P-values have been on of the reasons behind lack of reproducibility in scientific discoveries and especially in replicated studies and multiple testing(Benjamin et al., 2017). This problem is especially prevalent in Genome-Wide Association Studies (GWAS), where estimated effects have upward bias and often fail to replicate in validation studies. This phenomenon is known as the winner’s curse (Zöllner & Pritchard, 2007). To account for this discrepancy, previous studies perform two analyses: one with all the data together, and one only using the validation site data. However, this approach is based on the underlying assumption that the association found in discovery sites is true, which is problematic for multiple testing applications such as genome-wide association studies. Furthermore, if there is a true effect, leaving out the discovery data, which could be a large portion of the total dataset, reduces power.

One example of the winner’s curse in action is the analysis of the association between single nucleotide polymorphisms (SNPs) in the p53 protein, which is needed for cell growth and DNA repair, and invasive ovarian cancer. Three independent discovery studies focused on TP53 polymorphisms and risk of ovarian cancer: the North Carolina Ovarian Cancer Study (NCOCS), the Mayo Clinic Case-Control Study (MAYO), and the Polish Ovarian Cancer Study (POCS). These were restricted to non-Hispanic white women with newly diagnosed, histologically confirmed, primary invasive epithelial ovarian cancer and to non-Hispanic white controls. 23 SNPs were genotyped in total, with some overlap between sites. Ten other sites contributed data: the Australian Ovarian Cancer Study (AOCS) and the Australian Cancer Study (ACS) presented together as AUS, the Family Registry for Ovarian Cancer (FROC, presented as STA), the Hawaiian Ovarian Cancer Study (HAW), the Malignant Ovarian Cancer Study Denmark (MALOVA), the New England Case-Control Study (NEC), the Nurses’ Health Study (NHS), SEARCH Cambridge (SEA), the Los Angeles County Case-Control Study of Ovarian Cancer (LAC-CCOC, presented here as USC), the University of California at Irvine study (UCI), and the United Kingdom Ovarian Cancer Population Study (UKOPS, presented here as UKO). The combined data set (discovery and replication) comprised 5,206 white, non-Hispanic invasive epithelial ovarian cancer cases, of which 2,829 were classified as serous invasive ovarian cancer, and 8,790 white non-Hispanic controls. Analysis was restricted to white, non-Hispanic invasive serous ovarian cancer cases and white, non-Hispanic controls.

Mixed effect SNP-at-a-time analysis of 5 SNPs that were chosen for replication resulted in associations between 2 SNPs and serous invasive cancer (Joellen M. Schildkraut et al., 2009). Only one of these was strongly supported to be associated in a follow-up analysis using Multi-level Inference for SNP Association (MISA), which employs Bayesian Model Averaging and Bayes Factors for selection (Joellen M Schildkraut et al., 2010). However, most recent studies with added data have not found evidence of association between any TP53 SNPs and cancer (C. M. Phelan et al., 2017).

The aim of this project is twofold: to explore ways in which discovery findings can be reported to avoid the winner’s curse, and to combine discovery results with validation data in a coherent manner accounting for the selection effect.

After a review of existing literature, we propose three approaches to adress this: a fully Bayesian model, a conditional likelihood prior for discovery site data, and a Bayes Factor approximation to the probability of association. The performance of these methods is tested on normal simulations, and then on hierarchical simulations split into discovery and validation “sites”. All three proposed methods provide improvements over naive models. Finally, the models are used to reanalyze the tp53 SNPs; none of the SNPs are found to be significant under any model.