library(netmeta)
## Loading required package: meta
## Loading 'meta' package (version 4.8-4).
## Type 'help(meta)' for a brief overview.
## Loading 'netmeta' package (version 0.9-6).
## Type 'help(netmeta-package)' for a brief overview.
data(Senn2013)
data15 <- Senn2013
data15
## TE seTE treat1 treat2 studlab
## 1 -1.90 0.1414 metf plac DeFronzo1995
## 2 -0.82 0.0992 metf plac Lewin2007
## 3 -0.20 0.3579 metf acar Willms1999
## 4 -1.34 0.1435 rosi plac Davidson2007
## 5 -1.10 0.1141 rosi plac Wolffenbuttel1999
## 6 -1.30 0.1268 piog plac Kipnes2001
## 7 -0.77 0.1078 rosi plac Kerenyi2004
## 8 0.16 0.0849 piog metf Hanefeld2004
## 9 0.10 0.1831 piog rosi Derosa2004
## 10 -1.30 0.1014 rosi plac Baksi2004
## 11 -1.09 0.2263 rosi plac Rosenstock2008
## 12 -1.50 0.1624 rosi plac Zhu2003
## 13 -0.14 0.2239 rosi metf Yang2003
## 14 -1.20 0.1436 rosi sulf Vongthavaravat2002
## 15 -0.40 0.1549 acar sulf Oyama2008
## 16 -0.80 0.1432 acar plac Costa1997
## 17 -0.57 0.1291 sita plac Hermansen2007
## 18 -0.70 0.1273 vild plac Garber2008
## 19 -0.37 0.1184 metf sulf Alex1998
## 20 -0.74 0.1839 migl plac Johnston1994
## 21 -1.41 0.2235 migl plac Johnston1998a
## 22 0.00 0.2339 rosi metf Kim2007
## 23 -0.68 0.2828 migl plac Johnston1998b
## 24 -0.40 0.4356 metf plac Gonzalez-Ortiz2004
## 25 -0.23 0.3467 benf plac Stucci1996
## 26 -1.01 0.1366 benf plac Moulin2006
## 27 -1.20 0.3758 metf plac Willms1999
## 28 -1.00 0.4669 acar plac Willms1999
help("Senn2013")
## starting httpd help server ...
## done
willms <- data.frame(treatment=c("metf", "acar", "plac"),
n=c(29, 31, 29),
mean=c(-2.5, -2.3, -1.3),
sd=c(0.862, 1.782, 1.831),
stringsAsFactors=FALSE)
willms
## treatment n mean sd
## 1 metf 29 -2.5 0.862
## 2 acar 31 -2.3 1.782
## 3 plac 29 -1.3 1.831
comp12 <- metacont(n[1], mean[1], sd[1], n[2], mean[2], sd[2], data=willms, sm="MD")
comp13 <- metacont(n[1], mean[1], sd[1], n[3], mean[3], sd[3], data=willms, sm="MD")
comp23 <- metacont(n[2], mean[2], sd[2], n[3], mean[3], sd[3], data=willms, sm="MD")
TE <- c(comp12$TE, comp13$TE, comp23$TE)
seTE <- c(comp12$seTE, comp13$seTE, comp23$seTE)
treat1 <- c(willms$treatment[1], willms$treatment[1], willms$treatment[2])
treat2 <- c(willms$treatment[2], willms$treatment[3], willms$treatment[3])
data.frame(TE, seTE=round(seTE, 4), treat1, treat2, studlab="Willms1999")
## TE seTE treat1 treat2 studlab
## 1 -0.2 0.3579 metf acar Willms1999
## 2 -1.2 0.3758 metf plac Willms1999
## 3 -1.0 0.4669 acar plac Willms1999
args(netmeta)
## function (TE, seTE, treat1, treat2, studlab, data = NULL, subset = NULL,
## sm, level = 0.95, level.comb = 0.95, comb.fixed = TRUE, comb.random = !is.null(tau.preset),
## prediction = FALSE, level.predict = 0.95, reference.group = "",
## baseline.reference = TRUE, all.treatments = NULL, seq = NULL,
## tau.preset = NULL, tol.multiarm = 5e-04, details.chkmultiarm = FALSE,
## sep.trts = ":", title = "", warn = TRUE)
## NULL
mn0 <- netmeta(TE, seTE, treat1, treat2, data=data15)
