Bayesian inference in a generalized log-logistic proportional hazards model for the analysis of competing risk data: An application to stem-cell transplanted patients data

Typically, the parametric proportional hazard (PH) model is used to examine data on mortality occurrences. Competing risks are prevalent in health information, making it difficult to manage time to event data in clinical investigations. A Bayesian framework is being developed for managing conflicting risk occurrences in clinical data. The objective of this study is to identify the variables that affect patients' odds of surviving peripheral blood stem-cell transplantation, a therapy option for life-threatening blood disorders. In addition, we want to implement a Bayesian model capable of analysing time-to-event data in the context of competing risk. In this research, we analyse failure reasons in the setting of competing risk models using the generalised log-logistic with right-censored scheme. We present competing risks models for censored survival data in the presence of explanatory variables, where each system contains more than one component in series. We assume that each component's survival time follows a generalized log-logistic distribution. We obtain Bayesian estimates of the component's lifetime distribution parameters and regression coefficients. We present a comprehensive Markov chain Monte Carlo (McMC) method to evaluate the estimators' convergence diagnostics. A real-survival data set dealing with stem-cell transplants demonstrated the model's flexibility and advantages.