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Handling over-dispersion of performance indicators

Correspondence to:
Dr D J Spiegelhalter
Senior Scientist, MRC Biostatistics Unit, Institute of Public Health, Cambridge CB2 2SR, UK; david.spiegelhalter{at}mrc-bsu.cam.ac.uk Objectives: A problem can arise when a performance indicator shows substantially more variability than would be expected by chance alone, since ignoring such "over-dispersion" could lead to a large number of institutions being inappropriately classified as "abnormal". A number of options for handling this phenomenon are investigated, ranging from improved risk stratification to fitting a statistical model that robustly estimates the degree of over-dispersion.

Design: Retrospective analysis of publicly available data on survival following coronary artery bypass grafts, emergency readmission rates, and teenage pregnancies.

Setting: NHS trusts in England.

Results: Funnel plots clearly show the influence of the method chosen for dealing with over-dispersion on the "banding" a trust receives. Both multiplicative and additive approaches are feasible and give intuitively reasonable results, but the additive random effects formulation appears to have a stronger conceptual foundation.

Conclusion: A random effects model may offer a reasonable solution. This method has now been adopted by the UK Healthcare Commission in their derivation of star ratings.

Keywords: over-dispersion; risk stratification; random effects model; performance indicators

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