The selection, for further evaluation or reporting, of only SNPs that meet a statistical significance criterion affects the probability density of the ORs for these selected SNPs, thus potentially causing bias in the OR estimates. This is an example of the “regression to the mean” or “winner's curse” effect [Capen et al., 1971]. The magnitude of bias depends on various factors, including the power of the study. The effect sizes of individual variants, the need for stringent thresholds for establishing statistical significance, and financial constraints on numbers of variants that can be followed up inevitably constrain study power, which may result in profound bias in GWAS findings [COGENT Study, 2008]. Therefore, correcting the bias that attends standard OR estimators is particularly relevant in this context. The standard unadjusted CIs centering around the uncorrected point estimate may have far from the desired coverage rate for the selected ORs. This is a principal reason that many reported associations with common variants have not successfully replicated, and that the estimated effects from replication studies tend to be smaller than those reported in the initial discovery phase.
