Complexity and power in case-control association studies.

A general method is described for estimation of the power and sample size of studies relating a dichotomous phenotype to multiple interacting loci and environmental covariates. Either a simple case-control design or more complex stratified sampling may be used. The method can be used to design individual studies, to evaluate the power of alternative test statistics for complex traits, and to examine general questions of study design through explicit scenarios. The method is used here to study how the power of association tests is affected by problems of allelic heterogeneity and to investigate the potential role for collective testing of sets of related candidate genes 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 individual allelic variants. Joint testing of multiple candidate loci can also dramatically improve power, despite model misspecification and inclusion of irrelevant loci, but requires an a priori hypothesis defining the set of loci to investigate.