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Exponentially weighted moving average charts to compare observed and expected values for monitoring risk-adjusted hospital indicators
  1. D A Cook1,
  2. M Coory2,
  3. R A Webster3
  1. 1Princess Alexandra Hospital, Queensland Health, Queensland, Australia
  2. 2School of Population Health, Mayne Medical Centre, University of Queensland, Queensland, Australia
  3. 3Statistical Analysis Unit, Health Statistics Centre, Queensland Health, Queensland, Australia
  1. Correspondence to Dr David A Cook, Intensive Care Unit, Princess Alexandra Hospital, 199 Ipswich Road, Woolloongabba, Queensland 4102, Australia; david_cook{at}


Objective To introduce a new type of risk-adjusted (RA) exponentially weighted moving average (EWMA) chart and to compare it to a commonly used type of variable life adjusted display chart for analysis of patient outcomes.

Data Routine inpatient data on mortality following admission for acute myocardial infarction, from all public and private hospitals in Queensland, Australia.

Methods The RA-EWMA plots the EWMA of the observed and predicted values. Predicted values were obtained from a logistic regression model for all hospitals in Queensland. The EWMA of the predicted values is a moving centre line, reflecting current patient case mix at a particular hospital. Thresholds around this moving centre line provide a scale by which to assess the importance of trends in the EWMA of the observed values.

Results The RA-EWMA chart can be designed to have equivalent performance, in terms of average run lengths, as variable life adjusted display chart. The advantages of the RA-EWMA are that it communicates information about the current level of an indicator in a direct and understandable way, and it explicitly displays information about the current patient case mix. Also, because it is not reset, the RA-EWMA is a more natural chart to use in health, where it is exceedingly rare to stop or dramatically and abruptly alter a process of care.

Conclusion The RA-EWMA chart is a direct and intuitive way to display information about an indicator while accounting for differences in case mix.

  • Control charts
  • risk adjustment
  • EWMA
  • health care quality
  • statistical process control
  • patient outcomes

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  • Competing interests None.

  • Provenance and peer review Not commissioned; externally peer reviewed.