
        WlNi:WBV 257.58 33 < 0.0001
        AqET:Bal 257.88 33 < 0.0001
       WlNi:ReET 258.09 33 < 0.0001
       AeET:AqET 258.35 33 < 0.0001
        WlNi:McT 258.63 33 < 0.0001
         Acu:CBT 258.84 33 < 0.0001
       Acu:PlaSh 258.84 33 < 0.0001
        WlNi:CBT 259.08 33 < 0.0001
       AeET:FlET 259.33 33 < 0.0001
       WlNi:AeET 259.37 33 < 0.0001
        McT:ReET 259.38 33 < 0.0001
   WlNi:AeET:McT 257.07 32 < 0.0001
        WlNi:Mnt 259.52 33 < 0.0001
        MasT:Mnt 259.64 33 < 0.0001
       Mnt:PlaSh 259.68 33 < 0.0001
        AqET:Plt 259.68 33 < 0.0001
    WlNi:McT:WBV 257.30 32 < 0.0001
       FlET:ReET 259.73 33 < 0.0001
         CBT:McT 259.73 33 < 0.0001
   WlNi:McT:MiET 257.64 32 < 0.0001
  WlNi:FlET:ReET 258.98 32 < 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 38.80 34  0.2622     8.4193     70.8843

---

Node-splitting

# 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 0.37 -16.0434 -22.4000 -12.3032 -10.0968 -0.78  0.4350
  Acu:PlaSh  4 0.85 -15.8224 -14.2857 -24.3825  10.0968  0.78  0.4350
  AeET:AqET  3 0.45   1.3737   2.7344   0.2722   2.4622  0.31  0.7530
  AeET:FlET  1 0.20  -6.8942  -3.3100  -7.7854   4.4754  0.39  0.6935
   AeET:McT  2 0.31  -0.4816   0.1970  -0.7850   0.9819  0.12  0.9025
  AeET:MiET  2 0.32  -2.6440  -5.8609  -1.1378  -4.7231 -0.58  0.5606
   AeET:Plt  1 0.41   7.7832   4.5000  10.0236  -5.5236 -0.43  0.6680
  AeET:ReET  1 0.22   6.9266  -9.7400  11.5968 -21.3368 -1.80  0.0716
  AeET:WlNi  3 0.36 -13.4354 -12.0224 -14.2443   2.2220  0.31  0.7528
   AqET:Bal  1 0.34   1.3886  -1.8800   3.0497  -4.9297 -0.40  0.6916
   AqET:CBT  1 0.16  -7.0956  13.6000 -10.9971  24.5971  2.27  0.0234
  AqET:FlET  3 0.53  -8.2679 -12.1298  -3.9657  -8.1641 -0.97  0.3296
  AqET:MiET  1 0.16  -4.0177 -28.0000   0.7007 -28.7007 -2.59  0.0095
   AqET:Plt  1 0.38   6.4095   7.0000   6.0441   0.9559  0.07  0.9419
  AqET:WlNi  2 0.23 -14.8091  -7.3542 -17.0100   9.6559  1.11  0.2662
   Bal:MiET  1 0.36  -5.4063  -7.1000  -4.4598  -2.6402 -0.23  0.8206
   Bal:WlNi  2 0.44 -16.1977 -17.0236 -15.5372  -1.4864 -0.14  0.8919
    CBT:McT  5 0.35   5.2403   6.6447   4.4705   2.1742  0.38  0.7041
   CBT:MiET  2 0.16   3.0779  -1.6076   3.9904  -5.5980 -0.66  0.5070
   CBT:ReET  1 0.21  12.6486  25.7400   9.2663  16.4737  1.49  0.1364
   CBT:WlNi 15 0.70  -7.7135  -7.5411  -8.1097   0.5686  0.12  0.9027
  DryN:MasT  1 0.55  -7.5392 -23.8200  12.3964 -36.2164 -2.44  0.0148
  DryN:WlNi  1 0.58 -24.7308  -9.7000 -45.9164  36.2164  2.44  0.0148
  FlET:MasT  1 0.40  10.6505  17.4400   6.0449  11.3951  0.95  0.3399
  FlET:ReET  3 0.53  13.8209  12.4601  15.3339  -2.8738 -0.30  0.7648
  FlET:WlNi  2 0.32  -6.5412 -15.6756  -2.2195 -13.4560 -1.51  0.1309
   MasT:Mnt  1 0.32  -5.2106 -10.3000  -2.7903  -7.5097 -0.54  0.5903
 MasT:PlaSh  1 0.40  -9.2572  -6.6000 -11.0374   4.4374  0.37  0.7150
   MasT:Plt  1 0.49   4.0270   6.5600   1.6010   4.9590  0.37  0.7107
  MasT:WlNi  1 0.31 -17.1916 -33.6200  -9.9487 -23.6713 -2.14  0.0320
   McT:MiET  4 0.37  -2.1624   0.9154  -3.9497   4.8651  0.76  0.4485
  McT:PlaSh  1 0.18  -5.0193 -18.0000  -2.2073 -15.7927 -1.12  0.2630
   McT:ReET  1 0.20   7.4083   5.5500   7.8640  -2.3140 -0.20  0.8390
    McT:WBV  1 0.23  -0.3651   6.4100  -2.3808   8.7908  0.70  0.4845
   McT:WlNi 10 0.58 -12.9538 -11.8545 -14.4629   2.6083  0.54  0.5890
 MiET:PlaSh  1 0.32  -2.8569  -6.9300  -0.9754  -5.9546 -0.52  0.6063
  MiET:WlNi  8 0.54 -10.7914 -13.0721  -8.0744  -4.9976 -0.93  0.3520
  Mnt:PlaSh  1 0.42  -4.0465  -0.8000  -6.3627   5.5627  0.43  0.6657
   Mnt:WlNi  2 0.57 -11.9810 -16.0919  -6.4264  -9.6655 -0.84  0.4037
  ReET:WlNi  3 0.43 -20.3620 -19.0313 -21.3544   2.3231  0.27  0.7863
   WBV:WlNi  4 0.93 -12.5886 -11.7869 -22.9734  11.1865  0.59  0.5547

