Statistical design of the child and adolescent trial for cardiovascular health (catch): Implications of cluster randomization

Regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates. It is argued that binary response models that condition on some or all binary responses in a given "block" are useful for studying certain types of dependencies, but not for the estimation of marginal response probabilities or pairwise correlations. Fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data. Hence, a generalized estimating equation approach is advocated for inference on response probabilities and correlations. Illustrations involving both small and large block sizes are provided.

School-based drug-use prevention studies often apply interventions to entire schools. A major problem for these studies results from the intragroup dependence often seen when intact social groups are assigned to study conditions. Analysis of data from 2 such studies revealed intraclass correlation coefficients between 0.02 and 0.05 for common drug use measures. Because even such modest intragroup dependence can invalidate the traditional fixed-effects analyses, researchers should adopt alternative methods that acknowledge this dependence. These alternative methods are reviewed, and appropriate methods for computing sample size requirements are illustrated. Investigators should consider these analysis issues when planning future studies, because the number of schools required for an unbiased analysis may be substantially greater than for the traditional methods.