Hospital size, uncertainty, and pay-for-performance

We construct statistical models to assess whether hospital size will impact the ability to identify "true" hospital ranks in pay-for-performance (P4P) programs. We use Bayesian hierarchical models to estimate the uncertainty associated with the ranking of hospitals by their raw composite score values for three medical conditions: acute myocardial infarction (AMI), heart failure (HF), and community acquired pneumonia (PN). The results indicate a dramatic inverse relationship between the size of the hospital and its expected range of ranking positions for its true or stabilized mean rank. The smallest hospitals among the augmented dataset would likely experience five to seven times more uncertainty concerning their true ranks.