Over the past decade, a tremendous amount of resources have been dedicated to the pursuit of developing genomic signatures that effectively match patients with targeted therapies. Although dozens of therapies that target DNA mutations have been developed, the practice of studying single candidate genes has limited our understanding of cancer. Moreover, many studies of multiple-gene signatures have been conducted for the purpose of identifying prognostic risk cohorts, and thus are limited for selecting personalized treatments. Existing statistical methods for treatment selection often model treatment-by-covariate interactions that are difficult to specify, and require prohibitively large patient cohorts. In this article, we describe a Bayesian predictive failure time model for treatment selection that integrates multiple-gene signatures. Our approach relies on a heuristic measure of similarity that determines the extent to which historically treated patients contribute to the outcome prediction of new patients. The similarity measure, which can be obtained from existing clustering methods, imparts robustness to the underlying stochastic data structure, which enhances feasibility in the presence of small samples. Performance of the proposed method is evaluated in simulation studies, and its application is demonstrated through a study of lung squamous cell carcinoma. Our Bayesian predictive failure time approach is shown to effectively leverage genomic signatures to match patients to the therapies that are most beneficial for prolonging their survival.