Performance of risk-adjusted CUSUM chart under an incorrectly specified binary logistic regression model

Quality control charts used in a healthcare environment, for example, to monitor surgical performance are becoming more common. Risk-adjusted (RA) CUSUM charts, that utilize only raw risk scores like the Parsonnet score to assess the preoperative risk, may lead to a deterioration of the chart’s properties, in particular the false alarm behavior. Our approach considers the application of power transformations in the logistic regression model to improve the fit to the binary outcome data. From a list of alternatives, we derive an appropriate value for the power exponent δ. The average run length (ARL) to false alarm is calculated with the popular Markov chain approximation more efficiently by utilizing the Toeplitz structure of the transition matrix. A sensitivity analysis of the in-control ARL against the actually used value δ shows possible effects of incorrect choices of δ depending on the underlying patient mix. We show that these results can vary from robustness to severe effects (doubled number of false alarms).