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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr)

Forest plot of node-splitting for Network

---

Network heatmap

# Heatmap
netheat(nma_sr)

Heatmap of contribution matrix for Network

---

Funnel plot

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

Funnel plot for Network (Q | sh)

---

Q | Lg

# 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 = 11
Number of designs: d = 13
Number of networks: 2

Details on subnetworks: 
 subnetwork  k  m n
          1  2  2 3
          2 21 25 8

There are two sub-networks:

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

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

Tip

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

Note

Please: Select the treatment sub-networks before proceeding.

Subnet 1

Select the procedures performed

Important

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

Data preparation

# 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

---

Treatment exploration

# 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"

# Total number of treatments
length(trat_sr1)

[1] 3

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr1)

Forest plot of treatment effects for Subnet 1

---

League table

# 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)

---

Treatment ranking

# Treatment ranking
ranking_sr1 <- netrank(nma_sr1, small.values = "good")
print(ranking_sr1)

      P-score
rTMS   0.7629
MfT    0.6584
PlaSh  0.0786

---

Rankogram

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

Rankogram of treatments for Subnet 1

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr1)

Forest plot of node-splitting for Subnet 1

---

Network heatmap

# Heatmap
netheat(nma_sr1)

---

Funnel plot

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

Funnel plot for Subnet 1 (Q | Lg)

---

Subnet 2

Select the procedures performed

Important

The second subnet is more robust, containing 21 studies, 25 comparisons and 8 treatments. This is the main analysis network.

