Meta Analysis in R

Exercises from Doctrine UK Workshop: A Beginner’s Guide to the Meta-Analysis in R by Christ Billy Aryanto

Libraries

library(tidyverse)
library(esc)
library(meta)

Load data

data <- read_delim("fileLatihan.csv", delim = ";")

Rows: 10 Columns: 8── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ";"
chr (2): Study, Moderator
dbl (6): N1, M1, SD1, N2, M2, SD2
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

data

Exercise 1

n_exp    <- 103
n_con    <- 109
mean_exp <- 135.81
sd_exp   <-  18.72
mean_con <- 123.18
sd_con   <-  19.39

esc_mean_sd(grp1m = mean_exp, grp1sd = sd_exp, grp1n = n_exp,
            grp2m = mean_con, grp2sd = sd_con, grp2n = n_con,
            es.type = "d")

Effect Size Calculation for Meta Analysis

     Conversion: mean and sd to effect size d
    Effect Size:   0.6624
 Standard Error:   0.1411
       Variance:   0.0199
       Lower CI:   0.3858
       Upper CI:   0.9390
         Weight:  50.2062

Exercise 2

data.es <- esc_mean_sd(grp1m = data$M1, grp1sd = data$SD1, grp1n = data$N1,
                       grp2m = data$M2, grp2sd = data$SD2, grp2n = data$N2,
                       es.type = "d", study = data$Study) %>% 
           as.data.frame() %>% 
           inner_join(data %>% select(Study,Moderator), by=c("study"="Study"))
data.es

model1 <- metagen(data = data.es, TE = es, seTE = se, 
                  studlab = study, sm = "SMD", common = T, random = T,
                  method.tau = "REML", title = "Latihan Meta-Analysis")
summary(model1)

Review:     Latihan Meta-Analysis

                             SMD            95%-CI %W(common) %W(random)
Burhman et al (2013)      0.7036 [ 0.2403; 1.1670]        6.3       10.3
Fledderus et al (2012)    1.0863 [ 0.8213; 1.3513]       19.1       13.2
Gluck & Maerker (2011)   -0.3158 [-0.8851; 0.2534]        4.1        8.9
Hesser et all (2012)      0.7222 [ 0.2204; 1.2241]        5.3        9.8
Hjeff/Hayes (2012)        0.6624 [ 0.3858; 0.9390]       17.5       13.1
Johnson et al (2012)      0.7355 [-0.4171; 1.8881]        1.0        3.8
Lappalainen et al (2013)  0.2543 [-0.5491; 1.0577]        2.1        6.3
Morledge et al (2013)     0.2454 [ 0.0403; 0.4505]       31.9       14.0
Muto et al (2011)         0.1061 [-0.3962; 0.6084]        5.3        9.8
Thorsell et al (2011)     0.6097 [ 0.1821; 1.0374]        7.3       10.9

Number of studies combined: k = 10

                        SMD           95%-CI    z  p-value
Common effect model  0.5344 [0.4186; 0.6503] 9.04 < 0.0001
Random effects model 0.5007 [0.2396; 0.7619] 3.76   0.0002

Quantifying heterogeneity:
 tau^2 = 0.1159 [0.0271; 0.4769]; tau = 0.3405 [0.1646; 0.6906]
 I^2 = 76.5% [56.5%; 87.3%]; H = 2.06 [1.52; 2.80]

Test of heterogeneity:
     Q d.f.  p-value
 38.22    9 < 0.0001

Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau

Exercise 3

forest.meta(model1, 
            leftcols = c("study", "es", "se", "Moderator"),
            leftlabs = c("Author", "d", "SE", "Moderator"),
            sortvar = es)

Exercise 4

model2 <- metagen(data = data.es, TE = es, seTE = se, studlab = study, 
                  sm = "SMD", common = T, random = T,
                  method.tau = "REML", subgroup = Moderator, 
                  title = "Latihan Meta-Analysis")
summary(model2)

Review:     Latihan Meta-Analysis

                             SMD            95%-CI %W(common) %W(random) Moderator
Burhman et al (2013)      0.7036 [ 0.2403; 1.1670]        6.3       10.3  INTERNET
Fledderus et al (2012)    1.0863 [ 0.8213; 1.3513]       19.1       13.2      BOOK
Gluck & Maerker (2011)   -0.3158 [-0.8851; 0.2534]        4.1        8.9  INTERNET
Hesser et all (2012)      0.7222 [ 0.2204; 1.2241]        5.3        9.8  INTERNET
Hjeff/Hayes (2012)        0.6624 [ 0.3858; 0.9390]       17.5       13.1      BOOK
Johnson et al (2012)      0.7355 [-0.4171; 1.8881]        1.0        3.8      BOOK
Lappalainen et al (2013)  0.2543 [-0.5491; 1.0577]        2.1        6.3  INTERNET
Morledge et al (2013)     0.2454 [ 0.0403; 0.4505]       31.9       14.0  INTERNET
Muto et al (2011)         0.1061 [-0.3962; 0.6084]        5.3        9.8      BOOK
Thorsell et al (2011)     0.6097 [ 0.1821; 1.0374]        7.3       10.9      BOOK

Number of studies combined: k = 10

                        SMD           95%-CI    z  p-value
Common effect model  0.5344 [0.4186; 0.6503] 9.04 < 0.0001
Random effects model 0.5007 [0.2396; 0.7619] 3.76   0.0002

Quantifying heterogeneity:
 tau^2 = 0.1159 [0.0271; 0.4769]; tau = 0.3405 [0.1646; 0.6906]
 I^2 = 76.5% [56.5%; 87.3%]; H = 2.06 [1.52; 2.80]

Test of heterogeneity:
     Q d.f.  p-value
 38.22    9 < 0.0001

Results for subgroups (common effect model):
                       k    SMD           95%-CI     Q   I^2
Moderator = INTERNET   5 0.3078 [0.1434; 0.4721] 10.41 61.6%
Moderator = BOOK       5 0.7583 [0.5950; 0.9217] 13.29 69.9%

Test for subgroup differences (common effect model):
                   Q d.f. p-value
Between groups 14.53    1  0.0001
Within groups  23.69    8  0.0026

Results for subgroups (random effects model):
                       k    SMD            95%-CI  tau^2    tau
Moderator = INTERNET   5 0.3370 [-0.0193; 0.6934] 0.1019 0.3191
Moderator = BOOK       5 0.6640 [ 0.3195; 1.0085] 0.0977 0.3126

Test for subgroup differences (random effects model):
                    Q d.f. p-value
Between groups   1.67    1  0.1960

Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau

forest.meta(model2, 
            leftcols = c("study", "es", "se", "Moderator"),
            leftlabs = c("Author", "d", "SE", "Moderator"),
            sortvar = es)