Risk-Adjusted Cumulative Sum Charting Procedures

Abstract

Risk-adjusted charting procedures for monitoring the performances of a cardiac surgeon or a group of surgeons have recently gained prominence. Charting procedures developed for manufacturing processes are no longer appropriate because they do not take a patient’s risk into account. The first charting procedure, variable life-adjusted display (VLAD) that takes a patient’s risk into account was introduced in 1997. The VLAD plots the predicted mortality count minus the observed count cumulatively. The statistic plotted is intuitive and it has gained widespread attention and adoption. However, the run length performance of this chart is still not clearly understood because of the lack of a proper signalling rule. A risk-adjusted cumulative sum (RA-CUSUM) chart based on testing the odds ratio that a patient dies was proposed in 2000. In this paper, we developed and studied a general RA-CUSUM chart of which the RA-CUSUM chart based on odds ratio is a special case. The general RA-CUSUM chart allows testing to be done beyond just testing the odds ratio. One interesting note: although the VLAD and RA-CUSUM chart look seemingly different, we show that the RA-CUSUM chart and the RA-CUSUM chart based on the VLAD’s monitoring statistic are in fact the same chart.