data1 <- read.csv("data1.csv")
str(data1)
## 'data.frame': 17 obs. of 8 variables:
## $ author: Factor w/ 17 levels "Aishwarya","Anarkalli",..: 4 6 5 2 3 8 7 13 14 16 ...
## $ year : int 1998 1999 2007 1993 1994 1994 1997 2006 2008 1997 ...
## $ Ne : int 23 21 14 21 18 13 11 14 19 25 ...
## $ Me : num 23.5 17.5 22.3 16.9 18.8 ...
## $ Se : num 11.7 15.3 14.5 12.9 11.5 19.1 16.5 19.2 12.6 14.2 ...
## $ Nc : int 16 25 13 16 18 23 11 14 15 16 ...
## $ Mc : num 21.3 21.4 31.4 23.6 29.9 ...
## $ Sc : num 22.2 17.3 21.3 16.5 18.3 ...
data1
## author year Ne Me Se Nc Mc Sc
## 1 Bill 1998 23 23.54 11.70 16 21.33 22.22
## 2 Dick 1999 21 17.50 15.30 25 21.43 17.32
## 3 Chawla 2007 14 22.30 14.50 13 31.43 21.32
## 4 Anarkalli 1993 21 16.90 12.90 16 23.65 16.54
## 5 Biaggi 1994 18 18.80 11.50 18 29.88 18.32
## 6 Lundwig 1994 13 15.30 19.10 23 35.43 17.65
## 7 Dulquer 1997 11 14.90 16.50 11 29.87 18.43
## 8 Nivin 2006 14 24.56 19.20 14 45.44 16.32
## 9 Pauly 2008 19 18.60 12.60 15 43.67 18.43
## 10 Salmaan 1997 25 13.56 14.20 16 29.65 12.21
## 11 Aishwarya 1994 11 14.44 11.54 16 41.27 20.01
## 12 Rajesh 1993 14 19.32 9.21 21 38.65 12.07
## 13 Meena 1995 12 14.00 11.65 17 31.49 15.32
## 14 Mohanlal 1985 13 13.30 11.54 21 38.32 14.27
## 15 Mammooty 1999 11 13.50 19.43 10 45.67 18.54
## 16 Manju 2000 10 19.50 8.54 12 43.21 11.54
## 17 Warrier 2003 9 13.10 9.67 12 32.10 7.86
library(meta)
## Loading 'meta' package (version 4.8-4).
## Type 'help(meta)' for a brief overview.
m <- metacont(Ne, Me, Se, Nc, Mc, Sc,
studlab=paste(author, year),
data=data1)
m
## MD 95%-CI %W(fixed) %W(random)
## Bill 1998 2.2100 [ -9.6813; 14.1013] 4.2 5.3
## Dick 1999 -3.9300 [-13.3595; 5.4995] 6.6 6.5
## Chawla 2007 -9.1300 [-22.9866; 4.7266] 3.1 4.5
## Anarkalli 1993 -6.7500 [-16.5542; 3.0542] 6.2 6.3
## Biaggi 1994 -11.0800 [-21.0725; -1.0875] 5.9 6.2
## Lundwig 1994 -20.1300 [-32.7724; -7.4876] 3.7 5.0
## Dulquer 1997 -14.9700 [-29.5883; -0.3517] 2.8 4.2
## Nivin 2006 -20.8800 [-34.0797; -7.6803] 3.4 4.8
## Pauly 2008 -25.0700 [-35.9826; -14.1574] 5.0 5.8
## Salmaan 1997 -16.0900 [-24.2617; -7.9183] 8.9 7.1
## Aishwarya 1994 -26.8300 [-38.7732; -14.8868] 4.1 5.3
## Rajesh 1993 -19.3300 [-26.3957; -12.2643] 11.8 7.8
## Meena 1995 -17.4900 [-27.3126; -7.6674] 6.1 6.3
## Mohanlal 1985 -25.0200 [-33.7722; -16.2678] 7.7 6.8
## Mammooty 1999 -32.1700 [-48.4145; -15.9255] 2.2 3.7
## Manju 2000 -23.7100 [-32.1152; -15.3048] 8.4 7.0
## Warrier 2003 -19.0000 [-26.7259; -11.2741] 9.9 7.4
##
## Number of studies combined: k = 17
##
## MD 95%-CI z p-value
## Fixed effect model -17.0477 [-19.4791; -14.6163] -13.74 < 0.0001
## Random effects model -16.8843 [-20.8045; -12.9641] -8.44 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 38.5732; H = 1.57 [1.20; 2.05]; I^2 = 59.3% [30.5%; 76.1%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 39.29 16 0.0010
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
forest(m, xlab="difference in outcome measure")
MD <- with(data1[1,], Me - Mc)
seMD <- with(data1[1,], sqrt(Se^2/Ne + Sc^2/Nc))
round(c(MD, MD + c(-1,1) * qnorm(1-(0.05/2)) * seMD), 2)
## [1] 2.21 -9.68 14.10
with(data1[1, ],
print(metacont(Ne, Me, Se, Nc, Mc, Sc),
digits=2))
## MD 95%-CI z p-value
## 2.21 [-9.68; 14.10] 0.36 0.7157
##
## Details:
## - Inverse variance method
print(metacont(Ne, Me, Se, Nc, Mc, Sc, data=data1, subset=1), digits=2)
## MD 95%-CI z p-value
## 2.21 [-9.68; 14.10] 0.36 0.7157
##
## Details:
## - Inverse variance method
zscore <- MD/seMD
zscore
## [1] 0.3642594
data2 <- read.csv("data2.csv")
data2
## author Ne Me Se Nc Mc Sc
## 1 Balram 11 6.50 11.21 19 13.50 5.43
## 2 Shane 16 10.00 12.32 15 21.00 6.56
## 3 Neela 14 14.90 6.75 12 22.40 12.32
## 4 Kepler 16 15.10 4.56 14 17.60 10.43
## 5 Sunny 17 13.90 11.21 55 19.20 11.23
## 6 Leone 11 9.40 9.67 36 13.20 10.45
## 7 Antonio 12 21.60 16.78 17 23.50 12.34
## 8 Bilal 11 13.50 9.21 17 14.00 7.90
## 9 Bagra 15 5.40 4.56 49 -10.40 6.54
## 10 Jackson 15 28.10 5.43 26 19.40 2.34
## 11 Taylor 13 11.90 9.43 43 16.50 8.76
## 12 Anton 14 10.11 4.21 25 5.43 1.23
## 13 Dickson 17 8.88 2.13 24 13.43 12.34
## 14 Damon 11 17.50 0.54 65 16.54 6.56
## 15 Dogg 19 13.21 7.43 58 -7.65 8.76
## 16 Dice 12 -10.40 17.30 23 56.78 19.87
## 17 Digg 14 9.32 10.32 21 11.23 12.54
N <- with(data2[1,], Ne + Nc)
SMD <- with(data2[1,],
(1 - 3/(4 * N - 9)) * (Me - Mc) /
sqrt(((Ne - 1) * Se^2 + (Nc - 1) * Sc^2)/(N - 2)))
seSMD <- with(data2[1,],
sqrt(N/(Ne * Nc) + SMD^2/(2 * (N - 3.94))))
round(c(SMD, SMD + c(-1,1) * qnorm(1-(0.05/2)) * seSMD), 2)
## [1] -0.85 -1.63 -0.07
print(metacont(Ne, Me, Se, Nc, Mc, Sc, sm="SMD",
data=data2, subset=1), digits=2)
## SMD 95%-CI z p-value
## -0.85 [-1.63; -0.07] -2.15 0.0317
##
## Details:
## - Inverse variance method
## - Hedges' g (bias corrected standardised mean difference)
MD <- with(data1, Me - Mc)
varMD <- with(data1, Se^2/Ne + Sc^2/Nc)
weight <- 1/varMD
round(weighted.mean(MD, weight), 4)
## [1] -17.0477
round(1/sum(weight), 4)
## [1] 1.539
mc1 <- metacont(Ne, Me, Se, Nc, Mc, Sc,
data=data1,
studlab=paste(author, year))
round(c(mc1$TE.fixed, mc1$seTE.fixed^2), 4)
## [1] -17.0477 1.5390
mc1