## Warning in netmeta(TE, seTE, treat1, treat2, data = data15): No information
## given for argument 'studlab'. Assuming that comparisons are from
## independent studies.
## Warning: Note, treatments within a comparison have been re-sorted in
## increasing order.
mn0
## Original data:
##
## treat1 treat2 TE seTE
## 1 metf plac -1.90 0.1414
## 2 metf plac -0.82 0.0992
## 3 acar metf 0.20 0.3579
## 4 plac rosi 1.34 0.1435
## 5 plac rosi 1.10 0.1141
## 6 piog plac -1.30 0.1268
## 7 plac rosi 0.77 0.1078
## 8 metf piog -0.16 0.0849
## 9 piog rosi 0.10 0.1831
## 10 plac rosi 1.30 0.1014
## 11 plac rosi 1.09 0.2263
## 12 plac rosi 1.50 0.1624
## 13 metf rosi 0.14 0.2239
## 14 rosi sulf -1.20 0.1436
## 15 acar sulf -0.40 0.1549
## 16 acar plac -0.80 0.1432
## 17 plac sita 0.57 0.1291
## 18 plac vild 0.70 0.1273
## 19 metf sulf -0.37 0.1184
## 20 migl plac -0.74 0.1839
## 21 migl plac -1.41 0.2235
## 22 metf rosi 0.00 0.2339
## 23 migl plac -0.68 0.2828
## 24 metf plac -0.40 0.4356
## 25 benf plac -0.23 0.3467
## 26 benf plac -1.01 0.1366
## 27 metf plac -1.20 0.3758
## 28 acar plac -1.00 0.4669
##
## Number of treatment arms (by study):
## narms
## 1 2
## 2 2
## 3 2
## 4 2
## 5 2
## 6 2
## 7 2
## 8 2
## 9 2
## 10 2
## 11 2
## 12 2
## 13 2
## 14 2
## 15 2
## 16 2
## 17 2
## 18 2
## 19 2
## 20 2
## 21 2
## 22 2
## 23 2
## 24 2
## 25 2
## 26 2
## 27 2
## 28 2
##
## Results (fixed effect model):
##
## treat1 treat2 95%-CI Q leverage
## 1 metf plac -1.1148 [-1.2312; -0.9984] 30.84 0.18
## 2 metf plac -1.1148 [-1.2312; -0.9984] 8.83 0.36
## 3 acar metf 0.2803 [ 0.0604; 0.5001] 0.05 0.10
## 4 plac rosi 1.2022 [ 1.1088; 1.2955] 0.92 0.11
## 5 plac rosi 1.2022 [ 1.1088; 1.2955] 0.80 0.17
## 6 piog plac -1.0669 [-1.2154; -0.9184] 3.38 0.36
## 7 plac rosi 1.2022 [ 1.1088; 1.2955] 16.07 0.20
## 8 metf piog -0.0479 [-0.1847; 0.0888] 1.74 0.68
## 9 piog rosi 0.1353 [-0.0250; 0.2955] 0.04 0.20
## 10 plac rosi 1.2022 [ 1.1088; 1.2955] 0.93 0.22
## 11 plac rosi 1.2022 [ 1.1088; 1.2955] 0.25 0.04
## 12 plac rosi 1.2022 [ 1.1088; 1.2955] 3.36 0.09
## 13 metf rosi 0.0873 [-0.0450; 0.2197] 0.06 0.09
## 14 rosi sulf -0.7604 [-0.9404; -0.5804] 