An evaluation of methods for the stratified analysis of clustered binary data in community intervention trials

A simulation study is conducted in a community intervention setting. Several methods of stratified analysis of clustered binary data are compared in terms of empirical significance and empirical power levels. They are the Mantel-Haenszel test statistic (χ_MH²), the adjusted Mantel-Haenszel test statistic of Donald-Donner (χ_DD²), Rao-Scott (χ_RSN² and χ_RSP²), and Zhang-Boos (χ_ZBN² and χ_ZBP²), Wald (χ_W²), robust Wald (χ_RW²), score (χ_S²), robust score (χ_RS²), and the test statistic based on generalized linear mixed model (GLMM) (χ_GLMM². When ρ≠0, χ_MH² has inflated type I error, and it should not be used when observations are correlated. The results also warn of the use of χ_RSN² and χ_RW² due to their poor performance in terms of empirical significance level. χ_ZBP² and χ_GLMM² have better empirical significance levels as compared to other statistics; however, χ_ZBP² tends to have lower empirical powers than other statistics when the number of clusters (N) is less than 24. χ_RSP² provides the highest empirical powers when ρ≥0.1 and N ≤ 12. When ρ≤0.01, we recommend the use of χ_RS² and χ_GLMM² since they have better overall performance in terms of empirical significance levels and empirical power levels.