Identifying Carriers of a Genetic Modifier Using Nonparametric Bayesian Methods

Animals in a certain population of mice each carry a mutant allele called with probability one-half. This population is bred to a strain of mice which carry the Min allele of the APC gene, an allele which results in the development of intestinal tumors. Offspring from this cross are genotyped for Min and tumor counts are recorded. It is assumed that offspring carrying only Min have tumor counts distributed according to , while offspring having both Min and the allele have tumor counts distributed according to , a probability measure assumed to be stochastically smaller than . Presence of the Min allele is observable, but presence of the allele is not. Given the tumor count data and assuming the stochastic ordering constraint, our goal is to estimate , and the the unobserved genotype information. This is done by putting a nonparametric prior on the space of all pairs of stochastically ordered tumor count distributions, and computing posterior quantities of interest using MCMC.