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Background  Colon cancer is a leading cause of worldwide cancer death. It has become clear that microRNAs (miRNAs) play a role in the progress of colon cancer and understanding the effect of miRNAs on tumorigenesis could lead to better prognosis and improved treatment. However, most studies have focused on studying differentially expressed miRNAs between tumor and non-tumor samples or between stages in tumor tissue. Limited work has conducted to study the interactions or epistasis between miRNAs and how the epistasis brings about effect on tumor progression. In this study, we investigate the main and pair-wise epistatic effects of miRNAs on the pathological stages of colon cancer using datasets from The Cancer Genome Atlas.    Results  We develop a workflow composed of multiple steps for feature selection based on the Empirical Bayesian Elastic Net (EBEN) method. First, we identify the main effects using a model with only main effect on the phenotype. Second, a corrected phenotype is calculated by removing the significant main effect from the original phenotype. Third, we select features with epistatic effect on the corrected phenotype. Finally, we run the full model with main and epistatic effects on the previously selected main and epistatic features. Using the multi-step workflow, we identify a set of miRNAs with main and epistatic effect on the pathological stages of colon cancer. Many of miRNAs with main effect on colon cancer have been previously reported to be associated with colon cancer, and the majority of the epistatic miRNAs share common target genes that could explain their epistasis effect on the pathological stages of colon cancer. We also find many of the target genes of detected miRNAs are associated with colon cancer. Go Ontology Enrichment Analysis of the experimentally validates targets of main and epistatic miRNAs, shows that these target genes are enriched for biological processes associated with cancer progression.    Conclusion  Our results provide a set of candidate miRNAs associated with colon cancer progression that could have potential translational and therapeutic utility. Our analysis workflow offers a new opportunity to efficiently explore epistatic interactions among genetic and epigenetic factors that could be associated with human diseases. Furthermore, our workflow is flexible and can be applied to analyze the main and epistatic effect of various genetic and epigenetic factors on a wide range of phenotypes.    Electronic supplementary material  The online version of this article (10.1186/s12864-017-4130-7) contains supplementary material, which is available to authorized users.

Epistasis analysis of microRNAs on pathological stages in colon cancer based on an Empirical Bayesian Elastic Net method