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. 2009 Jul;33(5):406-18.
doi: 10.1002/gepi.20394.

Unbiased estimation of odds ratios: combining genomewide association scans with replication studies

Jack Bowden  1 , Frank Dudbridge
Affiliations
Free PMC article

Unbiased estimation of odds ratios: combining genomewide association scans with replication studies

Jack Bowden et al. Genet Epidemiol. 2009 Jul.
Free PMC article

Abstract

Odds ratios or other effect sizes estimated from genome scans are upwardly biased, because only the top-ranking associations are reported, and moreover only if they reach a defined level of significance. No unbiased estimate exists based on data selected in this fashion, but replication studies are routinely performed that allow unbiased estimation of the effect sizes. Estimation based on replication data alone is inefficient in the sense that the initial scan could, in principle, contribute information on the effect size. We propose an unbiased estimator combining information from both the initial scan and the replication study, which is more efficient than that based just on the replication. Specifically, we adjust the standard combined estimate to allow for selection by rank and significance in the initial scan. Our approach explicitly allows for multiple associations arising from a scan, and is robust to mis-specification of a significance threshold. We require replication data to be available but argue that, in most applications, estimates of effect sizes are only useful when associations have been replicated. We illustrate our approach on some recently completed scans and explore its efficiency by simulation.

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Figures

Fig. 1
Fig. 1
Top: Difference between the MLE and the corrected MLE of Zhong and Prenctice [2008]. Bottom: Difference between the MLE and the UMVCUE. MLE, maximum likelihood estimator.
Fig. 2
Fig. 2
Difference between the stage 2 estimates and the UMVCUE.
Fig. 3
Fig. 3
Top: Bias and MSE for T1D data. Bottom: bias and MSE for CD data. Numbers calculated using method A. TID, type-1 diabetes; CD, Crohn's disease.
Fig. 4
Fig. 4
Top: Bias and MSE for T1D data. Bottom: bias and MSE for CD data. Numbers calculated using method B. TID, type-1 diabetes; CD, Crohn's disease.
Fig. 5
Fig. 5
Top: Bias and MSE for T1D data. Bottom: bias and MSE for CD data. Numbers calculated using simulation method A, but with an assumed stage 1 of size 20,000 and stage 2 size 2,000. TID, type-1 diabetes; CD, Crohn's disease.
Fig. 6
Fig. 6
Point estimates and bootstrap confidence intervals for the MLE and UMVCUE for rs17696736, varying the stage 2 standard error relative to stage 1. The point estimates and bootstrap confidence intervals are calculated using method A.
See this image and copyright information in PMC

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