Abstract
Genome-wide association studies (GWAS) using survival time as phenotype deserve attention. Important examples include time to progression or recurrence free survival of a cancer patient underwent a specific treatment and onset time of certain disease or biological event. Most existing GWAS utilize single SNP analysis that does not model the problem properly and hence is not statistically efficient. Moreover, while GWAS results are often reproducible, the discoveries can explain only small amount of heritability. This dissertation proposes a Bayesian variable selection approach to GWAS with survival outcome by utilizing Weibull regression model, in which the parameter describing the proportion of the variance of the survival phenotype explained by the covariates (PVE) admits an analytic form. Treating GWAS as a Bayesian variable selection problem, we extend Bayesian variable selection regression (BVSR) for GWAS using multiple linear regression [1]. In particular, we compute posterior distribution of PVE and posterior inclusion probability of each SNP for inference. The former is useful in planning future genetic studies. The latter describes the confidence of the association results. A carefully designed MCMC algorithm is used to sample the posterior distribution. Simulation studies show that both PVE and PIP (posterior inclusion probability) can be studied successfully and this method outperforms the single SNP analysis methods in terms of the plot of the number of true positive findings versus the number of false positive findings. We illustrate the method by studying the association between SNPs and age at menarche based on healthy female in Taiwan. In particular, we get the 90% credible interval of PVE being (0.339, 0.401), smaller than the reported heritability of 0.50.