7.2 Subgroup Analyses using the Random-Effects-Model

Now, let us assume I want to know if intervention effects in my meta-analysis differ by region. I use a random-effects-model and the selected coutries Argentina, Australia, China and the Netherlands.

Again, I use the m.hksj meta-analysis output object. I can perform a random-effects-model for between-subgroup-differences using the update.meta function. For this function, we have to set two parameters.

Code Description
byvar Here, we specify the variable in which the subgroup of each study is stored
comb.random Weather we want to use a random-effects-model for between-subgroup-differences. In this case, we have to set comb.random = TRUE
region.subgroup<-update.meta(m.hksj, 
                             byvar=region, 
                             comb.random = TRUE, 
                             comb.fixed = FALSE)
region.subgroup
##                                          95%-CI %W(random)      region
## Call et al.            0.7091 [ 0.1979; 1.2203]        5.2 Netherlands
## Cavanagh et al.        0.3549 [-0.0300; 0.7397]        6.1 Netherlands
## DanitzOrsillo          1.7912 [ 1.1139; 2.4685]        4.2 Netherlands
## de Vibe et al.         0.1825 [-0.0484; 0.4133]        7.1         USA
## Frazier et al.         0.4219 [ 0.1380; 0.7057]        6.8         USA
## Frogeli et al.         0.6300 [ 0.2458; 1.0142]        6.1         USA
## Gallego et al.         0.7249 [ 0.2846; 1.1652]        5.7         USA
## Hazlett-Stevens & Oren 0.5287 [ 0.1162; 0.9412]        5.9   Argentina
## Hintz et al.           0.2840 [-0.0453; 0.6133]        6.5   Argentina
## Kang et al.            1.2751 [ 0.6142; 1.9360]        4.3   Argentina
## Kuhlmann et al.        0.1036 [-0.2781; 0.4853]        6.1   Australia
## Lever Taylor et al.    0.3884 [-0.0639; 0.8407]        5.6   Australia
## Phang et al.           0.5407 [ 0.0619; 1.0196]        5.4   Australia
## Rasanen et al.         0.4262 [-0.0794; 0.9317]        5.3       China
## Ratanasiripong         0.5154 [-0.1731; 1.2039]        4.1       China
## Shapiro et al.         1.4797 [ 0.8618; 2.0977]        4.5       China
## SongLindquist          0.6126 [ 0.1683; 1.0569]        5.7       China
## Warnecke et al.        0.6000 [ 0.1120; 1.0880]        5.4       China
## 
## Number of studies combined: k = 18
## 
##                                       95%-CI    t  p-value
## Random effects model 0.5935 [0.3891; 0.7979] 6.13 < 0.0001
## 
## Quantifying heterogeneity:
## tau^2 = 0.1337; H = 1.64 [1.27; 2.11]; I^2 = 62.6% [37.9%; 77.5%]
## 
## Quantifying residual heterogeneity:
## H = 1.68 [1.27; 2.24]; I^2 = 64.7% [37.6%; 80.0%]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  45.50   17  0.0002
## 
## Results for subgroups (random effects model):
##                        k                   95%-CI     Q  tau^2   I^2
## region = Netherlands   3 0.9142 [-0.9150; 2.7433] 13.06 0.4508 84.7%
## region = USA           4 0.4456 [ 0.0600; 0.8312]  6.87 0.0357 56.3%
## region = Argentina     3 0.6371 [-0.5837; 1.8580]  6.95 0.1826 71.2%
## region = Australia     3 0.3194 [-0.2427; 0.8815]  2.13 0.0204  6.1%
## region = China         5 0.7098 [ 0.2018; 1.2177]  7.81 0.1110 48.8%
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   4.52    4  0.3405
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Hartung-Knapp adjustment for random effects model

Here, we get the pooled effect for each subgroup (country). Under Test for subgroup differences (random effects model), we can see the test for subgroup differences using the random-effects-model, which is not significant (\(Q=4.52\),\(p=0.3405\)). This means that we did not find differences in the overall effect between different regions, represented by the country in which the study was conducted.

Using a fixed-effect-model for within-subgroup-pooling and a fixed-effects-model for between-subgroup-differences

To use a fixed-effect-model in combination with a fixed-effects-model, we can also use the update.meta function again. The procedure is the same as the one we described before, but we have to set comb.random as FALSE and comb.fixed as TRUE.




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