An Overview of Risk-Adjusted Charts

Abstract

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. Copyright 2004 Royal Statistical Society.

A comparison of CUSUM, EWMA, and temporal scan statistics for detection of increases in poisson rates

“…In other cases, the in-control rate depends on factors such as patient characteristics and methodological improvements. These cases require the application of a risk adjustment method 12,46,47 . Another important issue in health surveillance problems is that the quality of the baseline data can be readily contaminated by unexplained noise spikes.…”

On‐line evaluation of the stability of an inspection process

“…A better alternative when small shifts are present are control charts based on cumulative sums (CUSUM). Furthermore, the Shewhart p-chart is found to be less efficient than the CUSUM even when the change in parameter being tested for is large [17]. In this article we will use the so-called algorithmic CUSUM chart.…”

“…The aim of considering subgroups is to reduce as much as possible the sources of differences in defective probabilities between samples, other than the variability of the measurement instrument. This idea of evaluating each observation according to the properties of its own population is similar to the idea of the risk-adjusted monitoring [16,17]. For instance, in the case of a PMVI, the subgroups could be made by classifying the cars by age.…”

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

“…Here, we will concentrate on the RA-CUSUMs, but the reader is referred to the review by Woodall (2002) for other available methods. An early review on RA-CUSUM charts can be found in Grigg and Farewell (2004).…”