Complexity and power in case-control association studies

A general method is described for estimation of the power and sample size o f studies relating a dichotomous phenotype to multiple interacting loci and environmental covariates. Either a simple case-control design or more comp lex stratified sampling may be used. The method can be used to design indiv idual studies, to evaluate the power of alternative test statistics for com plex traits, and to examine general questions of study design through expli cit scenarios. The method is used here to study how the power of associatio n tests is affected by problems of allelic heterogeneity and to investigate the potential role for collective testing of sets of related candidate gen es in the presence of locus heterogeneity. The results indicate that allele -discovery efforts are crucial and that omnibus tests or collective testing of alleles can be substantially more powerful than separate testing of ind ividual allelic variants. Joint testing of multiple candidate loci can also dramatically improve power, despite model misspecification and inclusion o f irrelevant loci, but requires an a priori hypothesis defining the set of loci to investigate.