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 (chi(2) (MH)), the adjusted Mantel-Haenszel test statistic of Donald-Donner (chi(2) (DD)), Rao-Scott (chi(2) (RSN) and chi(2) (RSP)), and Zhang-Boos (chi(2) (ZBN) and chi(2) (ZBP)), Wald (chi(2) (W)), robust Wald (chi(2) (RW)), score (chi(2) (S)), robust score (chi(2) (RS)), and the test statistic based on generalized linear mixed model (GLMM) (chi(2) (GLMM)). When rho not equal 0, chi(2) (MH) has inflated type I error, and it should not be used when observations are correlated. The results also warn of the use of chi(2) (RSN) and chi(2) (RW) due to their poor performance in terms of empirical significance level. chi(2) (ZBP) and chi(2) (GLMM) have better empirical significance levels as compared to other statistics; however, chi(2) (ZBP) tends to have lower empirical powers than other statistics when the number of clusters (N) is less than 24. chi(2) (RSP) provides the highest empirical powers when rho > or = 0.1 and N < or = 12. When rho < or = 0.01, we recommend the use of chi(2) (RS) and chi(2) (GLMM) since they have better overall performance in terms of empirical significance levels and empirical power levels.