## MD 95%-CI %W(fixed) %W(random)
## Bill 1998 2.2100 [ -9.6813; 14.1013] 4.2 5.3
## Dick 1999 -3.9300 [-13.3595; 5.4995] 6.6 6.5
## Chawla 2007 -9.1300 [-22.9866; 4.7266] 3.1 4.5
## Anarkalli 1993 -6.7500 [-16.5542; 3.0542] 6.2 6.3
## Biaggi 1994 -11.0800 [-21.0725; -1.0875] 5.9 6.2
## Lundwig 1994 -20.1300 [-32.7724; -7.4876] 3.7 5.0
## Dulquer 1997 -14.9700 [-29.5883; -0.3517] 2.8 4.2
## Nivin 2006 -20.8800 [-34.0797; -7.6803] 3.4 4.8
## Pauly 2008 -25.0700 [-35.9826; -14.1574] 5.0 5.8
## Salmaan 1997 -16.0900 [-24.2617; -7.9183] 8.9 7.1
## Aishwarya 1994 -26.8300 [-38.7732; -14.8868] 4.1 5.3
## Rajesh 1993 -19.3300 [-26.3957; -12.2643] 11.8 7.8
## Meena 1995 -17.4900 [-27.3126; -7.6674] 6.1 6.3
## Mohanlal 1985 -25.0200 [-33.7722; -16.2678] 7.7 6.8
## Mammooty 1999 -32.1700 [-48.4145; -15.9255] 2.2 3.7
## Manju 2000 -23.7100 [-32.1152; -15.3048] 8.4 7.0
## Warrier 2003 -19.0000 [-26.7259; -11.2741] 9.9 7.4
##
## Number of studies combined: k = 17
##
## MD 95%-CI z p-value
## Fixed effect model -17.0477 [-19.4791; -14.6163] -13.74 < 0.0001
## Random effects model -16.8843 [-20.8045; -12.9641] -8.44 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 38.5732; H = 1.57 [1.20; 2.05]; I^2 = 59.3% [30.5%; 76.1%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 39.29 16 0.0010
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
forest(mc1)
mc1$w.fixed[1]
## [1] 0.0271667
sum(mc1$w.fixed)
## [1] 0.6497859
round(100*mc1$w.fixed[1] / sum(mc1$w.fixed), 2)
## [1] 4.18
forest(mc1, comb.random=FALSE, xlab= "Difference in mean response",
xlim=c(-50,10), xlab.pos=-20, smlab.pos=-20)
mc1.gen <- metagen(mc1$TE, mc1$seTE, sm="MD")
mc1.gen <- metagen(TE, seTE, data=mc1, sm="MD")
c(mc1$TE.fixed, mc1$TE.random)
## [1] -17.04771 -16.88430
c(mc1.gen$TE.fixed, mc1.gen$TE.random)
## [1] -17.04771 -16.88430
N <- with(data2, Ne + Nc)
SMD <- with(data2,
(1 - 3/(4 * N - 9)) * (Me - Mc)/
sqrt(((Ne - 1) * Se^2 + (Nc - 1) * Sc^2)/(N - 2)))
varSMD <- with(data2,
N/(Ne * Nc) + SMD^2/(2 * (N - 3.94)))
weight <- 1/varSMD
round(weighted.mean(SMD, weight), 4)
## [1] 0.1119
round(1/sum(weight), 4)
## [1] 0.0077
mc2 <- metacont(Ne, Me, Se, Nc, Mc, Sc, sm="SMD",
data=data2)
round(c(mc2$TE.fixed, mc2$seTE.fixed^2), 4)
## [1] 0.1119 0.0077
print(summary(mc2), digits=2)
## Number of studies combined: k = 17
##
## SMD 95%-CI z p-value
## Fixed effect model 0.11 [-0.06; 0.28] 1.28 0.2022
## Random effects model 0.05 [-0.58; 0.67] 0.15 0.8794
##
## Quantifying heterogeneity:
## tau^2 = 1.5904; H = 3.62 [3.05; 4.28]; I^2 = 92.4% [89.3%; 94.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 209.37 16 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Hedges' g (bias corrected standardised mean difference)
mc2.hk <- metacont(Ne, Me, Se, Nc, Mc, Sc, sm="SMD",
data=data2, comb.fixed=FALSE,
hakn=TRUE)
mc2.hk
## SMD 95%-CI %W(random)
## 1 -0.8525 [-1.6302; -0.0747] 5.8
## 2 -1.0752 [-1.8356; -0.3147] 5.9
## 3 -0.7482 [-1.5502; 0.0539] 5.8
## 4 -0.3098 [-1.0320; 0.4124] 5.9
## 5 -0.4671 [-1.0166; 0.0825] 6.1
## 6 -0.3634 [-1.0430; 0.3162] 6.0
## 7 -0.1290 [-0.8688; 0.6108] 5.9
## 8 -0.0576 [-0.8162; 0.7010] 5.9
## 9 2.5384 [ 1.8031; 3.2736] 5.9
## 10 2.2725 [ 1.4531; 3.0920] 5.8
## 11 -0.5089 [-1.1369; 0.1191] 6.0
## 12 1.7075 [ 0.9408; 2.4742] 5.8
## 13 -0.4660 [-1.0963; 0.1643] 6.0
## 14 0.1557 [-0.4838; 0.7952] 6.0
## 15 2.4410 [ 1.7890; 3.0930] 6.0
## 16 -3.4454 [-4.5505; -2.3403] 5.3
## 17 -0.1593 [-0.8367; 0.5181] 6.0
##
## Number of studies combined: k = 17
##
## SMD 95%-CI t p-value
## Random effects model 0.0484 [-0.7082; 0.8050] 0.14 0.8938
##
## Quantifying heterogeneity:
## tau^2 = 1.5904; H = 3.62 [3.05; 4.28]; I^2 = 92.4% [89.3%; 94.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 209.37 16 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference)
mc2.hk <- metagen(TE, seTE, data=mc2, comb.fixed=FALSE,
hakn=TRUE)
print(summary(mc2.hk), digits=2)
## Number of studies combined: k = 17
##
## 95%-CI t p-value
## Random effects model 0.05 [-0.71; 0.81] 0.14 0.8938
##
## Quantifying heterogeneity:
## tau^2 = 1.5904; H = 3.62 [3.05; 4.28]; I^2 = 92.4% [89.3%; 94.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 209.37 16 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Hartung-Knapp adjustment for random effects model
print(summary(mc1, prediction=TRUE), digits=2)
## Number of studies combined: k = 17
##
## MD 95%-CI z p-value
## Fixed effect model -17.05 [-19.48; -14.62] -13.74 < 0.0001
## Random effects model -16.88 [-20.80; -12.96] -8.44 < 0.0001
## Prediction interval [-30.79; -2.98]
##
## Quantifying heterogeneity:
## tau^2 = 38.5732; H = 1.57 [1.20; 2.05]; I^2 = 59.3% [30.5%; 76.1%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 39.29 16 0.0010
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
forest(mc1, prediction=TRUE, col.predict="black")
data3 <- read.csv("data3.csv")
data3
## author year Ne Me Se Nc Mc Sc duration
## 1 Lorenzo "1999" 43 0.84 4.56 26 2.31 5.41 <= 6 months
## 2 Faiman "1989" 35 0.45 0.18 30 1.56 1.22 <= 6 months
## 3 Matthew "2001" 54 0.28 0.35 200 0.96 0.56 <= 6 months
## 4 Lines "1992" 23 0.19 0.28 40 0.43 0.66 <= 6 months
## 5 Carl "1989" 76 0.12 0.54 68 0.25 0.32 <= 6 months
## 6 Ragazan "2005" 123 0.21 2.11 220 0.18 0.08 > 6 months
## 7 Daniel "1995" 321 0.45 0.14 128 0.96 0.21 > 6 months
## 8 Radcliffe "2004" 78 0.71 0.24 109 1.54 0.26 > 6 months
## 9 Emma "1991" 124 0.28 1.12 21 0.21 0.32 > 6 months
## 10 Stone "2012" 342 0.42 1.21 239 0.15 0.54 > 6 months
## 11 Stephen "1997" 37 0.18 0.96 42 0.22 0.87 > 6 months
## 12 Walters "1982" 76 0.64 0.43 68 0.10 0.32 > 6 months
## 13 Shanika "2011" 43 0.13 0.23 73 0.18 0.12 > 6 months
## 14 Gillespie "2009" 213 0.04 1.08 118 0.12 0.72 > 6 months
## 15 Brian "1993" 87 0.08 1.00 82 0.08 0.48 > 6 months
## 16 Bond "2001" 92 0.24 1.54 88 0.54 0.36 > 6 months
## 17 Heath "2007" 114 0.12 0.34 156 0.78 0.44 > 6 months
## 18 Bottle "1985" 58 0.08 4.32 56 0.65 0.24 > 6 months
## 19 Billington "1998" 129 0.05 0.36 192 0.12 0.51 > 6 months
## 20 Rachel "2005" 234 0.16 2.34 126 0.14 0.12 > 6 months
## 21 Blow "2017" 34 0.24 3.21 154 0.99 0.44 > 6 months
## 22 Amanda "2016" 89 0.24 0.65 88 0.28 0.31 > 6 months
## 23 Butz "2015" 57 0.15 0.45 48 0.36 0.33 > 6 months
mc3 <- metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3,
studlab=paste(author, year))
mc3
