Supplementary Material for: Application of the Optimal Discovery Procedure to Genetic Case-Control Studies: Comparison with p Values and Asymptotic Bayes Factors

Objectives: The power of genetic association studies is limited by stringent levels of statistical significance. To improve power, Bayes factors (BFs) have been suggested as an alternative measure to the p value, and Storey recently introduced an optimal discovery procedure (ODP) for multiple testing. We aimed to adapt the ODP to genetic case-control studies and to compare its power to p values and asymptotic BFs (ABFs). Methods: We propose estimators of the ODP based on prospective and retrospective likelihoods. We performed simulations based on independent common SNPs and on sequence data including rare variants. Effects of causal SNPs were simulated under various distributions of effect size. Results: The true ODP is never outperformed, but the estimated ODP has similar power to p values and ABFs. For common SNPs the ODP offers power advantages only in extreme scenarios. However, for rare variants the ODP and ABF detect more associations at low false-positive rates than do p values. Conclusions: The ODP can provide higher power than p values for genetic case-control studies of common variants. However, as the ABF has similar power to the ODP and is computed more rapidly, it is our currently preferred method.