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

Document Type : Research Paper


1 Department of Industrial Engineering, K.N Toosi University of Technology, Tehran, Iran.

2 Department of Industrial Engineering, K.N Toosi University of Technology, Tehran, Iran


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.


Main Subjects

Alemi, F. and Sullivan,T. (2001).Tutorial on Risk Adjusted X-Bar Chart: Application to Measurement of Diabetes Control. Quality Management in Healthcare, 9, 57-63.
Amiri, A., &Allahyari, S. (2012). Change Point Estimation Methods for Control Chart PostsignalDiagnostics: ALiterature Review. Quality and Reliability Engineering International, 28(7), 673-685.
Assareh, H . Smith, I. and Mengersen, K. (2011a). Bayesian Estimation of the Time of a Linear Trend in Risk Adjusted Control Charts. IAENG International Journal of Computer Science, 38, 409-417.
Assareh, H . Smith, I. and Mengersen, K. (2011b). Bayesian Change Point Detection in Monitoring Cardiac Surgery Outcomes .Quality Management In Healthcare, 20, 207-222.
Assareh, H . Smith, I.andMengersen, K. (2011c). Change Point Detection in Risk Adjusted Control Charts. Statistical Methods in Medical Research, 0, 1-22.
Assareh, H. and Mengersen, K. (2011b). Bayesian Estimation of the Time of a Decrease in Risk Adjusted Survival Time Control Charts. International Journal of Applied Mathematics, 41, 360-366.
Assareh, H. and Mengersen, K. (2012). Change Point Estimation in Monitoring Survival Time. PLoS ONE. 7,1-7.
Assareh, H. and Mengersen, K.(2011a). Detection of the Time of a Step Change in Monitoring Survival Time.Proceedings of the World Congress on Engineering, London, U.K. July 6-8, 1: 1-9.
Collins, G. S .Jibawi, A. and McCulloch, P. (2010). Control Chart Methods for Monitoring Surgical Performance: A Case Study from Gastro-Oesophageal Surgery. Journal of Cancer Surgery (EJSO). 37, 473-480.
Colosimo, B.M. Castillo, E.D. Editors.(2007). Bayesian Process Monitoring, Control and Optimization.US.CRC Press.47-66.
Cook, A.D. Duke, G. Hart, G.K. Pilcher, D. and Mullany, D. (2008). Review of the Application of Risk-Adjusted Charts to Analyse Mortality Outcomes in Critical Care.Critical Care Resuscitation. 10,239-251.
Fienberg, S.E. van der Linden, W.J. Editors. Lynch, S.M. (2007). Statistical for Social and Behavioral Science. Section11: Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. USA.Springer Science+ Business Media.105-150.
Gombay, E. Hussein, A.A. and Steiner, S.H.(2011). Monitoring Binary Outcomes Using Risk-Adjusted Charts: a Comparative Study.Statistics In Medicine. 30, 2815-2826.
Hogg, R.V. Craig, A.T. (2004). Introduction to Mathematical Statistics.Pearson Education. China. 413-420.
Jones, M.A. and Steiner, S.H. (2011).Assessing the Effect of Estimation Error on Risk-Adjusted CUSUM Chart Performance.International Journal for Quality in Healthcare.24, 1-6.
Matheny, M.E. Machado, L.O. and Resnic, F.S. (2007).Risk-Adjusted Sequential Probability Ratio Test Control Chart Methods for Monitoring Operator and Institutional Mortality Rates in Interventional Cardiology.American Heart Journal. 155, 114-120.
Matheny, M.E. Normand, S.L.T. Gross, T.P. Dabic, D.M. Berrios, N.L. Vidi,V.D. Donnely, S. and Resnic, F.S. (2011).Evaluation of an Automated Safety Surveillance System Using Risk-Adjusted Sequential Probability Ratio Testing. BMC Medical Informatics and Decision Making. 11,1-8.
Myers, R.H. Montgomery, D.C. Vining, G.G.(2002). Generalized Linear Models.John Wiley & Sons, Inc. New York. 322-328.
Paynabar, K. and Jin, J. (2012).Phase I Risk-Adjusted Control Charts for Monitoring Surgical Performance by Considering Categorical Covariates. Journal of Quality Technology. 44, 39-53.
Perry, M.B. PignatielloJr, J.J. Simpson, J.R. (2006). Estimating the Change Point of a Poisson Rate Parameter with a Linear Trend Disturbance.Quality and Reliability Engineering International.22,371-384. DOI: 10.1002/qre.715.
Sego, L.H. Marion, R. Reynolds, Jr. Woodall, W. (2009).Risk-Adjusted Monitoring of Survival Times.Statistics In Medicine. 28, 1386-1401.
Sibaanda, T. and Sibanda ,N. (2007). The CUSUM Chart Method as a Tool for Continuous Monitoring of Clinical Outcomes Using Routinely Collected Data. BMC Medical Research Methodology.7, 1-7.
Spiegelhalter, D., Grigg, O., Kinsman, R. and Treasure, T. (2003).Risk-Adjusted Sequential Probability Test. applications to Bristol, Shipman and adult cardiac surgery.International Journal for Quality in Health Care.15, 7-13.
Steiner, S.T. and Jones, M. (2009). Risk-Adjusted Survival Time Monitoring with an Updating Exponentially Weighted Moving Average (EWMA) Control Chart. Statistics In Medicine. 29, 444-454.
Steiner, S.T. Cook, R.J. Farewell, V.T. and Treasure, T. (2000).Monitoring Surgical Performance Using Risk-Adjusted Cumulative Sun Charts.Biostatistics. 1, 441-452.
Tsui, K.L. Goldsman, D. Jiang, W. and Wong, S.Y. (2010).Recent Research in Public Health Surveillance and Health Management.Prognostics & System Health Management Conference.Macau.MU 3059. 0,1-22.
Unkel, S. Farrington, P. Garthwaite. P.H. Robertson, C.and Andrews, N. (2011). Statistical Methods for the Prospective Detection of Infectious Disease Outbreaks: A review. Journal of the Royal Statistical Society: Series A (Statistics in Society). 175, 49-82.
Woodall, W. (2006).The Use of Control Charts in Health-Care and Public-Health Surveillance.Journal of Quality Technology.38, 89-104.
Woodall, W. H., & Montgomery, D. C. (2014).Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology, 46(1), 78-94.