## MD 95%-CI %W(fixed) %W(random)
## Lorenzo "1999" -1.4700 [-3.9564; 1.0164] 0.0 0.4
## Faiman "1989" -1.1100 [-1.5506; -0.6694] 0.3 3.8
## Matthew "2001" -0.6800 [-0.8014; -0.5586] 4.0 5.1
## Lines "1992" -0.2400 [-0.4744; -0.0056] 1.1 4.8
## Carl "1989" -0.1300 [-0.2733; 0.0133] 2.9 5.1
## Ragazan "2005" 0.0300 [-0.3430; 0.4030] 0.4 4.2
## Daniel "1995" -0.5100 [-0.5495; -0.4705] 38.2 5.2
## Radcliffe "2004" -0.8300 [-0.9022; -0.7578] 11.4 5.2
## Emma "1991" 0.0700 [-0.1700; 0.3100] 1.0 4.7
## Stone "2012" 0.2700 [ 0.1246; 0.4154] 2.8 5.0
## Stephen "1997" -0.0400 [-0.4461; 0.3661] 0.4 4.0
## Walters "1982" 0.5400 [ 0.4170; 0.6630] 3.9 5.1
## Shanika "2011" -0.0500 [-0.1241; 0.0241] 10.8 5.2
## Gillespie "2009" -0.0800 [-0.2747; 0.1147] 1.6 4.9
## Brian "1993" 0.0000 [-0.2344; 0.2344] 1.1 4.8
## Bond "2001" -0.3000 [-0.6235; 0.0235] 0.6 4.4
## Heath "2007" -0.6600 [-0.7531; -0.5669] 6.9 5.2
## Bottle "1985" -0.5700 [-1.6836; 0.5436] 0.0 1.6
## Billington "1998" -0.0700 [-0.1652; 0.0252] 6.6 5.2
## Rachel "2005" 0.0200 [-0.2805; 0.3205] 0.7 4.5
## Blow "2017" -0.7500 [-1.8312; 0.3312] 0.1 1.6
## Amanda "2016" -0.0400 [-0.1898; 0.1098] 2.7 5.0
## Butz "2015" -0.2100 [-0.3595; -0.0605] 2.7 5.0
##
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.3624 [-0.3868; -0.3381] -29.13 < 0.0001
## Random effects model -0.2176 [-0.3849; -0.0503] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
mc3$studlab[mc3$w.fixed==0]
## character(0)
print(summary(mc3), digits=2)
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.36 [-0.39; -0.34] -29.13 < 0.0001
## Random effects model -0.22 [-0.38; -0.05] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
mc3s <- metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3,
studlab=paste(author, year),
byvar=duration, print.byvar=FALSE)
mc3s
## MD 95%-CI %W(fixed) %W(random)
## Lorenzo "1999" -1.4700 [-3.9564; 1.0164] 0.0 0.4
## Faiman "1989" -1.1100 [-1.5506; -0.6694] 0.3 3.8
## Matthew "2001" -0.6800 [-0.8014; -0.5586] 4.0 5.1
## Lines "1992" -0.2400 [-0.4744; -0.0056] 1.1 4.8
## Carl "1989" -0.1300 [-0.2733; 0.0133] 2.9 5.1
## Ragazan "2005" 0.0300 [-0.3430; 0.4030] 0.4 4.2
## Daniel "1995" -0.5100 [-0.5495; -0.4705] 38.2 5.2
## Radcliffe "2004" -0.8300 [-0.9022; -0.7578] 11.4 5.2
## Emma "1991" 0.0700 [-0.1700; 0.3100] 1.0 4.7
## Stone "2012" 0.2700 [ 0.1246; 0.4154] 2.8 5.0
## Stephen "1997" -0.0400 [-0.4461; 0.3661] 0.4 4.0
## Walters "1982" 0.5400 [ 0.4170; 0.6630] 3.9 5.1
## Shanika "2011" -0.0500 [-0.1241; 0.0241] 10.8 5.2
## Gillespie "2009" -0.0800 [-0.2747; 0.1147] 1.6 4.9
## Brian "1993" 0.0000 [-0.2344; 0.2344] 1.1 4.8
## Bond "2001" -0.3000 [-0.6235; 0.0235] 0.6 4.4
## Heath "2007" -0.6600 [-0.7531; -0.5669] 6.9 5.2
## Bottle "1985" -0.5700 [-1.6836; 0.5436] 0.0 1.6
## Billington "1998" -0.0700 [-0.1652; 0.0252] 6.6 5.2
## Rachel "2005" 0.0200 [-0.2805; 0.3205] 0.7 4.5
## Blow "2017" -0.7500 [-1.8312; 0.3312] 0.1 1.6
## Amanda "2016" -0.0400 [-0.1898; 0.1098] 2.7 5.0
## Butz "2015" -0.2100 [-0.3595; -0.0605] 2.7 5.0
## duration
## Lorenzo "1999" 1
## Faiman "1989" 1
## Matthew "2001" 1
## Lines "1992" 1
## Carl "1989" 1
## Ragazan "2005" 2
## Daniel "1995" 2
## Radcliffe "2004" 2
## Emma "1991" 2
## Stone "2012" 2
## Stephen "1997" 2
## Walters "1982" 2
## Shanika "2011" 2
## Gillespie "2009" 2
## Brian "1993" 2
## Bond "2001" 2
## Heath "2007" 2
## Bottle "1985" 2
## Billington "1998" 2
## Rachel "2005" 2
## Blow "2017" 2
## Amanda "2016" 2
## Butz "2015" 2
##
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.3624 [-0.3868; -0.3381] -29.13 < 0.0001
## Random effects model -0.2176 [-0.3849; -0.0503] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Results for subgroups (fixed effect model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.4483 [-0.5327; -0.3638] 45.30 0.1226 91.2%
## > 6 months 18 -0.3546 [-0.3801; -0.3292] 702.80 0.1482 97.6%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.32 1 0.0376
## Within groups 748.10 21 < 0.0001
##
## Results for subgroups (random effects model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.5243 [-0.8859; -0.1628] 45.30 0.1226 91.2%
## > 6 months 18 -0.1441 [-0.3358; 0.0476] 702.80 0.1482 97.6%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 3.32 1 0.0686
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
mc3s <- update(mc3, byvar=duration, print.byvar=FALSE)
mc3s
## MD 95%-CI %W(fixed) %W(random)
## Lorenzo "1999" -1.4700 [-3.9564; 1.0164] 0.0 0.4
## Faiman "1989" -1.1100 [-1.5506; -0.6694] 0.3 3.8
## Matthew "2001" -0.6800 [-0.8014; -0.5586] 4.0 5.1
## Lines "1992" -0.2400 [-0.4744; -0.0056] 1.1 4.8
## Carl "1989" -0.1300 [-0.2733; 0.0133] 2.9 5.1
## Ragazan "2005" 0.0300 [-0.3430; 0.4030] 0.4 4.2
## Daniel "1995" -0.5100 [-0.5495; -0.4705] 38.2 5.2
## Radcliffe "2004" -0.8300 [-0.9022; -0.7578] 11.4 5.2
## Emma "1991" 0.0700 [-0.1700; 0.3100] 1.0 4.7
## Stone "2012" 0.2700 [ 0.1246; 0.4154] 2.8 5.0
## Stephen "1997" -0.0400 [-0.4461; 0.3661] 0.4 4.0
## Walters "1982" 0.5400 [ 0.4170; 0.6630] 3.9 5.1
## Shanika "2011" -0.0500 [-0.1241; 0.0241] 10.8 5.2
## Gillespie "2009" -0.0800 [-0.2747; 0.1147] 1.6 4.9
## Brian "1993" 0.0000 [-0.2344; 0.2344] 1.1 4.8
## Bond "2001" -0.3000 [-0.6235; 0.0235] 0.6 4.4
## Heath "2007" -0.6600 [-0.7531; -0.5669] 6.9 5.2
## Bottle "1985" -0.5700 [-1.6836; 0.5436] 0.0 1.6
## Billington "1998" -0.0700 [-0.1652; 0.0252] 6.6 5.2
## Rachel "2005" 0.0200 [-0.2805; 0.3205] 0.7 4.5
## Blow "2017" -0.7500 [-1.8312; 0.3312] 0.1 1.6
## Amanda "2016" -0.0400 [-0.1898; 0.1098] 2.7 5.0
## Butz "2015" -0.2100 [-0.3595; -0.0605] 2.7 5.0
## duration
## Lorenzo "1999" 1
## Faiman "1989" 1
## Matthew "2001" 1
## Lines "1992" 1
## Carl "1989" 1
## Ragazan "2005" 2
## Daniel "1995" 2
## Radcliffe "2004" 2
## Emma "1991" 2
## Stone "2012" 2
## Stephen "1997" 2
## Walters "1982" 2
## Shanika "2011" 2
## Gillespie "2009" 2
## Brian "1993" 2
## Bond "2001" 2
## Heath "2007" 2
## Bottle "1985" 2
## Billington "1998" 2
## Rachel "2005" 2
## Blow "2017" 2
## Amanda "2016" 2
## Butz "2015" 2
##
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.3624 [-0.3868; -0.3381] -29.13 < 0.0001
