University of Wisconsin - Madison - Departments of Statistics & Biostatistics
Germline mutation of the APC/Apc (adenomatous polyposis coli) tumor suppressor gene predisposes both humans and mice to intestinal tumorigenesis. The Min (multiple intestinal neoplasia) strain of laboratory mouse carries a mutant allele of Apc and consequently presents intestinal tumors according to a certain distribution, thus enabling a study of genetic modifiers of Apc. I will outline a mutagenesis experiment designed to uncover such modifiers. The first statistical problem is to confirm in a candidate kindred that tumor counts are consistent with the presence of the modifier. This is a hypothesis testing problem. A second statistical problem is to identify subkindreds which are likely to carry the modifier. I present a parametric, likelihood-based analysis and then a nonparametric approach. Technically, the model amounts to a certain finite mixture of stochastically ordered components. Tools from order-restricted inference, in particular the Fenchel duality, enable calculations. Elaborations of the model require different computational approaches, including Markov chain Monte Carlo and a novel constrained optimization method due to P. Hoff which uses the mixture representation of elements in a compact convex set.
This work is based on a collaboration with Bill Dove and colleagues at the McArdle Laboratory for Cancer Research and with my student Peter Hoff.