Applications of a mixture survival model with covariates to the analysis of a depression prevention trial

This paper presents a case study of model selection for survival analysis data. We use an approximate Bayesian method for model selection based on assessing the posterior probability of competing models given the data. We introduce the Schwarz criteria, an approximation to the logarithm of the Bayes factor, to provide an indication of evidence in favour of one model compared to another. Specifically, in the context of a depression prevention clinical trial we evaluate the efficacy of treatment in preventing or delaying the time to recurrence of depression, and evaluate how differences in the survival distributions between the two treatment groups depend on explanatory variables of interest. This investigation is based on a mixture survival model that explicitly incorporates the possibility of a surviving fraction.