9.37 0.41
## 15 acar sulf -0.3928 [-0.6120; -0.1736] 0.00 0.52
## 16 acar plac -0.8346 [-1.0423; -0.6268] 0.06 0.55
## 17 plac sita 0.5700 [ 0.3170; 0.8230] 0.00 1.00
## 18 plac vild 0.7000 [ 0.4505; 0.9495] 0.00 1.00
## 19 metf sulf -0.6731 [-0.8461; -0.5000] 6.55 0.56
## 20 migl plac -0.9439 [-1.1927; -0.6952] 1.23 0.48
## 21 migl plac -0.9439 [-1.1927; -0.6952] 4.35 0.32
## 22 metf rosi 0.0873 [-0.0450; 0.2197] 0.14 0.08
## 23 migl plac -0.9439 [-1.1927; -0.6952] 0.87 0.20
## 24 metf plac -1.1148 [-1.2312; -0.9984] 2.69 0.02
## 25 benf plac -0.9052 [-1.1543; -0.6561] 3.79 0.13
## 26 benf plac -0.9052 [-1.1543; -0.6561] 0.59 0.87
## 27 metf plac -1.1148 [-1.2312; -0.9984] 0.05 0.02
## 28 acar plac -0.8346 [-1.0423; -0.6268] 0.13 0.05
##
## Number of studies: k = 28
## Number of treatments: n = 10
## Number of pairwise comparisons: m = 28
## Number of designs: d = 15
##
## Fixed effect model
##
## Treatment estimate (sm = ''):
## acar benf metf migl piog plac rosi sita
## acar . 0.0706 0.2803 0.1094 0.2323 -0.8346 0.3676 -0.2646
## benf -0.0706 . 0.2096 0.0387 0.1617 -0.9052 0.2970 -0.3352
## metf -0.2803 -0.2096 . -0.1709 -0.0479 -1.1148 0.0873 -0.5448
## migl -0.1094 -0.0387 0.1709 . 0.1230 -0.9439 0.2582 -0.3739
## piog -0.2323 -0.1617 0.0479 -0.1230 . -1.0669 0.1353 -0.4969
## plac 0.8346 0.9052 1.1148 0.9439 1.0669 . 1.2022 0.5700
## rosi -0.3676 -0.2970 -0.0873 -0.2582 -0.1353 -1.2022 . -0.6322
## sita 0.2646 0.3352 0.5448 0.3739 0.4969 -0.5700 0.6322 .
## sulf 0.3928 0.4634 0.6731 0.5022 0.6251 -0.4418 0.7604 0.1282
## vild 0.1346 0.2052 0.4148 0.2439 0.3669 -0.7000 0.5022 -0.1300
## sulf vild
## acar -0.3928 -0.1346
## benf -0.4634 -0.2052
## metf -0.6731 -0.4148
## migl -0.5022 -0.2439
## piog -0.6251 -0.3669
## plac 0.4418 0.7000
## rosi -0.7604 -0.5022
## sita -0.1282 0.1300
## sulf . 0.2582
## vild -0.2582 .
##
## Lower 95%-confidence limit:
## acar benf metf migl piog plac rosi sita
## acar . -0.2537 0.0604 -0.2147 -0.0120 -1.0423 0.1481 -0.5920
## benf -0.3950 . -0.0653 -0.3133 -0.1283 -1.1543 0.0309 -0.6903
## metf -0.5001 -0.4846 . -0.4455 -0.1847 -1.2312 -0.0450 -0.8233
## migl -0.4335 -0.3908 -0.1037 . -0.1667 -1.1927 -0.0075 -0.7287
## piog -0.4767 -0.4517 -0.0888 -0.4127 . -1.2154 -0.0250 -0.7903
## plac 0.6268 0.6561 0.9984 0.6952 0.9184 . 