Statistical methodology for complex biological systems

My research program involves statistical modeling of complex biological phenomena, including genetic causes of disease and animal abundance estimation. Progress in these areas can ultimately lead to new medical therapies and new animal management strategies. My approach is interdisciplinary in that I work with excellent researchers in the sciences to identify and solve statistical aspects of important scientific problems.In genetics I will continue working on problems related to quantifying association between genetic loci and disease. In particular, I will explore methods for detecting rare genetic variants and for modeling epistasis, or interaction between two or more genetic loci. Many current studies are based on the common disease-common variant hypothesis, which suggests that commonly occurring complex diseases are caused by commonly occurring genetic variants (alleles). Recently, authors have proposed that complex diseases may be caused by rare polymorphisms in several genes. I will develop novel statistical methods for determining multiple rare and interacting genetic variants. I will begin by comparing some recently proposed techniques with respect to their power and their sensitivity to genotyping errors. I will extend a model we recently described for association at two genetic loci which allows for interaction, with the view to simplifying inferences so that many genetic loci can be examined efficiently. I will also continue investigation of recently developed methods for testing genetic association using genotypic counts for discordant relative pairs, based on penetrance odds ratios (penetrance is the conditional probability of the disease given the genotype). Further theoretical and simulation studies will be carried out to assess the performance of these methods in comparison with techniques currently in use.I will also investigate extensions to a recently developed technique for estimation abundance of whales using acoustic binary transects, based on the assumption of a homogeneous Poisson process. Such extensions will allow departure from homogeneity to be estimated and tested. The situation where the actual number of whales can be recorded, rather than just their presence or absence, will also be studied