With the development of genome-wide association studies, how to gain information from a large scale of data has become an issue of common concern, since traditional methods are not fully developed to solve problems such as identifying loci-to-loci interactions (also known as epistasis). Previous epistatic studies mainly focused on local information with a single outcome (phenotype), while in this paper, we developed a two-stage global search algorithm, Greedy Equivalence Search with Local Modification (GESLM), to implement a global search of directed acyclic graph in order to identify genome-wide epistatic interactions with multiple outcome variables (phenotypes) in a case–control design. GESLM integrates the advantages of score-based methods and constraint-based methods to learn the phenotype-related Bayesian network and is powerful and robust to find the interaction structures that display both genetic associations with phenotypes and gene interactions. We compared GESLM with some common phenotype-related loci detecting methods in simulation studies. The results showed that our method improved the accuracy and efficiency compared with others, especially in an unbalanced case–control study. Besides, its application on the UK Biobank dataset suggested that our algorithm has great performance when handling genome-wide association data with more than one phenotype.

Bayesian methods are widely used in the GWAS meta-analysis. But the considerable consumption in both computing time and memory space poses great challenges for large-scale meta-analyses. In this research, we propose an algorithm named SMetABF to rapidly obtain the optimal ABF in the GWAS meta-analysis, where shotgun stochastic search (SSS) is introduced to improve the Bayesian GWAS meta-analysis framework, MetABF. Simulation studies confirm that SMetABF performs well in both speed and accuracy, compared to exhaustive methods and MCMC. SMetABF is applied to real GWAS datasets to find several essential loci related to Parkinson’s disease (PD) and the results support the underlying relationship between PD and other autoimmune disorders. Developed as an R package and a web tool, SMetABF will become a useful tool to integrate different studies and identify more variants associated with complex traits.

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