This article considers the problem of selecting predictors of time to an event from a high-dimensional set of candidate predictors using data from multiple studies. As an alternative to the current multistage testing approaches, we propose to model the study-to-study heterogeneity explicitly using a hierarchical model to borrow strength. Our method incorporates censored data through an accelerated failure time model. Using a carefully formulated prior specification, we develop a fast approach to predictor selection and shrinkage estimation for high-dimensional predictors. For model fitting, we develop a Monte Carlo expectation maximization (MC-EM) algorithm to accommodate censored data. The proposed approach, which is related to the relevance vector machine (RVM), relies on maximum a posteriori estimation to rapidly obtain a sparse estimate. As for the typical RVM, there is an intrinsic thresholding property in which unimportant predictors tend to have their coefficients shrunk to zero. We compare our method with some commonly used procedures through simulation studies. We also illustrate the method using the gene expression barcode data from three breast cancer studies.