Assessing the effect of estimation error on risk-adjusted CUSUM chart performance

Background. Risk-adjusted control charts have become popular for monitoring processes that involve the management and treatment of patients in hospitals or other healthcare institutions. However, to date, the effect of estimation error on risk-adjusted control charts has not been studied. Methods. We studied the effect of estimation error on risk-adjusted binary cumulative sum (CUSUM) performance using actual and simulated data on patients undergoing coronary artery bypass surgery and assessed for mortality up to 30 days post-surgery. The effect of estimation error was indicated by the variability of the ‘true’ average run lengths (ARLs) obtained using repeated sampling of the observed data under various realistic scenarios. Results. Results showed that estimation error can have a substantial effect on risk-adjusted CUSUM chart performance in terms of variation of true ARLs. Moreover, the performance was highly dependent on the number of events used to derive the control chart parameters and the specified ARL for an in-control process (ARL0). However, the results suggest that it is the uncertainty in the overall adverse event rate that is the main component of estimation error. Conclusions. When designing a control chart, the effect of estimation error could be taken into account by generating a number of bootstrap samples of the available Phase I data and then determining the control limit needed to obtain an ARL0 of a pre-specified level 95% of the time. If limited Phase I data are available, it may be advisable to continue to update model parameters even after prospective patient monitoring is implemented.