Overdispersion in health care performance data: Laney’s approach

The use of statistical process control (SPC) based methods is increasing in health care.1,2 One issue that raises concern is that of overdispersion.3 Overdispersion, which often occurs when sample sizes are very large, is said to occur when the control limits are very close to each other leading to the identification of an “inappropriately” large number of data points signalling special cause variation. Overdispersion is not new to the general SPC literature,4–6 but it has been highlighted recently in healthcare applications of SPC by Spiegelhalter.3 Spiegelhalter explored a number of possible statistical and non-statistical strategies for dealing with overdispersion, favouring on balance a random effects modelling approach. We wish to highlight another approach to handling overdispersion which was developed by Laney.6 We illustrate this approach by using the proportion of emergency readmissions following live discharge data for 2002 from the NHS Performance Ratings dataset.7 In SPC the conventional control chart for handling a time sequence of proportions is the p-chart. Laney showed how to measure and correct for overdispersion …