Data preparation

# 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()

---

Treatment exploration

# Unique treatments in subnet 2
unique_treat1_sr2 <- sr2$treat1 |> unique()
print(unique_treat1_sr2)

[1] "AeET" "AqET" "MiET" "ReET" "McT"  "CBT" 

unique_treat2_sr2 <- sr2$treat2 |> unique()
print(unique_treat2_sr2)

[1] "AqET" "WlNi" "ReET" "MiET" "McT"  "FlET"

# 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"

# Total number of treatments
length(trat_sr2)

[1] 8

---

Dataset preparation for NMA

# 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

---

Network Meta-Analysis model

# 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 = 8
Number of designs: d = 11

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
           MD               95%-CI     z  p-value
AeET -11.9057 [-21.3554;  -2.4559] -2.47   0.0135
AqET -14.0260 [-24.5379;  -3.5141] -2.62   0.0089
CBT  -13.2516 [-32.9879;   6.4847] -1.32   0.1882
FlET  -4.7187 [-25.4248;  15.9875] -0.45   0.6551
McT  -18.6264 [-31.4095;  -5.8434] -2.86   0.0043
MiET -23.6043 [-35.2382; -11.9704] -3.98 < 0.0001
ReET -10.0046 [-32.4988;  12.4897] -0.87   0.3834
WlNi        .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 134.7067; tau = 11.6063; I^2 = 88.8% [83.7%; 92.3%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           142.90   16 < 0.0001
Within designs   60.07   10 < 0.0001
Between designs  82.83    6 < 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

---

Network visualization

# 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)

---

Detailed results

# 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  12.3298     2         
Andrade2019              AqET   WlNi -14.6000 3.3374  12.0766     2         
Assis2006                AeET   AqET   4.4600 5.1075  12.6804     2         
Baptista2012             AeET   WlNi -17.6300 3.3515  12.0805     2         
Etnier2009               MiET   WlNi -25.1800 9.0950  14.7454     2         
Kayo2012                 AeET   ReET  -5.6500 6.0952  16.4960     3        *
Kayo2012                 AeET   WlNi -18.9200 4.8426  15.1468     3        *
Kayo2012                 ReET   WlNi -13.2700 5.1235  15.3956     3        *
Larsson2015               McT   MiET   4.9000 3.3376  12.0767     2         
Letieri2013              AqET   WlNi -24.2400 7.3707  13.7490     2         
Mannerkorpi2000           McT   WlNi -11.9400 4.6207  12.4923     2         
Mannerkorpi2004           McT   WlNi   1.8300 5.4792  12.8347     2         
Munguia-Izquierdo 2007   AqET   WlNi   0.4000 3.4557  12.1099     2         
Rooks2007                 CBT    McT   8.3000 3.6542  15.0381     3        *
Rooks2007                 CBT   MiET   4.7500 3.3682  14.8273     3        *
Rooks2007                 McT   MiET  -3.5500 2.7539  14.4553     3        *
Sanudo2010b              AeET   MiET   0.0000 3.7033  12.1828     2         
Sanudo2011               MiET   WlNi -64.8400 5.5331  12.8578     2         
Sanudo2010c              AeET   MiET  11.9900 5.8375  12.9917     2         
Schachter2003            AeET   WlNi  -2.3000 2.8448  11.9499     2         
Tomas-Carus2008          AqET   WlNi -11.9400 4.4726  12.4383     2         
Valim2003                AeET   FlET  -9.0900 4.1151  12.3142     2         
Wang2018                  McT   MiET -11.6700 3.5984  12.1513     2         
Hernando-Garijo2021      AeET   WlNi  -2.9000 6.1852  13.1516     2         
Saranya2022               CBT   FlET  -6.8100 1.6075  11.7171     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   2.1203 [ -9.7123;  13.9528]
Andrade2019              AqET   WlNi -14.0260 [-24.5379;  -3.5141]
Assis2006                AeET   AqET   2.1203 [ -9.7123;  13.9528]
Baptista2012             AeET   WlNi -11.9057 [-21.3554;  -2.4559]
Etnier2009               MiET   WlNi -23.6043 [-35.2382; -11.9704]
Kayo2012                 AeET   ReET  -1.9011 [-24.5317;  20.7296]
Kayo2012                 AeET   WlNi -11.9057 [-21.3554;  -2.4559]
Kayo2012                 ReET   WlNi -10.0046 [-32.4988;  12.4897]
Larsson2015               McT   MiET   4.9779 [ -6.6464;  16.6021]
Letieri2013              AqET   WlNi -14.0260 [-24.5379;  -3.5141]
Mannerkorpi2000           McT   WlNi -18.6264 [-31.4095;  -5.8434]
Mannerkorpi2004           McT   WlNi -18.6264 [-31.4095;  -5.8434]
Munguia-Izquierdo 2007   AqET   WlNi -14.0260 [-24.5379;  -3.5141]
Rooks2007                 CBT    McT   5.3748 [-13.6454;  24.3951]
Rooks2007                 CBT   MiET  10.3527 [ -8.2307;  28.9361]
Rooks2007                 McT   MiET   4.9779 [ -6.6464;  16.6021]
Sanudo2010b              AeET   MiET  11.6987 [ -0.3271;  23.7244]
Sanudo2011               MiET   WlNi -23.6043 [-35.2382; -11.9704]
Sanudo2010c              AeET   MiET  11.6987 [ -0.3271;  23.7244]
Schachter2003            AeET   WlNi -11.9057 [-21.3554;  -2.4559]
Tomas-Carus2008          AqET   WlNi -14.0260 [-24.5379;  -3.5141]
Valim2003                AeET   FlET  -7.1870 [-26.7224;  12.3484]
Wang2018                  McT   MiET   4.9779 [ -6.6464;  16.6021]
Hernando-Garijo2021      AeET   WlNi -11.9057 [-21.3554;  -2.4559]
Saranya2022               CBT   FlET  -8.5329 [-27.5784;  10.5125]

