Measuring Hospital Performance: Modelling and Visualising Bivariate Outcomes

Quantitative indicators are used to objectively asses the performance of large institutions such as hospitals. However, different methods for accounting for structural and random variation can lead to different conclusions on relative performance. Using data from 92 hospitals and 24,000 colo-rectal cancer patients we show how ranking methods can give substantially different results depending on the casemix correction used and how individual hospital-level effects are accounted for. The funnel plot is a visualisation method used for plotting a performance indicator relative to the size or volume of a hospital. We extend the standard funnel plot to three dimensions to display the simultaneous performance of institutions on two outcomes relative to their volume of patients. An interactive 3D funnel plot is implemented and made freely available from the browser. We then propose a conditional bivariate logistic regression for modelling two particular outcomes relating to colo-rectal cancer surgery; complication and failure to rescue. The model allows the correlation between the two outcomes to be estimated after casemix correction. Finally the standard random effects model is extended by the use of a Bayesian semi-parametric model for modelling nonnormally distributed centre effects. We conclude that the choice of how to display and model performance indicators has important policy implications on performance assessment and that scope remains for refinement of such techniques.