A variable selection procedure is developed for a semi-competing risks regression model with three hazard functions that uses spike-and-slab priors and stochastic search variable selection algorithms for posterior inference. A rule is devised for choosing the threshold on the marginal posterior probability of variable inclusion based on the Deviance Information Criterion (DIC) that is examined in a simulation study. The method is applied to data from esophageal cancer patients from the MD Anderson Cancer Center, Houston, TX, where the most important covariates are selected in each of the hazards of effusion, death before effusion, and death after effusion. The DIC procedure that is proposed leads to similar selected models regardless of the choices of some of the hyperparameters. The application results show that patients with intensity-modulated radiation therapy have significantly reduced risks of pericardial effusion, pleural effusion, and death before either effusion type.
Keywords: Metropolis-Hastings; Semi-Competing Risks; Variable Selection.