Bayesian modelling for semi-competing risks data in the presence of censoring

In biomedical research, challenges to working with multiple events are often observed while dealing with time-to-event data. Studies on prolonged survival duration are prone to having numerous possibilities. In studies on prolonged survival, patients might die of other causes. Sometimes in the survival studies, patients experienced some events (e.g. cancer relapse) before dying within the study period. In this context, the semi-competing risks framework was found useful. Similarly, the prolonged duration of follow-up studies is also affected by censored observation, especially interval censoring, and right censoring. Some conventional approaches work with time-to-event data, like the Cox-proportional hazard model. However, the accelerated failure time (AFT) model is more effective than the Cox model because it overcomes the proportionality hazard assumption. We also observed covariates impacting the time-to-event data measured as the categorical format. No established method currently exists for fitting an AFT model that incorporates categorical covariates, multiple events, and censored observations simultaneously. This work is dedicated to overcoming the existing challenges by the applications of R programming and data illustration. We arrived at a conclusion that the developed methods are suitable to run and easy to implement in R software. The selection of covariates in the AFT model can be evaluated using model selection criteria such as the Deviance Information Criteria (DIC) and Log-pseudo marginal likelihood (LPML). Various extensions of the AFT model, such as AFT-DPM and AFT-LN, have been demonstrated. The final model was selected based on minimum DIC values and larger LPML values.