1.1088 0.3170
## rosi -0.5870 -0.5630 -0.2197 -0.5239 -0.2955 -1.2955 . -0.9019
## sita -0.0628 -0.0199 0.2663 0.0191 0.2035 -0.8230 0.3624 .
## sulf 0.1736 0.1568 0.5000 0.1959 0.4163 -0.6205 0.5804 -0.1816
## vild -0.1901 -0.1474 0.1395 -0.1084 0.0765 -0.9495 0.2357 -0.4854
## sulf vild
## acar -0.6120 -0.4592
## benf -0.7700 -0.5577
## metf -0.8461 -0.6901
## migl -0.8085 -0.5962
## piog -0.8339 -0.6573
## plac 0.2630 0.4505
## rosi -0.9404 -0.7686
## sita -0.4381 -0.2254
## sulf . -0.0487
## vild -0.5652 .
##
## Upper 95%-confidence limit:
## acar benf metf migl piog plac rosi sita sulf
## acar . 0.3950 0.5001 0.4335 0.4767 -0.6268 0.5870 0.0628 -0.1736
## benf 0.2537 . 0.4846 0.3908 0.4517 -0.6561 0.5630 0.0199 -0.1568
## metf -0.0604 0.0653 . 0.1037 0.0888 -0.9984 0.2197 -0.2663 -0.5000
## migl 0.2147 0.3133 0.4455 . 0.4127 -0.6952 0.5239 -0.0191 -0.1959
## piog 0.0120 0.1283 0.1847 0.1667 . -0.9184 0.2955 -0.2035 -0.4163
## plac 1.0423 1.1543 1.2312 1.1927 1.2154 . 1.2955 0.8230 0.6205
## rosi -0.1481 -0.0309 0.0450 0.0075 0.0250 -1.1088 . -0.3624 -0.5804
## sita 0.5920 0.6903 0.8233 0.7287 0.7903 -0.3170 0.9019 . 0.1816
## sulf 0.6120 0.7700 0.8461 0.8085 0.8339 -0.2630 0.9404 0.4381 .
## vild 0.4592 0.5577 0.6901 0.5962 0.6573 -0.4505 0.7686 0.2254 0.0487
## vild
## acar 0.1901
## benf 0.1474
## metf -0.1395
## migl 0.1084
## piog -0.0765
## plac 0.9495
## rosi -0.2357
## sita 0.4854
## sulf 0.5652
## vild .
##
## Quantifying heterogeneity / inconsistency:
## tau^2 = 0.1063; I^2 = 80.4%
##
## Tests of heterogeneity (within designs) and inconsistency (between designs):
## Q d.f. p-value
## Total 97.09 19 < 0.0001
## Within designs 74.64 13 < 0.0001
## Between designs 22.45 6 0.0010
mn1 <- netmeta(TE, seTE, treat1, treat2, studlab, data=data15, sm="MD")
## Warning: Note, treatments within a comparison have been re-sorted in
## increasing order.
netgraph(mn1, seq=c("plac", "benf", "migl", "acar", "sulf", "metf", "rosi", "piog", "sita", "vild"))
print(mn1, digits=2)
