Using hierarchical models to analyse clinical indicators: a comparison of the gamma-Poisson and beta-binomial models
by
Peter Howley
The University of Newcastle
Coauthors: Robert Gibberd (The University of Newcastle)

Clinical Indicators (CIs) are increasingly being used to assess, compare and determine the potential to improve the care provided by hospitals and physicians. Australian hospitals have been providing data for CIs for ten years but the results for 1998-2000 have been published using a new methodology. The publication uses the gamma-Poisson hierarchical model to firstly correct for the effects of sampling variation by obtaining the empirical Bayesian ‘shrunken’ estimates for the CI proportions for each hospital. Secondly, an estimate of the potential improvement that could be achieved if the mean proportion was shifted to the 20th centile is obtained for each of the 185 CIs. The method and usefulness of this measure of potential improvement are described.

Of some concern is whether the gamma-Poisson or the beta-binomial model should be used. A comparison of the formulae for the two shrinkage estimators shows that the gamma-Poisson model results in greater shrinkage towards the overall mean. This was verified empirically using the Obstetrics and Gynaecology CI data. Consequently, the gamma-Poisson model results in an underestimation of the potential improvement. The relative differences in potential improvements increased with increasing mean proportions. We recommend that the beta-binomial model should be used on the basis of theoretical and empirical grounds.

Date received: April 3, 2002