## Random effects model -0.2176 [-0.3849; -0.0503] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Results for subgroups (fixed effect model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.4483 [-0.5327; -0.3638] 45.30 0.1226 91.2%
## > 6 months 18 -0.3546 [-0.3801; -0.3292] 702.80 0.1482 97.6%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.32 1 0.0376
## Within groups 748.10 21 < 0.0001
##
## Results for subgroups (random effects model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.5243 [-0.8859; -0.1628] 45.30 0.1226 91.2%
## > 6 months 18 -0.1441 [-0.3358; 0.0476] 702.80 0.1482 97.6%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 3.32 1 0.0686
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
print(summary(mc3s), digits=2)
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.36 [-0.39; -0.34] -29.13 < 0.0001
## Random effects model -0.22 [-0.38; -0.05] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Results for subgroups (fixed effect model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.45 [-0.53; -0.36] 45.30 0.1226 91.2%
## > 6 months 18 -0.35 [-0.38; -0.33] 702.80 0.1482 97.6%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.32 1 0.0376
## Within groups 748.10 21 < 0.0001
##
## Results for subgroups (random effects model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.52 [-0.89; -0.16] 45.30 0.1226 91.2%
## > 6 months 18 -0.14 [-0.34; 0.05] 702.80 0.1482 97.6%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 3.32 1 0.0686
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
forest(mc3s,
xlab="Difference in mean response")
print(metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3,
subset=duration=="<= 6 months",
studlab=paste(author, year)),
digits=2)
## MD 95%-CI %W(fixed) %W(random)
## Lorenzo "1999" -1.47 [-3.96; 1.02] 0.1 2.0
## Faiman "1989" -1.11 [-1.55; -0.67] 3.7 19.7
## Matthew "2001" -0.68 [-0.80; -0.56] 48.4 26.9
## Lines "1992" -0.24 [-0.47; -0.01] 13.0 24.9
## Carl "1989" -0.13 [-0.27; 0.01] 34.8 26.6
##
## Number of studies combined: k = 5
##
## MD 95%-CI z p-value
## Fixed effect model -0.45 [-0.53; -0.36] -10.40 < 0.0001
## Random effects model -0.52 [-0.89; -0.16] -2.84 0.0045
##
## Quantifying heterogeneity:
## tau^2 = 0.1226; H = 3.37 [2.38; 4.76]; I^2 = 91.2% [82.4%; 95.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 45.30 4 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
print(update(mc3, subset=duration=="<= 6 months"),
digits=2)
## MD 95%-CI %W(fixed) %W(random)
## Lorenzo "1999" -1.47 [-3.96; 1.02] 0.1 2.0
## Faiman "1989" -1.11 [-1.55; -0.67] 3.7 19.7
## Matthew "2001" -0.68 [-0.80; -0.56] 48.4 26.9
## Lines "1992" -0.24 [-0.47; -0.01] 13.0 24.9
## Carl "1989" -0.13 [-0.27; 0.01] 34.8 26.6
##
## Number of studies combined: k = 5
##
## MD 95%-CI z p-value
## Fixed effect model -0.45 [-0.53; -0.36] -10.40 < 0.0001
## Random effects model -0.52 [-0.89; -0.16] -2.84 0.0045
##
## Quantifying heterogeneity:
## tau^2 = 0.1226; H = 3.37 [2.38; 4.76]; I^2 = 91.2% [82.4%; 95.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 45.30 4 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
data4 <- read.csv("data4.csv")
data4
## author year Ne Nc logHR selogHR
## 1 Charlie 1995 58 76 -0.654 0.321
## 2 Neelakasham 2000 278 456 -0.432 0.214
## 3 Satya 2001 156 274 -0.135 0.215
## 4 Tovino 2003 175 164 0.098 0.333
mg1 <- metagen(logHR, selogHR,
studlab=paste(author, year), data=data4,
sm="HR")
print(mg1, digits=2)
## HR 95%-CI %W(fixed) %W(random)
## Charlie 1995 0.52 [0.28; 0.98] 15.6 17.1
## Neelakasham 2000 0.65 [0.43; 0.99] 35.1 33.6
## Satya 2001 0.87 [0.57; 1.33] 34.8 33.3
## Tovino 2003 1.10 [0.57; 2.12] 14.5 16.0
##
## Number of studies combined: k = 4
##
## HR 95%-CI z p-value
## Fixed effect model 0.75 [0.59; 0.96] -2.26 0.0239
## Random effects model 0.75 [0.57; 0.99] -2.03 0.0428
##
## Quantifying heterogeneity:
## tau^2 = 0.0136; H = 1.10 [1.00; 2.80]; I^2 = 16.7% [0.0%; 87.2%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 3.60 3 0.3077
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
data5 <- read.csv("data5.csv")
data5
## author year N mean SE corr
## 1 Amal 1999 200 3.2 2.4 0.44
## 2 Kamal 2000 124 -1.5 1.8 0.32
## 3 Bimal 2002 125 -3.6 1.3 0.43
## 4 Udeni 2002 32 -2.2 1.6 0.23
## 5 Divakar 2004 48 -1.4 2.2 0.66
## 6 Devmi 2005 76 0.3 1.4 0.56
## 7 Shehan 2006 24 -5.2 1.8 0.87
## 8 Rose 2006 56 -4.2 2.6 0.37
## 9 Jack 2007 32 -4.2 1.7 0.73
## 10 Cal 2007 55 -2.4 2.6 0.55
## 11 Kim 2008 33 1.6 2.8 0.43
## 12 Mikael 2009 28 -0.8 1.6 0.67
## 13 Dan 2009 72 -3.6 2.6 0.44
## 14 Matt 2010 64 5.2 1.5 0.82
## 15 Dominik 2011 82 0.2 2.4 0.52
## 16 Shane 2012 32 -5.6 0.8 0.56
## 17 Nigam 2012 24 -3.3 2.2 0.46
## 18 Hemal 2013 32 -1.3 1.3 0.89
## 19 Naveen 2014 120 2.6 2.1 0.83
## 20 Raman 2015 224 -1.4 2.6 0.32
## 21 Preet 2017 180 -5.5 2.5 0.64
mg2 <- metagen(mean, SE, studlab=paste(author, year),
data=data5, sm="MD")
print(summary(mg2), digits=2)
## Number of studies combined: k = 21
##
## MD 95%-CI z p-value
## Fixed effect model -2.20 [-2.92; -1.47] -5.94 < 0.0001
## Random effects model -1.63 [-3.05; -0.20] -2.23 0.0255
##
## Quantifying heterogeneity:
## tau^2 = 7.2554; H = 1.85 [1.48; 2.31]; I^2 = 70.8% [54.6%; 81.2%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 68.54 20 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
data6 <- read.csv("data6.csv")
data6
