In this paper we discuss the use of charts derived from the sequential probability ratio test (SPRT): the cumulative sum (CUSUM) chart, RSPRT (resetting SPRT), and FIR (fast initial response) CUSUM. The theoretical development of the methods is described and some considerations one might address when designing a chart, explored, including the approximation of average run lengths (ARLs), the importance of detecting improvements in a process as well as detecting deterioration and estimation of the process parameter following a signal. Two examples are used to demonstrate the practical issues of quality control in the medical setting, the first a running example and the second a fully worked example at the end of the paper. The first example relates to 30-day mortality for patients of a single cardiac surgeon over the period 1994-1998, the second to patient deaths in the practice of a single GP, Harold Shipman. The charts' performances relative to each other are shown to be sensitive to the definition of the 'out of control' state of the process being monitored. In light of this, it is stressed that a suitable means by which to compare charts is chosen in any specific application.

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.

We consider the general problem of simultaneously monitoring multiple series of counts, applied in this case to methicillin resistant Staphylococcus aureus (MRSA) reports in 173 UK National Health Service acute trusts. Both within-trust changes from baseline ('local monitors') and overall divergence from the bulk of trusts ('relative monitors') are considered. After standardizing for type of trust and overall trend, a transformation to approximate normality is adopted and empirical Bayes shrinkage methods are used for estimating an appropriate baseline for each trust. Shewhart, exponentially weighted moving average and cumulative sum charts are then set up for both local and relative monitors: the current state of each is summarized by a p-value, which is processed by a signalling procedure that controls the false discovery rate. The performance of these methods is illustrated by using 4.5 years of MRSA data, and the appropriate use of such methods in practice is discussed.

The Sets method has been advocated in previous work as a method for monitoring adverse medical outcomes where the adverse event rate is low. Here, a risk-adjusted version of the refined Sets method is presented and an example is given to demonstrate its advantage over the unadjusted method. The method is suitable for any risk distribution and does not assume that changes in risk will be small. A graphical representation, referred to as the Grass plot, of the original and risk-adjusted methods is also given.