Bayesian Variable Selection Using Knockoffs with Applications to Genomics

Given the costliness of HIV drug therapy research, it is important not only to maximize true positive rate (TPR) by identifying which genetic markers are related to drug resistance, but also to minimize false discovery rate (FDR) by reducing the number of incorrect markers unrelated to drug resistance. In this study, we propose a multiple testing procedure that unifies key concepts in computational statistics, namely Model-free Knockoffs, Bayesian variable selection, and the local false discovery rate. We develop an algorithm that utilizes the augmented data-Knockoff matrix and implement Bayesian Lasso. We then identify signals using test statistics based on Markov Chain Monte Carlo outputs and local false discovery rate. We test our proposed methods against non-bayesian methods such as Benjamini-Hochberg (BHq) and Lasso regression in terms TPR and FDR. Using numerical studies, we show the proposed method yields lower FDR compared to BHq and Lasso for certain cases, such as for low and equi-dimensional cases. We also discuss an application to an HIV-1 data set, which aims to be applied analyzing genetic markers linked to drug resistant HIV in the Philippines in future work.