## author year b SE
## 1 Liam 1994 0.0321600 0.002320
## 2 Mattkel 1999 0.0219300 0.004200
## 3 Svank 2004 0.0093200 0.004320
## 4 Jacobsson 1995 0.1234000 0.078400
## 5 Nils 2003 0.0936000 0.034500
## 6 Luxumburg 2002 0.0932000 0.067900
## 7 Webb 2013 0.0543200 0.004360
## 8 Raini 2005 0.0002100 0.007520
## 9 Dickinson 2012 0.0003200 0.009320
## 10 Rochester 1995 0.0423100 0.043700
## 11 Thomson&Thompson 1995 0.0000000 0.006830
## 12 Danny 1996 0.3421000 0.092340
## 13 Blue 2002 0.3256700 0.003276
## 14 Mcguire 2001 0.0342167 0.005478
## 15 Dawson 2003 0.0075000 0.002657
## 16 Frogg 2017 -0.0003200 0.004378
mg3 <- metagen(b, SE, studlab=paste(author, year),
data=data6, sm="RR", backtransf=FALSE)
summary(mg3)
## Number of studies combined: k = 16
##
## logRR 95%-CI z p-value
## Fixed effect model 0.0600 [0.0577; 0.0623] 50.97 < 0.0001
## Random effects model 0.0652 [0.0080; 0.1224] 2.23 0.0255
##
## Quantifying heterogeneity:
## tau^2 = 0.0126; H = 22.71 [21.57; 23.91]; I^2 = 99.8% [99.8%; 99.8%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 7737.16 15 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
library(meta)
data7 <- read.csv("data7.csv")
data7
## study Ee Ne Ec Nc
## 1 Samson 12 24 15 32
## 2 Luca 37 44 32 44
## 3 Ekel 136 150 120 162
## 4 Ramnujam 18 48 18 71
## 5 Kurt 127 120 77 142
## 6 Dammer 63 80 66 82
## 7 Morelli 34 20 32 34
## 8 Jimmy 13 72 16 64
## 9 Dekles 82 88 51 88
## 10 Subaina 22 50 28 37
## 11 Rafael 48 72 46 44
## 12 Monicca 56 100 91 120
## 13 Veronica 36 41 20 30
## 14 Ludwig 46 72 72 60
summary(data7$Ee/data7$Ne)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1806 0.5150 0.7271 0.7475 0.8995 1.7000
summary(data7$Ec/data7$Nc)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2500 0.5516 0.7340 0.6954 0.7932 1.2000
logOR <- with(data7[data7$study=="Dekles",],
log((Ee*(Nc-Ec)) / (Ec*(Ne-Ee))))
selogOR <- with(data7[data7$study=="Dekles",],
sqrt(1/Ee + 1/(Ne-Ee) + 1/Ec + 1/(Nc-Ec)))
round(exp(c(logOR,
logOR + c(-1,1) *
qnorm(1-0.05/2) * selogOR)), 4)
## [1] 9.9150 3.9092 25.1478
metabin(Ee, Ne, Ec, Nc, sm="OR", method="I",
data=data7, subset=study=="Dekles")
## OR 95%-CI z p-value
## 9.9150 [3.9092; 25.1478] 4.83 < 0.0001
##
## Details:
## - Inverse variance method
logRR <- with(data7[data7$study=="Dekles",],
log((Ee/Ne) / (Ec/Nc)))
selogRR <- with(data7[data7$study=="Dekles",],
sqrt(1/Ee + 1/Ec - 1/Ne - 1/Nc))
round(exp(c(logRR,
logRR + c(-1,1) *
qnorm(1-0.05/2) * selogRR)), 4)
## [1] 1.6078 1.3340 1.9379
metabin(Ee, Ne, Ec, Nc, sm="RR", method="I",
data=data7, subset=study=="Dekles")
## RR 95%-CI z p-value
## 1.6078 [1.3340; 1.9379] 4.98 < 0.0001
##
## Details:
## - Inverse variance method
metabin(Ee, Ne, Ec, Nc, sm="RD", method="I",
data=data7, subset=study=="Dekles")
## RD 95%-CI z p-value
## 0.3523 [0.2365; 0.4681] 5.96 < 0.0001
##
## Details:
## - Inverse variance method
ASD <- with(data7[data7$study=="Dekles",],
asin(sqrt(Ee/Ne)) - asin(sqrt(Ec/Nc)))
seASD <- with(data7[data7$study=="Dekles",],
sqrt(1/(4*Ne) + 1/(4*Nc)))
round(c(ASD, ASD + c(-1,1) * qnorm(1-0.05/2) * seASD), 4)
## [1] 0.4413 0.2936 0.5891
metabin(Ee, Ne, Ec, Nc, sm="ASD", method="I", data=data7, subset=study=="Dekles")
## ASD 95%-CI z p-value
## 0.4413 [0.2936; 0.5891] 5.85 < 0.0001
##
## Details:
## - Inverse variance method
data8 <- read.csv("data8.csv")
data8
## study Ee Ne Ec Nc
## 1 Poland 0 280 1 240
## 2 Jerman 5 242 7 188
## 3 Karl 6 280 5 332
## 4 ABCD 11 269 16 282
## 5 BRFL 10 1000 13 956
## 6 Andrew 8 1900 8 1900
## 7 Bigg 13 1421 13 1234
## 8 Roger 1 600 15 500
## 9 Krikka 6 1200 4 1256
## 10 Prifd 3 200 1 78
## 11 JJKL 14 1508 15 1400
summary(data8$Ee/data8$Ne)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000000 0.004605 0.009284 0.012481 0.017831 0.040892
summary(data8$Ec/data8$Nc)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.003185 0.007373 0.012821 0.018024 0.022530 0.056738
logOR <- with(data8[data8$study=="Poland",],
log(((Ee+0.5)*(Nc-Ec+0.5)) /
((Ec+0.5)*(Ne-Ee+0.5))))
selogOR <- with(data8[data8$study=="Poland",],
sqrt(1/(Ee+0.5) + 1/(Ne-Ee+0.5) +
1/(Ec+0.5) + 1/(Nc-Ec+0.5)))
round(exp(c(logOR,
logOR + c(-1,1) * qnorm(1-0.05/2) * selogOR)), 4)
## [1] 0.2846 0.0115 7.0190
metabin(Ee, Ne, Ec, Nc, sm="OR", method="I",
data=data8, subset=study=="Poland")
## OR 95%-CI z p-value
## 0.2846 [0.0115; 7.0190] -0.77 0.4422
##
## Details:
## - Inverse variance method
## - Continuity correction of 0.5 in studies with zero cell frequencies
metabin(Ee, Ne, Ec, Nc, sm="OR", method="I",
data=data8, subset=study=="Poland",
incr=0.1)
## OR 95%-CI z p-value
## 0.0776 [0.0001; 50.3847] -0.77 0.4391
##
## Details:
## - Inverse variance method
## - Continuity correction of 0.1 in studies with zero cell frequencies
metabin(Ee, Ne, Ec, Nc, sm="OR", method="I",
data=data8, subset=study=="Poland",
incr="TACC")
## OR 95%-CI z p-value
## 0.3145 [0.0138; 7.1880] -0.72 0.4687
##
## Details:
## - Inverse variance method
## - Treatment arm continuity correction in studies with zero cell frequencies
metabin(Ee, Ne, Ec, Nc, sm="RR", method="I",
data=data8, subset=study=="Poland")
## RR 95%-CI z p-value
## 0.2858 [0.0117; 6.9832] -0.77 0.4424
##
## Details:
## - Inverse variance method
## - Continuity correction of 0.5 in studies with zero cell frequencies
metabin(Ee, Ne, Ec, Nc, sm="OR", method="P",
data=data7, subset=study=="Dekles")
## OR 95%-CI z p-value
## 6.6671 [3.3585; 13.2353] 5.42 < 0.0001
##
## Details:
## - Peto method
metabin(Ee, Ne, Ec, Nc, sm="OR", method="P",
data=data8, subset=study=="Poland")
## OR 95%-CI z p-value
## 0.1146 [0.0022; 5.8410] -1.08 0.2801
##
## Details:
## - Peto method
logOR <- with(data7,
log((Ee*(Nc-Ec)) / (Ec*(Ne-Ee))))
## Warning in log((Ee * (Nc - Ec))/(Ec * (Ne - Ee))): NaNs produced
varlogOR <- with(data7,
1/Ee + 1/(Ne-Ee) + 1/Ec + 1/(Nc-Ec))
weight <- 1/varlogOR
round(exp(weighted.mean(logOR, weight)), 4)
## [1] NaN
round(1/sum(weight), 4)
## [1] -0.0165
mb1 <- metabin(Ee, Ne, Ec, Nc, sm="OR", method="I",
data=data7, studlab=study)
