Evaluating the risk of stroke is important in reducing the incidence of this devastating disease. Here, we apply Bayesian model averaging to variable selection in Cox proportional hazard models in the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for stroke. We introduce a technique based on the leaps and bounds algorithm which e ciently locates and ts the best models in the very large model space and thereby extends all subsets regression to Cox models. For each independent variable considered, the method provides the posterior probability that it belongs in the model. This is more directly interpretable than the corresponding P-values, and also more valid in that it takes account of model uncertainty. P-values from models preferred by stepwise methods tend to overstate the evidence for the predictive value of a variable. In our data Bayesian model averaging predictively outperforms standard model selection methods for assessing