## Original data (with adjusted standard errors for multi-arm studies):
##
## treat1 treat2 TE seTE seTE.adj narms multiarm
## DeFronzo1995 metf plac -1.90 0.14 0.14 2
## Lewin2007 metf plac -0.82 0.10 0.10 2
## Willms1999 acar metf 0.20 0.36 0.39 3 *
## Davidson2007 plac rosi 1.34 0.14 0.14 2
## Wolffenbuttel1999 plac rosi 1.10 0.11 0.11 2
## Kipnes2001 piog plac -1.30 0.13 0.13 2
## Kerenyi2004 plac rosi 0.77 0.11 0.11 2
## Hanefeld2004 metf piog -0.16 0.08 0.08 2
## Derosa2004 piog rosi 0.10 0.18 0.18 2
## Baksi2004 plac rosi 1.30 0.10 0.10 2
## Rosenstock2008 plac rosi 1.09 0.23 0.23 2
## Zhu2003 plac rosi 1.50 0.16 0.16 2
## Yang2003 metf rosi 0.14 0.22 0.22 2
## Vongthavaravat2002 rosi sulf -1.20 0.14 0.14 2
## Oyama2008 acar sulf -0.40 0.15 0.15 2
## Costa1997 acar plac -0.80 0.14 0.14 2
## Hermansen2007 plac sita 0.57 0.13 0.13 2
## Garber2008 plac vild 0.70 0.13 0.13 2
## Alex1998 metf sulf -0.37 0.12 0.12 2
## Johnston1994 migl plac -0.74 0.18 0.18 2
## Johnston1998a migl plac -1.41 0.22 0.22 2
## Kim2007 metf rosi 0.00 0.23 0.23 2
## Johnston1998b migl plac -0.68 0.28 0.28 2
## Gonzalez-Ortiz2004 metf plac -0.40 0.44 0.44 2
## Stucci1996 benf plac -0.23 0.35 0.35 2
## Moulin2006 benf plac -1.01 0.14 0.14 2
## Willms1999 metf plac -1.20 0.38 0.41 3 *
## Willms1999 acar plac -1.00 0.47 0.82 3 *
##
## Number of treatment arms (by study):
## narms
## Alex1998 2
## Baksi2004 2
## Costa1997 2
## Davidson2007 2
## DeFronzo1995 2
## Derosa2004 2
## Garber2008 2
## Gonzalez-Ortiz2004 2
## Hanefeld2004 2
## Hermansen2007 2
## Johnston1994 2
## Johnston1998a 2
## Johnston1998b 2
## Kerenyi2004 2
## Kim2007 2
## Kipnes2001 2
## Lewin2007 2
## Moulin2006 2
## Oyama2008 2
## Rosenstock2008 2
## Stucci1996 2
## Vongthavaravat2002 2
## Willms1999 3
## Wolffenbuttel1999 2
## Yang2003 2
## Zhu2003 2
##
## Results (fixed effect model):
##
## treat1 treat2 MD 95%-CI Q leverage
## DeFronzo1995 metf plac -1.11 [-1.23; -1.00] 30.89 0.18
## Lewin2007 metf plac -1.11 [-1.23; -1.00] 8.79 0.36
## Willms1999 acar metf 0.29 [ 0.06; 0.51] 0.05 0.09
## Davidson2007 plac rosi 1.20 [ 1.11; 1.30] 0.93 0.11
## Wolffenbuttel1999 plac rosi 1.20 [ 1.11; 1.30] 0.80 0.17
## Kipnes2001 piog plac -1.07 [-1.22; -0.92] 3.39 0.36
## Kerenyi2004 plac rosi 1.20 [ 1.11; 1.30] 16.05 0.20
## Hanefeld2004 metf piog -0.05 [-0.18; 0.09] 1.75 0.68
## Derosa2004 piog rosi 0.14 [-0.02; 0.30] 0.04 0.20
## Baksi2004 plac rosi 1.20 [ 1.11; 1.30] 0.94 0.22
## Rosenstock2008 plac rosi 1.20 [ 1.11; 1.30] 0.24 0.04
## Zhu2003 plac rosi 1.20 [ 1.11; 1.30] 3.37 0.09
## Yang2003 metf rosi 0.09 [-0.04; 0.22] 0.05 0.09
## Vongthavaravat2002 rosi sulf -0.76 [-0.94; -0.58] 9.29 0.41
## Oyama2008 acar sulf -0.39 [-0.61; -0.17] 0.01 0.53
## Costa1997 acar plac -0.83 [-1.04; -0.61] 0.04 0.57
## Hermansen2007 plac sita 0.57 [ 0.32; 0.82] 0.00 1.00
## Garber2008 plac vild 0.70 [ 0.45; 0.95] 0.00 1.00
## Alex1998 metf sulf -0.67 [-0.85; -0.50] 6.62 0.56
## Johnston1994 migl plac -0.94 [-1.19; -0.70] 1.23 0.48
## Johnston1998a migl plac -0.94 [-1.19; -0.70] 4.35 0.32
## Kim2007 metf rosi 0.09 [-0.04; 0.22] 0.14 0.08
## Johnston1998b migl plac -0.94 [-1.19; -0.70] 0.87 0.20
## Gonzalez-Ortiz2004 metf plac -1.11 [-1.23; -1.00] 2.69 0.02
## Stucci1996 benf plac -0.91 [-1.15; -0.66] 3.79 0.13
## Moulin2006 benf plac -0.91 [-1.15; -0.66] 0.59 0.87
## Willms1999 metf plac -1.11 [-1.23; -1.00] 0.04 0.02
## Willms1999 acar plac -0.83 [-1.04; -0.61] 0.04 0.02
##
## Number of studies: k = 26
## Number of treatments: n = 10
## Number of pairwise comparisons: m = 28
## Number of designs: d = 15
##
## Fixed effect model
##
## Treatment estimate (sm = 'MD'):
## acar benf metf migl piog plac rosi sita sulf vild
## acar . 0.08 0.29 0.12 0.24 -0.83 0.37 -0.26 -0.39 -0.13
## benf -0.08 . 0.21 0.04 0.16 -0.91 0.30 -0.34 -0.47 -0.21
## metf -0.29 -0.21 . -0.17 -0.05 -1.11 0.09 -0.54 -0.67 -0.41
## migl -0.12 -0.04 0.17 . 0.12 -0.94 0.26 -0.37 -0.50 -0.24
## piog -0.24 -0.16 0.05 -0.12 . -1.07 0.14 -0.50 -0.63 -0.37
## plac 0.83 0.91 1.11 0.94 1.07 . 1.20 0.57 0.44 0.70
## rosi -0.37 -0.30 -0.09 -0.26 -0.14 -1.20 . -0.63 -0.76 -0.50
## sita 0.26 0.34 0.54 0.37 0.50 -0.57 0.63 . -0.13 0.13
## sulf 0.39 0.47 0.67 0.50 0.63 -0.44 0.76 0.13 . 0.26
## vild 0.13 0.21 0.41 0.24 0.37 -0.70 0.50 -0.13 -0.26 .
##
## Lower 95%-confidence limit:
## acar benf metf migl piog plac rosi sita sulf vild
## acar . -0.25 0.06 -0.21 -0.01 -1.04 0.15 -0.59 -0.61 -0.46
## benf -0.41 . -0.07 -0.31 -0.13 -1.15 0.03 -0.69 -0.77 -0.56
## metf -0.51 -0.48 . -0.44 -0.18 -1.23 -0.04 -0.82 -0.85 -0.69
## migl -0.44 -0.39 -0.10 . -0.17 -1.19 -0.01 -0.73 -0.81 -0.60
## piog -0.49 -0.45 -0.09 -0.41 . -1.22 -0.02 -0.79 -0.84 -0.66
## plac 0.61 0.66 1.00 0.70 0.92 . 1.11 0.32 0.26 0.45
## rosi -0.60 -0.56 -0.22 -0.52 -0.30 -1.30 . -0.90 -0.94 -0.77
## sita -0.07 -0.02 0.27 0.02 0.20 -0.82 0.36 . -0.44 -0.23
## sulf 0.17 0.16 0.50 0.20 0.42 -0.62 0.58 -0.18 . -0.05
## vild -0.20 -0.15 0.14 -0.11 0.08 -0.95 0.24 -0.49 -0.57 .
##
## Upper 95%-confidence limit:
## acar benf metf migl piog plac rosi sita sulf vild
## acar . 0.41 0.51 0.44 0.49 -0.61 0.60 0.07 -0.17 0.20
## benf 0.25 . 0.48 0.39 0.45 -0.66 0.56 0.02 -0.16 0.15
## metf -0.06 0.07 . 0.10 0.09 -1.00 0.22 -0.27 -0.50 -0.14
## migl 0.21 0.31 0.44 . 0.41 -0.70 0.52 -0.02 -0.20 0.11
## piog 0.01 0.13 0.18 0.17 . -0.92 0.30 -0.20 -0.42 -0.08
## plac 1.04 1.15 1.23 1.19 1.22 . 1.30 0.82 0.62 0.95
## rosi -0.15 -0.03 0.04 0.01 0.02 -1.11 . -0.36 -0.58 -0.24
## sita 0.59 0.69 0.82 0.73 0.79 -0.32 0.90 . 0.18 0.49
## sulf 0.61 0.77 0.85 0.81 0.84 -0.26 0.94 0.44 . 0.57
## vild 0.46 0.56 0.69 0.60 0.66 -0.45 0.77 0.23 0.05 .
##
## Quantifying heterogeneity / inconsistency:
## tau^2 = 0.1087; I^2 = 81.4%
##
## Tests of heterogeneity (within designs) and inconsistency (between designs):
## Q d.f. p-value
## Total 96.99 18 < 0.0001
## Within designs 74.46 11 < 0.0001
## Between designs 22.53 7 0.0021
mn1$n
## [1] 10
mn1$m
## [1] 28
mean(mn1$leverage.fixed)
## [1] 0.3214286
(mn1$n-1)/mn1$m
## [1] 0.3214286
print(summary(mn1))
