Bayesian mapping of genomewide interacting quantitative trait loci for ordinal traits

Development of statistical methods and software for mapping interacting QTL has been the focus of much recent research. We previously developed a Bayesian model selection framework, based on the composite model space approach, for mapping multiple epistatic QTL affecting continuous traits. In this study we extend the composite model space approach to complex ordinal traits in experimental crosses. We jointly model main and epistatic effects of QTL and environmental factors on the basis of the ordinal probit model (also called threshold model) that assumes a latent continuous trait underlies the generation of the ordinal phenotypes through a set of unknown thresholds. A data augmentation approach is developed to jointly generate the latent data and the thresholds. The proposed ordinal probit model, combined with the composite model space framework for continuous traits, offers a convenient way for genome wide interacting QTL analysis of ordinal traits. We illustrate the proposed method by detecting new QTL and epistatic effects for an ordinal trait, dead fetuses, in a F-2 intercross of mice. Utility and flexibility of the method are also demonstrated using a simulated data set. Our method has been implemented in the freely available package R/qtlbim, which greatly, facilitates the general usage of the Bayesian methodology for genomewide interacting QTL analysis for continuous, binary, and ordinal traits in experimental crosses.