Number of studies: k = 21
Number of pairwise comparisons: m = 25
Number of observations: o = 1321
Number of treatments: n = 8
Number of designs: d = 11

Random effects model

Treatment estimate (sm = 'MD', comparison: other treatments vs 'WlNi'):
           MD               95%-CI     z  p-value
AeET -11.9057 [-21.3554;  -2.4559] -2.47   0.0135
AqET -14.0260 [-24.5379;  -3.5141] -2.62   0.0089
CBT  -13.2516 [-32.9879;   6.4847] -1.32   0.1882
FlET  -4.7187 [-25.4248;  15.9875] -0.45   0.6551
McT  -18.6264 [-31.4095;  -5.8434] -2.86   0.0043
MiET -23.6043 [-35.2382; -11.9704] -3.98 < 0.0001
ReET -10.0046 [-32.4988;  12.4897] -0.87   0.3834
WlNi        .                    .     .        .

Quantifying heterogeneity / inconsistency:
tau^2 = 134.7067; tau = 11.6063; I^2 = 88.8% [83.7%; 92.3%]

Tests of heterogeneity (within designs) and inconsistency (between designs):
                     Q d.f.  p-value
Total           142.90   16 < 0.0001
Within designs   60.07   10 < 0.0001
Between designs  82.83    6 < 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

---

Forest plot

# Forest plot
forest(nma_sr2)

Forest plot of treatment effects for Subnet 2

---

League table

# Pairwise comparison table with confidence intervals
netleague(nma_sr2, ci = TRUE)

League table (random effects model):
                                                            
                          AeET   6.3310 [-10.9948;  23.6568]
   2.1203 [ -9.7123;  13.9528]                          AqET
   1.3459 [-18.1630;  20.8549]  -0.7744 [-22.3878;  20.8391]
  -7.1870 [-26.7224;  12.3484]  -9.3073 [-31.5239;  12.9093]
   6.7208 [ -7.3745;  20.8160]   4.6005 [-11.3939;  20.5948]
  11.6987 [ -0.3271;  23.7244]   9.5784 [ -5.2222;  24.3789]
  -1.9011 [-24.5317;  20.7296]  -4.0214 [-28.2836;  20.2409]
 -11.9057 [-21.3554;  -2.4559] -14.0260 [-24.5379;  -3.5141]
                                                           
