Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping

Background: Complex binary traits are influenced by many factors including the main effects of many quantitative trait loci (QTLs), the epistatic effects involving more than one QTLs, environmental effects and the effects of gene-environment interactions. Although a number of QTL mapping methods for binary traits have been developed, there still lacks an efficient and powerful method that can handle both main and epistatic effects of a relatively large number of possible QTLs. Results: In this paper, we use a Bayesian logistic regression model as the QTL model for binary traits that includes both main and epistatic effects. Our logistic regression model employs hierarchical priors for regression coefficients similar to the ones used in the Bayesian LASSO linear model for multiple QTL mapping for continuous traits. We develop efficient empirical Bayesian algorithms to infer the logistic regression model. Our simulation study shows that our algorithms can easily handle a QTL model with a large number of main and epistatic effects on a personal computer, and outperform five other methods examined including the LASSO, HyperLasso, BhGLM, RVM and the single-QTL mapping method based on logistic regression in terms of power of detection and false positive rate. The utility of our algorithms is also demonstrated through analysis of a real data set. A software package implementing the empirical Bayesian algorithms in this paper is freely available upon request. Conclusions: The EBLASSO logistic regression method can handle a large number of effects possibly including the main and epistatic QTL effects, environmental effects and the effects of gene-environment interactions. It will be a very useful tool for multiple QTLs mapping for complex binary traits.