Using individual patient data (IPD) from various studies, do I need to weight observations in a meta-analysis? Each study used a two-stage cluster sampling design with uniform samples per cluster and unequal cluster sizes.

In a regression analysis, I have incorporated random effects on the intercept at the study level. Do I also have to incorporate clusters nested within studies? Do I need find out the total size of each cluster and weight observations accordingly? These do not seem to be common practice in the IDP meta-analyses that I have read.

My question also applies to drawing inference on prevalence using IDP data in a meta-analysis. Population estimates of total instance of occurrence would be:

$$x'_{clu} = \big(\frac{M}{m}\big) \sum_{i=1}^m \big(\frac{N_{i}}{n_{i}}\big) \sum_{j=1}^{n_{i}}x_{ij}$$ Where M is the number of clusters in the population, m is the number of clusters in the sample, N is the total cluster population, n is the sample in each cluster, and $x_{ij}$ is the occurrence in each cluster of j observations and i clusters.

In this instance would I have to weight by study and cluster?

Equation source: Levy & Lemeshow, 2008, p. 303


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