The Winner's Curse

Abstract

Winners in competitive bidding are losers in that they frequently pay too high a price. This phenomenon has recently been noted in genetic association studies of common diseases. The winner's curse in genetic association studies appears as upward bias in the estimated effect of a newly identified allele on disease risk when the study design lacks sufficient statistical power. The winner's curse manifests mostly in genome‐wide association (GWA) studies in which 300 000–1 000 000 single‐nucleotide polymorphisms are tested. The winner's curse also occurs in meta‐analysis of several GWA data sets. To counter this effect, construction of a large‐scale GWA study or a consortium‐based meta‐analysis of GWA studies that is sufficiently powered to account for the presence of between‐study heterogeneity is required.

Key Concepts:

  • ‘Winner's curse’ is named for the phenomenon whereby winners at competitive auctions are likely to pay in excess of the value of the item.

  • Genetic association studies have been conducted to identify susceptibility genes underlying common diseases such as diabetes, schizophrenia and coronary artery disease. In genetic association studies, the winner's curse is the phenomenon whereby the disease risk of a newly identified genetic association is overestimated when the statistical power of original study is not sufficient.

  • The winner's curse implies that the sample size required for confirmatory study will be underestimated, resulting in failure of replication study to corroborate the association.

  • The winner's curse is common in genome‐wide association (GWA) studies because most single‐GWA studies are underpowered to detect small genetic effects at a stringent genome‐wide significance level.

  • In consortium‐based meta‐analyses of several GWA studies having high between‐study heterogeneity, there is an increased probability of the winner's curse.

  • In the discovery phase, construction of a larger scale GWA study or a consortium‐based meta‐analysis of GWA studies that evaluates between‐study heterogeneity is required to reduce probability of occurrence of the winner's curse.

  • In the replication phase, methodologies for reducing bias in the estimates of genetic effect are helpful to calculate the sample sizes required to replicate the discovered associations.

Keywords: auction; common disease‐common variant hypothesis; genetics; genome‐wide association study; heterogeneity; linkage disequilibrium; meta‐analysis; multiple testing; single‐nucleotide polymorphism; winner's curse

Figure 1.

Flowchart of a typical genome‐wide association (GWA) study (a) and a consortium‐based meta‐analysis of GWA studies (b).

Figure 2.

Sample sizes required to detect an association of per allele odds ratio (OR) of 1.1, 1.2, 1.3, 1.5 and 2.0 with power of 80% at the genome‐wide significance level of 5.0×10−7 as a function of disease‐susceptibility allele frequency ranging from 0.05 to 0.95.

Figure 3.

Graphical representation of theoretical consideration on the winner's curse using mathematical modelling. (a) Three PDFs of test statistic Z: black curve shows Z under the null hypothesis of no association; blue curve shows Z under the assumption that μ=4.3 corresponding to the power to detect the association at the significance level (P<5.7×10−7) is 0.24 and green curve shows Z conditional on |Z|>c. The area highlighted in blue shows p(|Z|>c). For visualisation, we set c and μ as 5.0 and 4.3, respectively. (b) Bias in test statistic due to the restriction in range of |Z|>c as a function of μ.

Figure 4.

Simulations for (a) the powers in random effects model (REM) meta‐analyses of detecting a gene–disease association at the significance level of 5.7×10−7 and (b) the mean OR of the simulations passing the threshold as the function of τ2, disease allele frequency fA=0.3, the overall OR=1.4 or 2.0. When overall OR=2.0, the lines of the powers for scenarios II, III and IV are overlapping. The description of each simulation scenario is in Table. The between‐study variance (τ2) varied from 0.0 to 0.02 with increments of 0.001. Adapted from Nakaoka and Inoue , with permission from Nature Publishing Group.

Figure 5.

Frequency distribution of estimated summary odds ratios (ORs) of simulated meta‐analyses passing the genome‐wide significance threshold in simulation scenario I in Table. The true OR is assumed to be 1.4 under dominant model with disease susceptibility allele frequency of 0.30.

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Nakaoka, Hirofumi, and Inoue, Ituro(Nov 2010) The Winner's Curse. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0022495]