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

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Abstract
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 (χ2MH), the adjusted Mantel–Haenszel test statistic of Donald–Donner (χ2DD), Rao–Scott (χ2RSN and χ2RSP), and Zhang–Boos (χ2ZBN and χ2ZBP), Wald (χ2W), robust Wald (χ2RW), score (χ2S), robust score (χ2RS), and the test statistic based on generalized linear mixed model (GLMM) (χ2GLMM). When ρ ≠ 0, χ2MH has inflated type I error, and it should not be used when observations are correlated. The results also warn of the use of χ2RSN and χ2RW due to their poor performance in terms of empirical significance level. χ2ZBP and χ2GLMM have better empirical significance levels as compared to other statistics; however, χ2ZBP tends to have lower empirical powers than other statistics when the number of clusters (N) is less than 24. χ2RSP provides the highest empirical powers when ρ ≥ 0.1 and N ≤ 12. When ρ ≤ 0.01, we recommend the use of χ2RS and χ2GLMM since they have better overall performance in terms of empirical significance levels and empirical power levels. Copyright © 2003 John Wiley & Sons, Ltd.