## Warning in metabin(Ee, Ne, Ec, Nc, sm = "OR", method = "I", data = data7, :
## Studies with event.e > n.e get no weight in meta-analysis.
## Warning in metabin(Ee, Ne, Ec, Nc, sm = "OR", method = "I", data = data7, :
## Studies with event.c > n.c get no weight in meta-analysis.
round(c(exp(mb1$TE.fixed), mb1$seTE.fixed^2), 4)
## [1] 1.2188 0.0174
print(summary(mb1), digits=2)
## Number of studies combined: k = 10
##
## OR 95%-CI z p-value
## Fixed effect model 1.22 [0.94; 1.58] 1.50 0.1339
## Random effects model 1.37 [0.69; 2.74] 0.90 0.3691
##
## Quantifying heterogeneity:
## tau^2 = 1.0398; H = 2.61 [1.99; 3.42]; I^2 = 85.3% [74.8%; 91.5%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 61.43 9 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
forest(mb1, comb.random=FALSE, hetstat=FALSE)
logOR <- with(data8,
log((Ee*(Nc-Ec)) / (Ec*(Ne-Ee))))
varlogOR <- with(data8,
1/Ee + 1/(Ne-Ee) + 1/Ec + 1/(Nc-Ec))
weight <- 1/varlogOR
weight[data8$study=="Poland"]
## [1] 0
mb2 <- metabin(Ee, Ne, Ec, Nc, sm="OR", method="I",
data=data8, studlab=study)
print(summary(mb2), digits=2)
## Number of studies combined: k = 11
##
## OR 95%-CI z p-value
## Fixed effect model 0.8 [0.59; 1.10] -1.37 0.1712
## Random effects model 0.8 [0.59; 1.10] -1.36 0.1744
##
## Quantifying heterogeneity:
## tau^2 = 0.0039; H = 1.01 [1.00; 1.60]; I^2 = 1.3% [0.0%; 60.7%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 10.13 10 0.4290
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
## - Continuity correction of 0.5 in studies with zero cell frequencies
as.data.frame(mb2)[,c("studlab", "incr.e", "incr.c")]
## studlab incr.e incr.c
## 1 Poland 0.5 0.5
## 2 Jerman 0.0 0.0
## 3 Karl 0.0 0.0
## 4 ABCD 0.0 0.0
## 5 BRFL 0.0 0.0
## 6 Andrew 0.0 0.0
## 7 Bigg 0.0 0.0
## 8 Roger 0.0 0.0
## 9 Krikka 0.0 0.0
## 10 Prifd 0.0 0.0
## 11 JJKL 0.0 0.0
mb1.mh <- metabin(Ee, Ne, Ec, Nc, sm="OR",
data=data7, studlab=study)
## Warning in metabin(Ee, Ne, Ec, Nc, sm = "OR", data = data7, studlab =
## study): Studies with event.e > n.e get no weight in meta-analysis.
## Warning in metabin(Ee, Ne, Ec, Nc, sm = "OR", data = data7, studlab =
## study): Studies with event.c > n.c get no weight in meta-analysis.
print(summary(mb1.mh), digits=2)
## Number of studies combined: k = 10
##
## OR 95%-CI z p-value
## Fixed effect model 1.30 [1.02; 1.65] 2.15 0.0314
## Random effects model 1.37 [0.69; 2.74] 0.90 0.3698
##
## Quantifying heterogeneity:
## tau^2 = 1.0444; H = 2.62 [2.00; 3.43]; I^2 = 85.4% [74.9%; 91.5%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 61.66 9 < 0.0001
##
## Details on meta-analytical method:
## - Mantel-Haenszel method
## - DerSimonian-Laird estimator for tau^2
forest(mb1.mh, comb.random=FALSE, hetstat=FALSE,
text.fixed="MH estimate")
mb2.mh <- metabin(Ee, Ne, Ec, Nc, sm="OR", method="MH",
data=data8, studlab=study)
print(summary(mb2.mh), digits=2)
## Number of studies combined: k = 11
##
## OR 95%-CI z p-value
## Fixed effect model 0.73 [0.54; 0.98] -2.08 0.0373
## Random effects model 0.80 [0.58; 1.11] -1.33 0.1834
##
## Quantifying heterogeneity:
## tau^2 = 0.0155; H = 1.03 [1.00; 1.63]; I^2 = 5.0% [0.0%; 62.2%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 10.53 10 0.3954
##
## Details on meta-analytical method:
## - Mantel-Haenszel method
## - DerSimonian-Laird estimator for tau^2
## - Continuity correction of 0.5 in studies with zero cell frequencies
mb1.peto <- metabin(Ee, Ne, Ec, Nc, sm="OR", method="P",
data=data7, studlab=study)
## Warning in metabin(Ee, Ne, Ec, Nc, sm = "OR", method = "P", data = data7, :
## Studies with event.e > n.e get no weight in meta-analysis.
## Warning in metabin(Ee, Ne, Ec, Nc, sm = "OR", method = "P", data = data7, :
## Studies with event.c > n.c get no weight in meta-analysis.
print(summary(mb1.peto), digits=2)
## Number of studies combined: k = 10
##
## OR 95%-CI z p-value
## Fixed effect model 1.31 [1.03; 1.67] 2.21 0.0274
## Random effects model 1.33 [0.68; 2.61] 0.83 0.4043
##
## Quantifying heterogeneity:
## tau^2 = 0.9982; H = 2.72 [2.09; 3.54]; I^2 = 86.5% [77.1%; 92.0%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 66.63 9 < 0.0001
##
## Details on meta-analytical method:
## - Peto method
## - DerSimonian-Laird estimator for tau^2
mb2.peto <- metabin(Ee, Ne, Ec, Nc, sm="OR", method="Peto",
data=data8, studlab=study)
print(summary(mb2.peto), digits=2)
## Number of studies combined: k = 11
##
## OR 95%-CI z p-value
## Fixed effect model 0.73 [0.54; 0.98] -2.10 0.0359
## Random effects model 0.72 [0.49; 1.07] -1.62 0.1049
##
## Quantifying heterogeneity:
## tau^2 = 0.1472; H = 1.25 [1.00; 1.78]; I^2 = 35.6% [0.0%; 68.3%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 15.52 10 0.1141
##
## Details on meta-analytical method:
## - Peto method
## - DerSimonian-Laird estimator for tau^2
print(summary(mb1), digits=2)
## Number of studies combined: k = 10
##
## OR 95%-CI z p-value
## Fixed effect model 1.22 [0.94; 1.58] 1.50 0.1339
## Random effects model 1.37 [0.69; 2.74] 0.90 0.3691
##
## Quantifying heterogeneity:
## tau^2 = 1.0398; H = 2.61 [1.99; 3.42]; I^2 = 85.3% [74.8%; 91.5%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 61.43 9 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
restmp1 <- rbind(c(exp(mb1$TE.fixed), exp(mb1$lower.fixed), exp(mb1$upper.fixed),
exp(mb1$TE.random), exp(mb1$lower.random), exp(mb1$upper.random),
mb1$tau^2),
c(exp(mb1.mh$TE.fixed), exp(mb1.mh$lower.fixed), exp(mb1.mh$upper.fixed),
exp(mb1.mh$TE.random), exp(mb1.mh$lower.random), exp(mb1.mh$upper.random),
mb1.mh$tau^2),
c(exp(mb1.peto$TE.fixed), exp(mb1.peto$lower.fixed), exp(mb1.peto$upper.fixed),
exp(mb1.peto$TE.random), exp(mb1.peto$lower.random), exp(mb1.peto$upper.random),
mb1.peto$tau^2)
)
restmp1 <- as.data.frame(restmp1)
restmp1[,1:6] <- round(restmp1[,1:6], 2)
restmp1[,7] <- round(restmp1[,7], 4)
names(restmp1) <- c("OR (fixed)", "lower", "upper", "OR (random)", "lower", "upper", "tau^2")
row.names(restmp1) <- c("IV", "MH", "Peto")
restmp2 <- rbind(c(exp(mb2$TE.fixed), exp(mb2$lower.fixed), exp(mb2$upper.fixed),
exp(mb2$TE.random), exp(mb2$lower.random), exp(mb2$upper.random),
mb2$tau^2),
c(exp(mb2.mh$TE.fixed), exp(mb2.mh$lower.fixed), exp(mb2.mh$upper.fixed),
exp(mb2.mh$TE.random), exp(mb2.mh$lower.random), exp(mb2.mh$upper.random),
mb2.mh$tau^2),
c(exp(mb2.peto$TE.fixed), exp(mb2.peto$lower.fixed), exp(mb2.peto$upper.fixed),
exp(mb2.peto$TE.random), exp(mb2.peto$lower.random), exp(mb2.peto$upper.random),
mb2.peto$tau^2)
)
restmp2 <- as.data.frame(restmp2)
restmp2[,1:6] <- round(restmp2[,1:6], 2)
