Abstract
BackgroundGenome-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 (). 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.ResultsThe 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).ConclusionsIn 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.
Highlights
Genome-wide association studies (GWASs) have done a remarkable progress in searching for susceptibility genes
There are more common variants truly associated with disease. These variants are highly likely to be expression quantitative trait loci. eQTLs are derived from polymorphisms in the genome that result in differential measurable transcript levels
Two closely related inferential procedures for multiple testing have been discussed in this work-afrequentist approach based on Benjamini and Hochberg’s ([2]) false discovery rate procedure, and an empirical Bayes methodology developed in Efron et al [3,4]
Summary
Simulation study To assess the proposed methodology, a small sample simulation study has been performed. The degrees of freedom corresponding to the null distribution for eack SNP is estimates. Parameters related to the mixture model (4) are estimated using proposed ECME algorithm after estimating the null distribution using permutation method. The distribution of minor allele frequency (MAF) over SNPs is given in the histogram (Figure 4). We fit the mixture model using the ECME algorithm in R 2.15.1 after estimating the null distribution using permutation method. For the sake of parsimony, we further filtered the data and ECME algorithm is used for only top SNPs with p − value < 10−3. For these top SNPs, the mixture model is fitted and estimates are obtained. To compute lfdr and FDR from (5) and (6) respectively, these estimates are used
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