An overview of risk-adjusted charts

Summary.  The paper provides an overview of risk-adjusted charts, with examples based on two data sets: the first consisting of outcomes following cardiac surgery and patient factors contributing to the Parsonnet score; the second being age–sex-adjusted death-rates per year under a single general practitioner. Charts presented include the cumulative sum (CUSUM), resetting sequential probability ratio test, the sets method and Shewhart chart. Comparisons between the charts are made. Estimation of the process parameter and two-sided charts are also discussed. The CUSUM is found to be the least efficient, under the average run length (ARL) criterion, of the resetting sequential probability ratio test class of charts, but the ARL criterion is thought not to be sensible for comparisons within that class. An empirical comparison of the sets method and CUSUM, for binary data, shows that the sets method is more efficient when the in-control ARL is small and more efficient for a slightly larger range of in-control ARLs when the change in parameter being tested for is larger. The Shewart p -chart is found to be less efficient than the CUSUM even when the change in parameter being tested for is large.