## Number of studies: k = 26
## Number of treatments: n = 10
## Number of pairwise comparisons: m = 28
## Number of designs: d = 15
##
## Fixed effect model
##
## Treatment estimate (sm = 'MD'):
## acar benf metf migl piog plac rosi sita
## acar . 0.0778 0.2867 0.1166 0.2391 -0.8274 0.3745 -0.2574
## benf -0.0778 . 0.2089 0.0387 0.1612 -0.9052 0.2967 -0.3352
## metf -0.2867 -0.2089 . -0.1702 -0.0477 -1.1141 0.0877 -0.5441
## migl -0.1166 -0.0387 0.1702 . 0.1225 -0.9439 0.2579 -0.3739
## piog -0.2391 -0.1612 0.0477 -0.1225 . -1.0664 0.1354 -0.4964
## plac 0.8274 0.9052 1.1141 0.9439 1.0664 . 1.2018 0.5700
## rosi -0.3745 -0.2967 -0.0877 -0.2579 -0.1354 -1.2018 . -0.6318
## sita 0.2574 0.3352 0.5441 0.3739 0.4964 -0.5700 0.6318 .
## sulf 0.3879 0.4657 0.6746 0.5044 0.6269 -0.4395 0.7623 0.1305
## vild 0.1274 0.2052 0.4141 0.2439 0.3664 -0.7000 0.5018 -0.1300
## sulf vild
## acar -0.3879 -0.1274
## benf -0.4657 -0.2052
## metf -0.6746 -0.4141
## migl -0.5044 -0.2439
## piog -0.6269 -0.3664
## plac 0.4395 0.7000
## rosi -0.7623 -0.5018
## sita -0.1305 0.1300
## sulf . 0.2605
## vild -0.2605 .
##
## Lower 95%-confidence limit:
## acar benf metf migl piog plac rosi sita
## acar . -0.2497 0.0622 -0.2107 -0.0094 -1.0401 0.1506 -0.5879
## benf -0.4054 . -0.0662 -0.3133 -0.1288 -1.1543 0.0306 -0.6903
## metf -0.5113 -0.4841 . -0.4450 -0.1845 -1.2309 -0.0449 -0.8228
## migl -0.4438 -0.3908 -0.1046 . -0.1673 -1.1927 -0.0078 -0.7287
## piog -0.4876 -0.4513 -0.0891 -0.4123 . -1.2151 -0.0249 -0.7899
## plac 0.6147 0.6561 0.9973 0.6952 0.9178 . 1.1084 0.3170
## rosi -0.5983 -0.5627 -0.2203 -0.5236 -0.2957 -1.2953 . -0.9016
## sita -0.0732 -0.0199 0.2654 0.0191 0.2030 -0.8230 0.3621 .
## sulf 0.1662 0.1588 0.5011 0.1978 0.4178 -0.6188 0.5820 -0.1796
## vild -0.2005 -0.1474 0.1386 -0.1084 0.0760 -0.9495 0.2354 -0.4854
## sulf vild
## acar -0.6095 -0.4552
## benf -0.7726 -0.5577
## metf -0.8482 -0.6896
## migl -0.8111 -0.5962
## piog -0.8361 -0.6569
## plac 0.2602 0.4505
## rosi -0.9427 -0.7683
## sita -0.4406 -0.2254
## sulf . -0.0467
## vild -0.5677 .
##
## Upper 95%-confidence limit:
## acar benf metf migl piog plac rosi sita sulf
## acar . 0.4054 0.5113 0.4438 0.4876 -0.6147 0.5983 0.0732 -0.1662
## benf 0.2497 . 0.4841 0.3908 0.4513 -0.6561 0.5627 0.0199 -0.1588
## metf -0.0622 0.0662 . 0.1046 0.0891 -0.9973 0.2203 -0.2654 -0.5011
## migl 0.2107 0.3133 0.4450 . 0.4123 -0.6952 0.5236 -0.0191 -0.1978
## piog 0.0094 0.1288 0.1845 0.1673 . -0.9178 0.2957 -0.2030 -0.4178
## plac 1.0401 1.1543 1.2309 1.1927 1.2151 . 1.2953 0.8230 0.6188
## rosi -0.1506 -0.0306 0.0449 0.0078 0.0249 -1.1084 . -0.3621 -0.5820
## sita 0.5879 0.6903 0.8228 0.7287 0.7899 -0.3170 0.9016 . 0.1796
## sulf 0.6095 0.7726 0.8482 0.8111 0.8361 -0.2602 0.9427 0.4406 .
## vild 0.4552 0.5577 0.6896 0.5962 0.6569 -0.4505 0.7683 0.2254 0.0467
## vild
## acar 0.2005
## benf 0.1474
## metf -0.1386
## migl 0.1084
## piog -0.0760
## plac 0.9495
## rosi -0.2354
## sita 0.4854
## sulf 0.5677
## vild .
##
## Quantifying heterogeneity / inconsistency:
## tau^2 = 0.1087; I^2 = 81.4%
##
## Tests of heterogeneity (within designs) and inconsistency (between designs):
## Q d.f. p-value
## Total 96.99 18 < 0.0001
## Within designs 74.46 11 < 0.0001
## Between designs 22.53 7 0.0021
netgraph(mn1, start="random", iterate=TRUE, col="darkgray", cex=1.5, multiarm=FALSE,
