I understand how to find the weighted mean. However, I am wondering if it is possible to find mean overall age (for all the studies) when I have a list of means and medians for the ages (e.g., some studies present age as a mean and other present it as a median… some simply present a range). Do I just take the mean of the studies that present age as a mean?
Solved – Meta-analysis: How to find the mean age of all studies
meanmedianmeta-analysisstatistical significanceweighted mean
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I thought I would summarize people's suggestions and what I found on my own. It looks like there are meta-analysis methods for analyzing means but not for analyzing medians. These are some sources that are useful for meta-analyzing means:
- http://www.stat.rutgers.edu/home/gyang/researches/gmetaRpackage/gmeta.tutorial_2.2-3.pdf
- http://www.medicine.mcgill.ca/epidemiology/joseph/pbelisle/forest-plot.html
I was mostly interested in analyzing medians because BLL measurements are almost always highly skewed. However, provided the sample sizes of individual studies are not small, and you are meta-analyzing many studies, the central limit theorem allows you to collapse the individual study means into an overall mean. See the following paper for more explanation: Julian P. T. Higgins et al., Meta-analysis of skewed data: Combining results reported on log-transformed or raw scales, Statist. Med. 2008; 27:6072–6092.
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:
- As you correctly state later, simply averaging the studies will not give appropriate weight to more accurate studies. So scratch this approach.
- This is closer to the typically taken approach in meta-analysis (good intuition). Often a weighted average of the observed effect sizes is calculated where the weights correspond to the inverse standard deviations of the effect size estimates from your studies. This is also the approach used in a fixed-effects regression that meta-analyses often include.
- It is not entirely clear what you mean by "reported mean weights" but I suppose it is the observed effect sizes from your studies. As mentioned in the previous bullet, it is indeed common to perform a weighted fixed effects regression, using the inverse standard deviation or variance as weight. Below, I will point you to some options.
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.
- If you have the observed effect sizes and their variances, you can use the function rma.uni with method = "FE" to perform a fixed effects meta-analysis.
- A fixed effect analysis is not appropriate if there is heterogeneity in the studies. Use the Q-test to assess this. If there is heterogeneity, you should consider using a random effects model if you have enough studies. Set method = "REML" in rma.uni to perform one.
- You may also want to examine your data for publication bias. Once you have a model from rma.uni you can create a funnel plot to see if you might have this problem (funnel plots do not prove publication bias is present, but indicate visually that it might be).
- You can also use your output from rma.uni to create a forest plot, which may be helpful in visualizing your studies.
Best Answer
So this does not go unanswered I copy my comment here as an answer.