There is now a large literature on objective Bayesian model selection in the linear model based on the g-prior. The methodology has been recently extended to generalized linear models using test-based Bayes factors (TBFs). In this paper we show that TBFs can also be applied to the Cox proportional hazards model. If the goal is to select a single model, then both the maximum {\em a posteriori} and the median probability model can be calculated. For clinical prediction of survival, we shrink the model-specific log hazard ratio estimates with subsequent calculation of the Breslow estimate of the cumulative baseline hazard function. A Bayesian model average can also be employed. We illustrate the proposed methodology with the analysis of survival data on primary biliary cirrhosis (PBC) patients and the development of a clinical prediction model for future cardiovascular events based on data from the SMART cohort study. Cross-validation is applied to compare the predictive performance with alternative model selection approaches based on Harrell's c-Index, the calibration slope and the integrated Brier score. Finally a novel application of Bayesian variable selection to optimal conditional prediction via landmarking is described. <br