restmp2[,7] <- round(restmp2[,7], 4)
names(restmp2) <- c("OR (fixed)", "lower", "upper", "OR (random)", "lower", "upper", "tau^2")
row.names(restmp2) <- c("IV", "MH", "Peto")
restmp1
## OR (fixed) lower upper OR (random) lower upper tau^2
## IV 1.22 0.94 1.58 1.37 0.69 2.74 1.0398
## MH 1.30 1.02 1.65 1.37 0.69 2.74 1.0444
## Peto 1.31 1.03 1.67 1.33 0.68 2.61 0.9982
restmp2
## OR (fixed) lower upper OR (random) lower upper tau^2
## IV 0.80 0.59 1.10 0.80 0.59 1.10 0.0039
## MH 0.73 0.54 0.98 0.80 0.58 1.11 0.0155
## Peto 0.73 0.54 0.98 0.72 0.49 1.07 0.1472
data9 <- read.csv("data9.csv")
data9
## study Ee Ne Ec Nc blind
## 1 Shay 1 12 5 12 Blinded
## 2 Michael 25 60 37 61 Blinded
## 3 Drew 21 50 21 55 Blinded
## 4 Sebastian 16 36 15 35 No
## 5 Taylor 12 38 32 47 No
## 6 Reign 8 21 12 21 No
## 7 Xavier 5 25 15 22 No
## 8 Arroyo 7 19 9 15 No
## 9 Shane 6 32 13 37 No
## 10 Frost 8 28 21 23 No
summary(data9$Ee/data9$Ne)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.08333 0.22143 0.34211 0.31028 0.40774 0.44444
summary(data9$Ec/data9$Nc)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3514 0.4196 0.5857 0.5632 0.6623 0.9130
mb3 <- metabin(Ee, Ne, Ec, Nc, sm="RR", method="I",
data=data9, studlab=study)
print(summary(mb3), digits=2)
## Number of studies combined: k = 10
##
## RR 95%-CI z p-value
## Fixed effect model 0.64 [0.53; 0.76] -4.83 < 0.0001
## Random effects model 0.59 [0.44; 0.80] -3.44 0.0006
##
## Quantifying heterogeneity:
## tau^2 = 0.1162; H = 1.51 [1.06; 2.14]; I^2 = 55.9% [10.3%; 78.3%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 20.39 9 0.0157
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
mb3s <- update(mb3, byvar=blind, print.byvar=FALSE)
print(summary(mb3s), digits=2)
## Number of studies combined: k = 10
##
## RR 95%-CI z p-value
## Fixed effect model 0.64 [0.53; 0.76] -4.83 < 0.0001
## Random effects model 0.59 [0.44; 0.80] -3.44 0.0006
##
## Quantifying heterogeneity:
## tau^2 = 0.1162; H = 1.51 [1.06; 2.14]; I^2 = 55.9% [10.3%; 78.3%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 20.39 9 0.0157
##
## Results for subgroups (fixed effect model):
## k RR 95%-CI Q tau^2 I^2
## Blinded 3 0.80 [0.60; 1.06] 4.32 0.099 53.7%
## No 7 0.54 [0.43; 0.69] 11.95 0.1067 49.8%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.12 1 0.0425
## Within groups 16.27 8 0.0387
##
## Results for subgroups (random effects model):
## k RR 95%-CI Q tau^2 I^2
## Blinded 3 0.78 [0.47; 1.30] 4.32 0.099 53.7%
## No 7 0.53 [0.37; 0.75] 11.95 0.1067 49.8%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 1.54 1 0.2140
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
round(mc1$Q, 2) # Cochran's Q statistic
## [1] 39.29
round(100*c(mc1$I2, mc1$lower.I2, mc1$upper.I2), 1) # I-squared
## [1] 59.3 30.5 76.1
round(mc1$tau^2, 4) # Between-study variance tau-squared
## [1] 38.5732
# Conduct meta-analysis for first subgroup:
mc3s1 <- metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3, studlab=paste(author, year), subset=duration=="<= 6 months")
# Conduct meta-analysis for second subgroup:
mc3s2 <- metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3, studlab=paste(author, year), subset=duration=="> 6 months")
# Subgroup treatment effects (fixed effect model)
TE.duration <- c(mc3s1$TE.fixed, mc3s2$TE.fixed)
# Corresponding standard errors (fixed effect model)
seTE.duration <- c(mc3s1$seTE.fixed, mc3s2$seTE.fixed)
mh1 <- metagen(TE.duration, seTE.duration, sm="MD",
studlab=c("<= 6 months", " > 6 months"), comb.random=FALSE)
print(mh1, digits=2)
## MD 95%-CI %W(fixed)
## <= 6 months -0.45 [-0.53; -0.36] 8.3
## > 6 months -0.35 [-0.38; -0.33] 91.7
##
## Number of studies combined: k = 2
##
## MD 95%-CI z p-value
## Fixed effect model -0.36 [-0.39; -0.34] -29.13 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 0.0034; H = 2.08; I^2 = 76.9% [0.0%; 94.7%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 4.32 1 0.0376
##
## Details on meta-analytical method:
## - Inverse variance method
print(summary(mc3s), digits=2)
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.36 [-0.39; -0.34] -29.13 < 0.0001
## Random effects model -0.22 [-0.38; -0.05] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Results for subgroups (fixed effect model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.45 [-0.53; -0.36] 45.30 0.1226 91.2%
## > 6 months 18 -0.35 [-0.38; -0.33] 702.80 0.1482 97.6%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.32 1 0.0376
## Within groups 748.10 21 < 0.0001
##
## Results for subgroups (random effects model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.52 [-0.89; -0.16] 45.30 0.1226 91.2%
## > 6 months 18 -0.14 [-0.34; 0.05] 702.80 0.1482 97.6%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 3.32 1 0.0686
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2
mh1$Q
## [1] 4.323644
mc3s$Q.b.fixed
## [1] 4.323644
data.frame(duration=c("<= 6 months", " > 6 months"), tau2=round(c(mc3s1$tau^2, mc3s2$tau^2), 4))
## duration tau2
## 1 <= 6 months 0.1226
## 2 > 6 months 0.1482
round((mc3s1$Q - (mc3s1$k-1))/mc3s1$C, 4)
## [1] 0.1226
# Subgroup treatment effects (random effects model)
TE.duration.r <- c(mc3s1$TE.random, mc3s2$TE.random)
# Corresponding standard errors (random effects model)
seTE.duration.r <- c(mc3s1$seTE.random, mc3s2$seTE.random)
# Do meta-analysis of subgroup estimates
mh1.r <- metagen(TE.duration.r, seTE.duration.r, sm="MD",
studlab=c("<= 6 months", " > 6 months"), comb.random=FALSE)
print(mh1.r, digits=2)
## MD 95%-CI %W(fixed)
## <= 6 months -0.52 [-0.89; -0.16] 21.9
## > 6 months -0.14 [-0.34; 0.05] 78.1
##
## Number of studies combined: k = 2
##
## MD 95%-CI z p-value
## Fixed effect model -0.23 [-0.40; -0.06] -2.63 0.0085
##
## Quantifying heterogeneity:
## tau^2 = 0.0505; H = 1.82; I^2 = 69.9% [0.0%; 93.2%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 3.32 1 0.0686
##
## Details on meta-analytical method:
## - Inverse variance method
# Q-statistic within subgroups
Q.g <- c(mc3s1$Q, mc3s2$Q)
# Degrees of freedom within subgroups
df.Q.g <- c(mc3s1$k-1, mc3s2$k-1)
# Scaling factor within subgroups
C.g <- c(mc3s1$C, mc3s2$C)
# Calculate common estimate of tau-squared
tau2.common <- (sum(Q.g) - sum(df.Q.g)) / sum(C.g)
# Set negative value of tau.common to zero
tau2.common <- ifelse(tau2.common < 0, 0, tau2.common)
# Print common between-study variance
round(tau2.common, 4)
## [1] 0.1465
mc3s.p <- metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3, studlab=paste(author, year),
byvar=duration, print.byvar=FALSE, tau.preset=sqrt(tau2.common))
