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

Junji Morisawa,Shigeyuki Matsui,Takahiro Otani,Kunihiko Takahashi,Jo Nishino,Ryo Emoto

doi:10.1038/s41431-020-00800-x

Abstract

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.

Highlights

Genome-wide association studies (GWASs) are comprehensive studies on the relationship between disease traits and single nucleotide polymorphisms (SNPs), throughout the Supplementary information The online version of this article contains supplementary material, which is available to authorized users. far, increasing numbers of studies have used the Bayes factor (BF), in addition to the P value [12,13,14]
With the use of appropriate prior distributions, our method aims to realize the inherent effectiveness of the BF analysis, potentially rendering it superior to traditional GWAS analysis based only on the P value
The applications to real-life GWAS datasets indicated that the approximate BF (ABF) prior was excessively dispersed compared to the effect-size distribution estimated by our method

Summary

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Wakefield [16] sidestepped the specification of the prior distribution for the nuisance parameters and derived an explicit form of an approximate BF (ABF) for the association parameter of interest based on two approximations, (1) asymptotic normality of the estimated effect size and (2) a normal prior N(0, W) with the variance W for the effect-size distribution [16]. More complex specifications incorporating dependence of the effect on the minor allele frequency (MAF) are possible [16] Even with these arguments, there is always a risk of mis-specifying the prior distribution, especially in exploratory GWASs with limited prior information. We propose an empirical Bayes method with a flexible, nonparametric prior for the effect-size distribution to address the issue of misspecification. With the use of appropriate (nonparametric) prior distributions, our method aims to realize the inherent effectiveness of the BF analysis, potentially rendering it superior to traditional GWAS analysis based only on the P value

Methods

Discussion

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