Bayesian information criterion for censored survival models

We investigate the Bayesian Information Criterion (BIC) for variable select ion in models for censored survival data. Kass and Wasserman (1995, Journal of the American Statistical Association 90, 928-934) showed that BIC provi des a close approximation to the Bayes factor when a unit-information prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is defined in terms of the number of uncensored events in stead of the number of observations. For a simple censored data model, this revision results in a better approximation to the exact Bayes factor based on a conjugate unit-information Drier. In the Cox proportional hazards reg ression model, we propose defining BIC in terms of the maximized partial li kelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parame ter space and is shown to improve predictive performance for assessing stro ke risk in the Cardiovascular Health Study.