Background
I am writing a systematic review and meta-analysis of the association of exposure to X with the outcome Y. I have identified ten studies that report on this subject. This will be a meta-analysis of the published literature, not of individual participant data. I want to report the overall mean age and standard deviation of all patients in all of the studies together. The studies all have different sample sizes. How should I do this?
Possibilities
(1) I imagine that I cannot just add up the reported mean values and divide by ten. This would give smaller studies an undue weight in contributing to the overall mean.
(2) I thought perhaps that I could just do a simple weighted average, using the sample size of each study as the weight. Is this appropriate? Can I also just do a weighted average of the reported standard deviations and ranges? If not, how would I compute those?
(3) Another thought I had was actually taking each of the ten reported mean weights along with their standard deviations and actually plugging them into a meta-analysis program to get a "pooled weight" with a fixed effects model. But perhaps this would be a strange approach?
Any advice on which technique to use? Is there another possibility that I'm not thinking of? Thanks!
Best Answer
Your goal of obtaining a combined effect estimate is the central problem of meta-analysis, as you probably know. Before going too far, it may help you to have a textbook such as this one at hand to use as a reference and to give you some illustrative examples.
Regarding your question:
A very useful R package for performing meta-analysis is metafor. This will provide you with many tools. Of particular interest might be the following.