Bias-reduced estimators and confidence intervals for odds ratios in genome-wide association studies

Abstract

Genome-wide association studies (GWAS) provide an important approach to identifying common genetic variants that predispose to human disease. A typical GWAS may genotype hundreds of thousands of single nucleotide polymorphisms (SNPs) located throughout the human genome in a set of cases and controls. Logistic regression is often used to test for association between a SNP genotype and case versus control status, with corresponding odds ratios (ORs) typically reported only for those SNPs meeting selection criteria. However, when these estimates are based on the original data used to detect the variant, the results are affected by a selection bias sometimes referred to the "winner's curse" (Capen and others, 1971). The actual genetic association is typically overestimated. We show that such selection bias may be severe in the sense that the conditional expectation of the standard OR estimator may be quite far away from the underlying parameter. Also standard confidence intervals (CIs) may have far from the desired coverage rate for the selected ORs. We propose and evaluate 3 bias-reduced estimators, and also corresponding weighted estimators that combine corrected and uncorrected estimators, to reduce selection bias. Their corresponding CIs are also proposed. We study the performance of these estimators using simulated data sets and show that they reduce the bias and give CI coverage close to the desired level under various scenarios, even for associations having only small statistical power.

Fig. 1.

Bias versus β in 1-stage designs. c = Z_{1 − α / 2}, σ is set as the mean of in simulation studies, where number of case–control pairs = N. Minor allele frequency used in simulations is 20%; 10 000 studies were simulated for each scenario.

Fig. 2.

Simulation results under various heterozygote OR values. Bias and SE of based on 100 significant associations. N = 2000 case–control pairs in 1-stage design, and n = 1000 case–control pairs at each stage in 2-stage design.

Fig. 3.

Simulation results under various sample size. N is total case–control pairs in 1-stage design and N/2 is case–control pairs at each stage in 2-stage design. Bias and SE of based on 100 significant associations. Heterozygote OR = 1.2.