16.3 Subgroup Analyses

Often when conducting a test for subgroup differences within a meta-analysis, we might be interested which effect size difference is needed between the two subgroups for the difference to become significant given the data material at hand. To evaluate this, a power analysis for subgroup differences may be helpful.

We have created a function called power.analysis.subgroup, which calculates the power of a subgroup difference test (using only two subgroups) by implementing the formulae described by Hedges and Pigott (2001). The function is part of the dmetar package. If you have the package installed already, you have to load it into your library first.

library(dmetar)

If you don’t want to use the dmetar package, you can find the source code for this function here. In this case, R doesn’t know this function yet, so we have to let R learn it by copying and pasting the code in its entirety into the console in the bottom left pane of RStudio, and then hit Enter ⏎. The function then requires the ggplot2 package to work.

Let’s assume we have a subgroup analysis in which the pooled effect size of subgroup 1 is \(g=0.30\), with a standard error of \(0.13\), and an effect size of \(g=0.66\) for subgroup 2, with a standard error of \(0.14\). We can then use the function like this:

power.analysis.subgroup(TE1=0.30, 
                        TE2=0.66, 
                        seTE1=0.13, 
                        seTE2=0.14)

## Minimum effect size difference needed for sufficient power: 0.536 (input: 0.36)
## Power for subgroup difference test (two-tailed):

## [1] 0.4698997

From the output, we can see that the power for our subgroup test (47%) is not sufficient. We also see that the effect size difference must be at least 0.536, leaving all other parameters the same, to reach sufficient power.

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References

Hedges, Larry V, and Therese D Pigott. 2001. “The Power of Statistical Tests in Meta-Analysis.” Psychological Methods 6 (3). American Psychological Association: 203.