Simultaneous inferences based on empirical Bayes methods and false discovery rates ineQTL data analysis

Abstract

Background: Genome-wide association studies (GWAS) have identified hundreds of genetic variants associated with complex human diseases, clinical conditions and traits. Genetic mapping of expression quantitative trait loci (eQTLs) is providing us with novel functional effects of thousands of single nucleotide polymorphisms (SNPs). In a classical quantitative trail loci (QTL) mapping problem multiple tests are done to assess whether one trait is associated with a number of loci. In contrast to QTL studies, thousands of traits are measured alongwith thousands of gene expressions in an eQTL study. For such a study, a huge number of tests have to be performed (~10(6)). This extreme multiplicity gives rise to many computational and statistical problems. In this paper we have tried to address these issues using two closely related inferential approaches: an empirical Bayes method that bears the Bayesian flavor without having much a priori knowledge and the frequentist method of false discovery rates. A three-component t-mixture model has been used for the parametric empirical Bayes (PEB) method. Inferences have been obtained using Expectation/Conditional Maximization Either (ECME) algorithm. A simulation study has also been performed and has been compared with a nonparametric empirical Bayes (NPEB) alternative.

Results: The results show that PEB has an edge over NPEB. The proposed methodology has been applied to human liver cohort (LHC) data. Our method enables to discover more significant SNPs with FDR<10% compared to the previous study done by Yang et al. (Genome Research, 2010).

Conclusions: In contrast to previously available methods based on p-values, the empirical Bayes method uses local false discovery rate (lfdr) as the threshold. This method controls false positive rate.

Figure 1

A part of the simulated data for $p_1=0.05$.

Figure 2

Effect of minor allele frequency (MAF) on the null distribution. Only upper quantiles (from 80%) have been considered as lower quantiles showing almost no difference.

Figure 3

QQ-plot for eight SNPs.

Figure 4

Minor allele frequency (MAF) distribution. X axis corresponds to minor allele frequency 25% to 50%.