Bayesian two-step Lasso strategy for biomarker selection in personalized medicine development for time-to-event endpoints

Clinical trial designs for targeted therapy development are progressing toward the goal of personalized medicine. Motivated by the need of ongoing efforts to develop targeted agents for lung cancer patients, we propose a Bayesian two-step Lasso procedure for biomarker selection under the proportional hazards model. We seek to identify the key markers that are either prognostic or predictive with respect to treatment from a large number of biomarkers. In the first step of our two-step strategy, we use the Bayesian group Lasso to identify the important marker groups, wherein each group contains the main effect of a single marker and its interactions with treatments. Applying a loose selection criterion in the first step, the goal of first step is to screen out unimportant biomarkers. In the second step, we zoom in to select the individual markers and interactions between markers and treatments in order to identify prognostic or predictive markers using the Bayesian adaptive Lasso. Our strategy takes a full Bayesian approach and is built upon rapid advancement of Lasso methodologies with variable selection. The proposed method is generally applicable to the development of targeted therapies in clinical trials. Our simulation study demonstrates the good performance of the two-step Lasso: Important biomarkers can typically be selected with high probabilities, and unimportant markers can be effectively eliminated from the model.