Nonparametric Bayesian Variable Selection With Applications to Multiple Quantitative Trait Loci Mapping With Epistasis and Gene–Environment Interaction

The joint action of multiple genes is an important source of variation for complex traits and human diseases. However, mapping genes with epistatic effects and gene-environment interactions is a difficult problem because of relatively small sample sizes and very large parameter spaces for quantitative trait locus models that include such interactions. Here we present a nonparametric Bayesian method to map multiple quantitative trait loci (QTL) by considering epistatic and gene-environment interactions. The proposed method is not restricted to pairwise interactions among genes, as is typically done in parametric QTL analysis. Rather than modeling each main and interaction term explicitly, our nonparametric Bayesian method measures the importance of each QTL, irrespective of whether it is mostly due to a main effect or due to some interaction effect(s), via an unspecified function of the genotypes at all candidate QTL. A Gaussian process prior is assigned to this unknown function. In addition to the candidate QTL, nongenetic factors and covariates, such as age, gender, and environmental conditions, can also be included in the unspecified function. The importance of each genetic factor (QTL) and each nongenetic factor/covariate included in the function is estimated by a single hyperparameter, which enters the covariance function and captures any main or interaction effect associated with a given factor/covariate. An initial evaluation of the performance of the proposed method is obtained via analysis of simulated and real data.