points=TRUE, col.points="green", cex.points=3)
netgraph(mn1, start="circle", iterate=TRUE, col="darkgray", cex=1.5,
points=TRUE, col.points="black", cex.points=3, col.multiarm="gray")
netgraph(mn1, start="circle", iterate=TRUE, col="darkgray", cex=1.5,
points=TRUE, col.points="black", cex.points=3, col.multiarm="gray", allfigures=TRUE)
summary(mn1, ref="plac")
## Number of studies: k = 26
## Number of treatments: n = 10
## Number of pairwise comparisons: m = 28
## Number of designs: d = 15
##
## Fixed effect model
##
## Treatment estimate (sm = 'MD', comparison: other treatments vs 'plac'):
## MD 95%-CI
## acar -0.8274 [-1.0401; -0.6147]
## benf -0.9052 [-1.1543; -0.6561]
## metf -1.1141 [-1.2309; -0.9973]
## migl -0.9439 [-1.1927; -0.6952]
## piog -1.0664 [-1.2151; -0.9178]
## plac . .
## rosi -1.2018 [-1.2953; -1.1084]
## sita -0.5700 [-0.8230; -0.3170]
## sulf -0.4395 [-0.6188; -0.2602]
## vild -0.7000 [-0.9495; -0.4505]
##
## Quantifying heterogeneity / inconsistency:
## tau^2 = 0.1087; I^2 = 81.4%
##
## Tests of heterogeneity (within designs) and inconsistency (between designs):
## Q d.f. p-value
## Total 96.99 18 < 0.0001
## Within designs 74.46 11 < 0.0001
## Between designs 22.53 7 0.0021
forest(mn1, ref="plac")
forest(mn1, xlim=c(-1.5, 1), ref="plac", leftlabs="Contrast to Placebo", xlab="HbA1c difference")
forest(mn1, xlim=c(-1.5, 1), ref="plac", leftlabs="Contrast to placebo", xlab="HbA1c difference", pooled="random")
round(decomp.design(mn1)$Q.decomp, 3)
## Q df pval
## Total 96.986 18 0.000
## Within designs 74.455 11 0.000
## Between designs 22.530 7 0.002
print(decomp.design(mn1)$Q.het.design, digits=2)
## design Q df pval
## 1 acar:plac 0.00 0 NA
## 2 acar:sulf 0.00 0 NA
## 3 benf:plac 4.38 1 3.6e-02
## 4 metf:piog 0.00 0 NA
## 5 metf:plac 42.16 2 7.0e-10
## 6 metf:rosi 0.19 1 6.7e-01
## 7 metf:sulf 0.00 0 NA
## 8 migl:plac 6.45 2 4.0e-02
## 9 piog:plac 0.00 0 NA
## 10 piog:rosi 0.00 0 NA
## 11 plac:rosi 21.27 5 7.2e-04
## 12 plac:sita 0.00 0 NA
## 13 plac:vild 0.00 0 NA
## 14 rosi:sulf 0.00 0 NA
## 15 acar:metf:plac 0.00 0 NA
round(decomp.design(mn1)$Q.inc.random, 3)
## Q df pval tau.within
## Between designs 2.194 7 0.948 0.38
netheat(mn1)
round(decomp.design(mn1)$Q.inc.design, 2)
## acar:plac acar:sulf benf:plac metf:piog metf:plac
## 0.04 0.01 0.00 1.75 0.20
## metf:rosi metf:sulf migl:plac piog:plac piog:rosi
## 0.01 6.62 0.00 3.39 0.04
## plac:rosi plac:sita plac:vild rosi:sulf acar:metf:plac
## 1.05 0.00 0.00 9.29 0.01
## acar:metf:plac
## 0.13
netheat(mn1, random=TRUE)
set.seed(123)
fe <- mn1$TE.nma.fixed
re <- mn1$TE.nma.random
plot(jitter((fe+re)/2, 5), jitter(fe-re, 5), xlim=c(-1.2, 1.2),
ylim=c(-0.25, 0.25), xlab="Mean treatment effect (in fixed effect and random effects model)", ylab="Difference of treatment effect (fixed effect minus random effects model)")
abline(h=0)
summary(mn1$seTE.nma.random / mn1$seTE.nma.fixed)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.826 2.265 2.588 2.502 2.681 3.231