                             . -9.0900 [-33.2255;  15.0455]
                             .                            .
                           CBT -6.8100 [-29.7751;  16.1551]
  -8.5329 [-27.5784;  10.5125]                         FlET
   5.3748 [-13.6454;  24.3951] 13.9078 [ -7.6828;  35.4983]
  10.3527 [ -8.2307;  28.9361] 18.8857 [ -1.8952;  39.6665]
  -3.2470 [-32.3982;  25.9041]  5.2859 [-24.2307;  34.8025]
 -13.2516 [-32.9879;   6.4847] -4.7187 [-25.4248;  15.9875]
                                                            
                             .   5.6102 [-11.8076;  23.0279]
                             .                             .
   8.3000 [-15.5488;  32.1488]   4.7500 [-18.9365;  28.4365]
                             .                             .
                           McT  -3.4074 [-17.0443;  10.2294]
   4.9779 [ -6.6464;  16.6021]                          MiET
  -8.6219 [-34.0039;  16.7601] -13.5997 [-38.1779;  10.9784]
 -18.6264 [-31.4095;  -5.8434] -23.6043 [-35.2382; -11.9704]
                                                            
  -5.6500 [-31.3441;  20.0441] -10.5282 [-22.6928;   1.6365]
                             . -11.9070 [-24.1978;   0.3839]
                             .                             .
                             .                             .
                             .  -5.2411 [-22.7867;  12.3044]
                             . -47.7095 [-66.7033; -28.7156]
                          ReET -13.2700 [-38.1358;  11.5958]
 -10.0046 [-32.4988;  12.4897]                          WlNi

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

---

Treatment ranking

# Treatment ranking
ranking_sr2 <- netrank(nma_sr2, small.values = "good")
print(ranking_sr2)

     P-score
MiET  0.9078
McT   0.7273
AqET  0.5673
CBT   0.5365
AeET  0.4765
ReET  0.4369
FlET  0.2582
WlNi  0.0895

---

Rankogram

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

Rankogram of treatments for Subnet 2

---

Inconsistency assessment

# Design decomposition
decomp_sr2 <- decomp.design(nma_sr2)
print(decomp_sr2)

Q statistics to assess homogeneity / consistency

                     Q df  p-value
Total           142.90 16 < 0.0001
Within designs   60.07 10 < 0.0001
Between designs  82.83  6 < 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  9.70  5   0.0843
        WlNi:McT 62.24  5 < 0.0001
       AeET:MiET 78.31  5 < 0.0001
       AeET:AqET 78.47  5 < 0.0001
       WlNi:AqET 78.47  5 < 0.0001
        McT:MiET 79.86  5 < 0.0001
       WlNi:AeET 80.25  5 < 0.0001
       AeET:FlET 82.08  5 < 0.0001
        CBT:FlET 82.08  5 < 0.0001
    CBT:McT:MiET 79.01  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 15.55  6  0.0164     9.6818     93.7369

