Stochastic search gene suggestion: Hierarchical Bayesian model selection meets gene mapping
Swartz, Michael D.
Kimmel, Marek; Amos, Chris
Doctor of Philosophy
This dissertation introduces a novel approach for addressing the complexities of mapping a complex disease by adjusting a Bayesian Model Selection method. Mapping the genes for a complex disease, such as Rheumatoid Arthritis, involves finding multiple genetic loci that may contribute to the onset of the disease. Pairwise testing of the loci leads to the problem of multiple testing. To avoid multiple tests, one can look at haplotypes, or linear sets of loci, but this results in a contingency table with sparse counts, especially when using marker loci with multiple alleles. In order to jointly consider all loci in the problem, we applied a Hierarchical Bayesian Model Selection method to a conditional logistic regression model used in gene mapping. We chose Stochastic Search Variable Selection for its use of latent indicator variables to indicate those covariates, in this case genes, important to the model. We extended the latent variable structure to mirror genetics through a latent allele indicator conditional on a latent locus indicator. We also examined using a prior correlation structure on the allele coefficients that mirrors linkage disequilibrium, a between-locus genetic correlation structure. Ultimately, we ruled out the usefulness of a dependent covariance structure on the prior for allele main effects, but we developed a preliminary method of fitting a positive definite matrix to data based on adjusting the kriging covariance functions commonly used in geostatistics or spatial statistics. We developed a Metropolis-within-Gibbs algorithm to sample our gene suggestion posterior, and evaluated the algorithm's performance on simulated data and completed the research with application to real data, searching for genes associated with Rheumatoid Arthritis. On simulated data, we found that our method successfully recognized disease loci and nondisease loci. Despite complications when analyzing the real data, our method did indicate the genes more strongly associated with Rheumatoid Arthritis.