## Warning in metacont(Ne, Me, Se, Nc, Mc, Sc, data = data3, studlab =
## paste(author, : Argument 'tau.common' set to TRUE as argument tau.preset is
## not NULL.
print(summary(mc3s.p), digits=2)
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Fixed effect model -0.36 [-0.39; -0.34] -29.13 < 0.0001
## Random effects model -0.22 [-0.39; -0.05] -2.50 0.0125
##
## Quantifying heterogeneity:
## tau^2 = 0.1465; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Results for subgroups (fixed effect model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.45 [-0.53; -0.36] 45.30 0.1465 91.2%
## > 6 months 18 -0.35 [-0.38; -0.33] 702.80 0.1465 97.6%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.32 1 0.0376
## Within groups 748.10 21 < 0.0001
##
## Results for subgroups (random effects model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.53 [-0.92; -0.14] 45.30 0.1465 91.2%
## > 6 months 18 -0.14 [-0.33; 0.05] 702.80 0.1465 97.6%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 3.05 1 0.0809
##
## Details on meta-analytical method:
## - Inverse variance method
## - Preset between-study variance: tau^2 = 0.1465
mc3s.c <- metacont(Ne, Me, Se, Nc, Mc, Sc, data=data3, studlab=paste(author, year),
byvar=duration, print.byvar=FALSE, tau.common=TRUE, comb.fixed=FALSE)
print(summary(mc3s.c), digits=2)
## Number of studies combined: k = 23
##
## MD 95%-CI z p-value
## Random effects model -0.22 [-0.38; -0.05] -2.55 0.0108
##
## Quantifying heterogeneity:
## tau^2 = 0.1389; H = 5.85 [5.25; 6.51]; I^2 = 97.1% [96.4%; 97.6%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 752.43 22 < 0.0001
##
## Results for subgroups (random effects model):
## k MD 95%-CI Q tau^2 I^2
## <= 6 months 5 -0.53 [-0.92; -0.14] 45.30 0.1465 91.2%
## > 6 months 18 -0.14 [-0.33; 0.05] 702.80 0.1465 97.6%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 3.05 1 0.0809
## Within groups 748.10 21 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2 (assuming common tau^2 in subgroups)
mc3s.mr <- metareg(mc3s.c, duration)
print(mc3s.mr, digits=2)
##
## Mixed-Effects Model (k = 23; tau^2 estimator: DL)
##
## tau^2 (estimated amount of residual heterogeneity): 0.15 (SE = 0.08)
## tau (square root of estimated tau^2 value): 0.38
## I^2 (residual heterogeneity / unaccounted variability): 97.19%
## H^2 (unaccounted variability / sampling variability): 35.62
## R^2 (amount of heterogeneity accounted for): 0.00%
##
## Test for Residual Heterogeneity:
## QE(df = 21) = 748.10, p-val < .01
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 3.05, p-val = 0.08
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.53 0.20 -2.66 <.01 -0.92 -0.14 **
## duration> 6 months 0.39 0.22 1.75 0.08 -0.05 0.82 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Variance-covariance matrix
varcov <- vcov(mc3s.mr)
# Estimated treatment effect in studies with longer duration
TE.s2 <- sum(coef(mc3s.mr))
# Standard error of treatment effect
seTE.s2 <- sqrt(sum(diag(varcov)) + 2*varcov[1,2])
print(metagen(TE.s2, seTE.s2, sm="MD"), digits=2)
## MD 95%-CI z p-value
## -0.14 [-0.33; 0.05] -1.48 0.1387
##
## Details:
## - Inverse variance method
mb3s.c <- metabin(Ee, Ne, Ec, Nc, sm="RR", method="I", data=data9, studlab=study, byvar=blind, print.byvar=FALSE, tau.common=TRUE)
print(summary(mb3s.c), digits=2)
## Number of studies combined: k = 10
##
## RR 95%-CI z p-value
## Fixed effect model 0.64 [0.53; 0.76] -4.83 < 0.0001
## Random effects model 0.59 [0.44; 0.80] -3.44 0.0006
##
## Quantifying heterogeneity:
## tau^2 = 0.1162; H = 1.51 [1.06; 2.14]; I^2 = 55.9% [10.3%; 78.3%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 20.39 9 0.0157
##
## Results for subgroups (fixed effect model):
## k RR 95%-CI Q tau^2 I^2
## Blinded 3 0.80 [0.60; 1.06] 4.32 0.1044 53.7%
## No 7 0.54 [0.43; 0.69] 11.95 0.1044 49.8%
##
## Test for subgroup differences (fixed effect model):
## Q d.f. p-value
## Between groups 4.12 1 0.0425
## Within groups 16.27 8 0.0387
##
## Results for subgroups (random effects model):
## k RR 95%-CI Q tau^2 I^2
## Blinded 3 0.78 [0.46; 1.31] 4.32 0.1044 53.7%
## No 7 0.53 [0.37; 0.75] 11.95 0.1044 49.8%
##
## Test for subgroup differences (random effects model):
## Q d.f. p-value
## Between groups 1.49 1 0.2215
## Within groups 16.27 8 0.0387
##
## Details on meta-analytical method:
## - Inverse variance method
## - DerSimonian-Laird estimator for tau^2 (assuming common tau^2 in subgroups)
mb3s.mr <- metareg(mb3s.c)
print(mb3s.mr, digits=2)
##
## Mixed-Effects Model (k = 10; tau^2 estimator: DL)
##
## tau^2 (estimated amount of residual heterogeneity): 0.10 (SE = 0.11)
## tau (square root of estimated tau^2 value): 0.32
## I^2 (residual heterogeneity / unaccounted variability): 50.83%
## H^2 (unaccounted variability / sampling variability): 2.03
## R^2 (amount of heterogeneity accounted for): 10.15%
##
## Test for Residual Heterogeneity:
## QE(df = 8) = 16.27, p-val = 0.04
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 1.49, p-val = 0.22
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.25 0.26 -0.94 0.35 -0.77 0.27
## .byvarNo -0.39 0.32 -1.22 0.22 -1.01 0.23
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Treatment effect in blinded trials
round(exp(coef(mb3s.mr)["intrcpt"]), 2)
## intrcpt
## 0.78
# Treatment effect in trials without blinding employed
round(exp(sum(coef(mb3s.mr))), 2)
## [1] 0.53
data(dat.colditz1994, package="metafor")
data10 <- dat.colditz1994
mh2 <- metabin(tpos, tpos+tneg, cpos, cpos+cneg, data=data10, studlab=paste(author, year))
summary(mh2)
## Number of studies combined: k = 13
##
## RR 95%-CI z p-value
## Fixed effect model 0.6353 [0.5881; 0.6862] -11.53 < 0.0001
## Random effects model 0.4896 [0.3448; 0.6952] -3.99 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 0.3095; H = 3.57 [2.93; 4.34]; I^2 = 92.1% [88.3%; 94.7%]
##
## Test of heterogeneity:
## Q d.f. p-value
## 152.57 12 < 0.0001
##
## Details on meta-analytical method:
## - Mantel-Haenszel method
## - DerSimonian-Laird estimator for tau^2
table(data10$ablat)
##
## 13 18 19 27 33 42 44 52 55
## 2 1 1 1 2 2 2 1 1
mh2.mr <- metareg(mh2, ablat)
print(mh2.mr, digits=2)
##
## Mixed-Effects Model (k = 13; tau^2 estimator: DL)
##
## tau^2 (estimated amount of residual heterogeneity): 0.06 (SE = 0.05)
## tau (square root of estimated tau^2 value): 0.25
## I^2 (residual heterogeneity / unaccounted variability): 64.21%
## H^2 (unaccounted variability / sampling variability): 2.79
## R^2 (amount of heterogeneity accounted for): 79.50%
##
## Test for Residual Heterogeneity:
## QE(df = 11) = 30.73, p-val < .01
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 18.85, p-val < .01
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt 0.26 0.23 1.12 0.26 -0.20 0.71
## ablat -0.03 0.01 -4.34 <.01 -0.04 -0.02 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
bubble(mh2.mr)
mean(data10$ablat)
## [1] 33.46154
ablat.c <- with(data10, ablat - mean(ablat))
mh2.mr.c <- metareg(mh2, ablat.c)
print(mh2.mr.c, digits=2)
##
## Mixed-Effects Model (k = 13; tau^2 estimator: DL)
##
## tau^2 (estimated amount of residual heterogeneity): 0.06 (SE = 0.05)
## tau (square root of estimated tau^2 value): 0.25
## I^2 (residual heterogeneity / unaccounted variability): 64.21%
## H^2 (unaccounted variability / sampling variability): 2.79
## R^2 (amount of heterogeneity accounted for): 79.50%
##
## Test for Residual Heterogeneity:
## QE(df = 11) = 30.73, p-val < .01
##
## Test of Moderators (coefficient(s) 2):
## QM(df = 1) = 18.85, p-val < .01
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## intrcpt -0.72 0.10 -7.09 <.01 -0.92 -0.52 ***
## ablat.c -0.03 0.01 -4.34 <.01 -0.04 -0.02 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
round(exp(coef(mh2.mr.c)["intrcpt"]), 2)
## intrcpt
## 0.49
TE.33.5 <- coef(mh2.mr.c)["intrcpt"]
seTE.33.5 <- sqrt(vcov(mh2.mr.c)["intrcpt", "intrcpt"])
print(metagen(TE.33.5, seTE.33.5, sm="RR"), digits=2)
## RR 95%-CI z p-value
## 0.49 [0.40; 0.59] -7.09 < 0.0001
##
## Details:
## - Inverse variance method