---

Node-splitting

# 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   2.1203   6.3310  -1.5603   7.8914  0.65  0.5143
  AeET:FlET 1 0.66  -7.1870  -9.0900  -3.5718  -5.5182 -0.26  0.7924
  AeET:MiET 2 0.48  11.6987   5.6102  17.2449 -11.6348 -0.95  0.3436
  AeET:ReET 1 0.78  -1.9011  -5.6500  11.0682 -16.7182 -0.60  0.5459
  AeET:WlNi 4 0.60 -11.9057 -10.5282 -14.0019   3.4737  0.35  0.7245
  AqET:WlNi 4 0.73 -14.0260 -11.9070 -19.7983   7.8914  0.65  0.5143
   CBT:FlET 1 0.69  -8.5329  -6.8100 -12.3282   5.5182  0.26  0.7924
    CBT:McT 1 0.64   5.3748   8.3000   0.2626   8.0374  0.40  0.6903
   CBT:MiET 1 0.62  10.3527   4.7500  19.3225 -14.5725 -0.75  0.4547
   McT:MiET 3 0.73   4.9779  -3.4074  27.2637 -30.6712 -2.30  0.0212
   McT:WlNi 2 0.53 -18.6264  -5.2411 -33.7693  28.5282  2.18  0.0290
  MiET:WlNi 2 0.38 -23.6043 -47.7095  -9.1310 -38.5785 -3.15  0.0017
  ReET:WlNi 1 0.82 -10.0046 -13.2700   4.7060 -17.9760 -0.60  0.5459

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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr2)

Forest plot of node-splitting for Subnet 2

---

Network heatmap

# Heatmap
netheat(nma_sr2)

Heatmap of contribution matrix for Subnet 2

---

Funnel plot

# 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.

A | Lg

# 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.

Subnet 1

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.

Data preparation

# 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()

---

Treatment exploration

# 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"

# Total number of treatments
length(trat_sr1_alg)

[1] 8

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_sr1_alg$studlab))

[1] 25

---

Network Meta-Analysis model

# 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

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr1_alg)

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

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 1 (A | Lg)

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr1_alg)

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

---

Network heatmap

# Heatmap
netheat(nma_sr1_alg)

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

---

Funnel plot

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

Funnel plot for Subnet 1 (A | Lg)

---

Subnet 2

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.

Data preparation

# 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

---

Treatment exploration

# 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"

# Total number of treatments
length(trat_sr2_alg)

[1] 2

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_sr2_alg$studlab))

[1] 1

---

Network Meta-Analysis model

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Subnet 3

Select the procedures performed

Important

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

Data preparation

# 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

---

Treatment exploration

# 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"

# Total number of treatments
length(trat_sr3_alg)

[1] 4

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_sr3_alg$studlab))

[1] 4

---

Network Meta-Analysis model

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr3_alg)

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

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 3 (A | Lg)

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr3_alg)

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

---

Network heatmap

# Heatmap
netheat(nma_sr3_alg)

---

Funnel plot

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

Funnel plot for Subnet 3 (A | Lg)

---

A | Im

# 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.

Data preparation

# 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()

---

Treatment exploration

# 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" 

# Total number of treatments
length(trat_sr_aim)

[1] 8

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_sr_aim$studlab))

[1] 25

---

Network Meta-Analysis model

# 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

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr_aim)

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

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 1 (A | Im)

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr_aim)

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

---

Network heatmap

# Heatmap
netheat(nma_sr_aim)

---

Funnel plot

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

Funnel plot for Network (A | Im)

---

A | Sh

# 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.

Data preparation

# 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()

---

Treatment exploration

# 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" 

# Total number of treatments
length(trat_sr_ash)

[1] 22

---

Dataset preparation for NMA

# 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

# Number of unique studies
length(unique(pw_sr_ash$studlab))

[1] 119

---

Network Meta-Analysis model

# 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

# 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

---

Network visualization

# 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)

---

Detailed results

# 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

---

Forest plot

# Forest plot
forest(nma_sr_ash)

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

---

League table

# 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)

---

Treatment ranking

# 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

---

Rankogram

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

Rankogram of treatments for Subnet 1 (A | Sh)

---

Inconsistency assessment

# 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

---

Node-splitting

# 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)

---

Forest plot of node-splitting

# Forest plot of node-splitting
forest(split_sr_ash)

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

---

Network heatmap

# Heatmap
netheat(nma_sr_ash)

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

---

Funnel plot

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

Funnel plot for Network (A | Sh)

---