Multi-SNP genetic association analysis has become increasingly important in analyzing data from genome-wide association studies (GWASs) and molecular quantitative trait loci (QTL) mapping studies. In this paper, we propose novel computational approaches to address two outstanding issues in Bayesian multi-SNP genetic association analysis: namely, the control of false positive discoveries of identified association signals and the maximization of the efficiency of statistical inference by utilizing summary statistics. Quantifying the strength and uncertainty of genetic association signals has been a long-standing theme in statistical genetics. However, there is a lack of formal statistical procedures that can rigorously control type I errors in multi-SNP analysis. We propose an intuitive hierarchical representation of genetic association signals based on Bayesian posterior probabilities, which subsequently enables rigorous control of false discovery rate (FDR) and construction of Bayesian credible sets. From the perspective of statistical data reduction, we examine the computational approaches of multi-SNP analysis using z-statistics from single-SNP association testing and conclude that they likely yield conservative results comparing to using individual-level data. Built on this result, we propose a set of sufficient summary statistics that can lead to identical results as individual-level data without sacrificing power. Our novel computational approaches are implemented in the software package, DAP-G (https://github.com/xqwen/dap), which applies to both GWASs and genome-wide molecular QTL mapping studies. It is highly computationally efficient and approximately 20 times faster than the state-of-the-art implementation of Bayesian multi-SNP analysis software. We demonstrate the proposed computational approaches using carefully constructed simulation studies and illustrate a complete workflow for multi-SNP analysis of cis expression quantitative trait loci using the whole blood data from the GTEx project.
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