Bayesian Modeling of Survival Data in the Presence of Competing Risks with Cure Fractions and Masked Causes

In handling the presence of multiple competing risks, methods such as the multivariate failure times model, mixture model, subdistribution model (partially and fully specified), and the cause-specific hazard model have historically been used under the assumption that all individuals will either “fail" or are censored. However, in practice, there may be a group of individuals who are actually cured of a given cause (but not necessarily all causes). The proposed model addresses this issue of cured fractions, using a mixture cure rate model with cause-specific hazards for the non-cured survival time. To handle the common issue of masked causes, where cause of death is not known, we incorporate these individuals into the likelihood function directly. A Bayesian approach to inference is proposed, rooted in the augmentation of the joint posterior distribution, using baseline survival covariates to model non-cured survival time. A more informative Jeffrey’s-type prior is used for the cure rate model coefficients to help address identifiability in the model, necessitating the proposal of a more efficient sampling algorithm to avoid direct calculation of the derivative of the Jeffreys-type prior. A variation of the DIC and C-index measures are developed to allow for cause-specific assessment of the utility of the proposed methodology not dependent upon the latent structure of the masked causes and cure rate indicators. Findings are demonstrated empirically using prostate cancer diagnosis data from the National Cancer Institute’s Surveillance, Epidemiology, and End Results Program.