Bayesian Estimation of Change Point in Phase One Risk Adjusted Control Charts

Use of risk adjusted control charts for monitoring patients’ surgical outcomes is now popular.These charts are developed based on considering the patient’s pre-operation risks. Change point detection is a crucial problem in statistical process control (SPC).It helpsthe managers toanalyzeroot causes of out-of-control conditions more effectively. Since the control chart signals do not necessarily indicate the real change point of the process, in this researcha Bayesian estimation methodis applied to find the time and the size of a change in patients’ post-surgery death or survival outcome. The process is monitored in phase Iusing Risk Adjusted Log-likelihood Ratio Test (RALRT) chart,in whichthe logistic regression model is applied to take into accountpre-operation individual risks. Markov Chain Monte Carlo method is applied to obtain the posterior distribution of the change pointmodel including time and size of the change in the Bayesian framework and also to obtain the corresponding credible intervals. Performance evaluations of the Bayesian estimator in comparison with the maximum likelihood estimator (MLE) are conducted by means of different simulation studies. When the magnitude of the change is small, simulation results indicate superiority of the Bayesian estimator over MLE, especially when a more accurate estimation of the change point is of interest.