Winner's Curse Correction

A resampling-based method that estimates the optimism bias introduced by selecting the most significant variants. The procedure involves repeatedly drawing bootstrap samples from the discovery dataset, re-running the GWAS on each, and measuring how much the effect sizes in the bootstrap samples deflate when applied to the original data. This estimated bias is then subtracted from the naive estimates.

• Procedure:
  1. Generate B bootstrap replicates of the discovery data
  2. Identify top hits in each bootstrap sample
  3. Measure the drop in effect size when applied to the original sample
  4. Subtract the average drop from the original estimates
• Advantage: Non-parametric—does not assume a specific distribution of effects

When combining multiple GWAS, standard fixed-effects or random-effects meta-analysis can propagate Winner's Curse bias from the discovery study. Correction methods integrate the selection event into the meta-analytic likelihood, down-weighting the discovery estimate or explicitly modeling the truncated distribution from which it was drawn.

• Approach: Treat the discovery study estimate as coming from a conditional distribution given significance
• Implementation: Use a weighted average where the discovery weight is penalized based on its expected bias
• Benefit: Prevents the replication study from being contaminated by overestimated discovery effects

A pragmatic correction that transforms p-values into adjusted effect sizes by leveraging the relationship between significance and overestimation. Variants with smaller p-values (more significant) receive larger downward adjustments because they are more likely to be affected by Winner's Curse. The method uses the false discovery rate (FDR) framework to estimate the proportion of null variants and calibrate shrinkage accordingly.

• Mechanism: Maps each variant's p-value to an estimated bias factor
• Output: Shrunken effect sizes where the degree of shrinkage is proportional to the original significance
• Use Case: Particularly effective when working only with summary statistics and no individual-level data

The gold-standard approach: use an independent replication sample to obtain unbiased effect size estimates for variants that were significant in discovery. The replication estimate is free from selection bias because the variant was not selected based on its significance in that dataset. The final estimate is typically a weighted average of discovery and replication, with the replication estimate receiving more weight when Winner's Curse is suspected.

• Design Requirement: Discovery and replication cohorts must be non-overlapping
• Best Practice: Report the replication estimate as the primary effect size
• Limitation: Requires access to a second, adequately powered dataset