Meta-Analysis of Odds Ratio in Cluster-Randomized Design

This technical report details the methodology for conducting a meta-analysis of tests for the odds ratio of two proportions using a random-effects model in a cluster-randomized design. The document outlines the procedure for calculating power and the number of studies required for random-effect meta-analyses involving two-group studies summarized by odds ratios. It explains the distinction between fixed-effects and random-effects models, emphasizing that the latter accounts for variability both within and between studies. The report also discusses the technical details of the power formulas adapted from various sources and describes the assumptions made regarding the data distribution. Additionally, it presents the calculation of odds ratios and the methods for estimating sample sizes adjusted for cluster-randomization. The report concludes with an example illustrating how to determine the number of studies needed for a meta-analysis based on specified parameters, including significance levels and power requirements.