Bayesian Estimation of the Time of a Decrease in Risk-Adjusted Survival Time Control Charts

Change point detection has been recognized as an essential effort of root cause analyses within quality control programs since enables clinical experts to search for potential causes of disturbance in hospital outcomes more effectively. In this paper, we consider estimation of the time when a drop has occurred in the mean survival time observed over patients undergone an in-control cardiac surgery with death and survive outcomes in the presence of variable patient mix. The data are right censored since the monitoring is conducted over a limited follow-up period. The effect of risk factors prior to the surgery is captured using a Weibull accelerated failure time regression model. We apply Bayesian hierarchical models to formulate the change point. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of drops and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. This advantage enhances when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.