Comparing apples and oranges: equating the power of case-control and quantitative trait association studies.

Genome-wide association studies have achieved unprecedented success in the identification of novel genes and pathways implicated in complex traits. Typically, studies for disease use a case-control (CC) design and studies for quantitative traits (QT) are population based. The question that we address is what is the equivalence between CC and QT association studies in terms of detection power and sample size? We compare the binary and continuous traits by assuming a threshold model for disease and assuming that the effect size on disease liability has similar feature as on QT. We derive the approximate ratio of the non-centrality parameter (NCP) between CC and QT association studies, which is determined by sample size, disease prevalence (K) and the proportion of cases (v) in the CC study. For disease with prevalence <0.1, CC association study with equal numbers of cases and controls (v=0.5) needs smaller sample size than QT association study to achieve equivalent power, e.g. a CC association study of schizophrenia (K=0.01) needs only approximately 55% sample size required for association study of height. So a planned meta-analysis for height on approximately 120,000 individuals has power equivalent to a CC study on 33,100 schizophrenia cases and 33,100 controls, a size not yet achievable for this disease. With equal sample size, when v=K, the power of CC association study is much less than that of QT association study because of the information lost by transforming a quantitative continuous trait to a binary trait.