Semi-parametric empirical Bayes factor for genome-wide association studies

Bayes factor analysis has the attractive property of accommodating the risks of both false negatives and false positives when identifying susceptibility gene variants in genome-wide association studies (GWASs). For a particular SNP, the critical aspect of this analysis is that it incorporates the probability of obtaining the observed value of a statistic on disease association under the alternative hypotheses of non-null association. An approximate Bayes factor (ABF) was proposed by Wakefield (Genetic Epidemiology 2009;33:79-86) based on a normal prior for the underlying effect-size distribution. However, misspecification of the prior can lead to failure in incorporating the probability under the alternative hypothesis. In this paper, we propose a semi-parametric, empirical Bayes factor (SP-EBF) based on a nonparametric effect-size distribution estimated from the data. Analysis of several GWAS datasets revealed the presence of substantial numbers of SNPs with small effect sizes, and the SP-EBF attributed much greater significance to such SNPs than the ABF. Overall, the SP-EBF incorporates an effect-size distribution that is estimated from the data, and it has the potential to improve the accuracy of Bayes factor analysis in GWASs.

Automated summary

Bayes factor analysis can accommodate risks of false negatives and false positives in identifying susceptibility gene variants. The proposed SP-EBF, based on a nonparametric effect-size distribution estimated from the data, assigns greater significance to SNPs with small effect sizes compared to ABF. Incorporating an effect-size distribution estimated from the data, SP-EBF has the potential to improve the accuracy of Bayes factor analysis in GWASs.