An Efficient Frontier Approach to Scoring and Ranking Hospital Performance

The Centers for Medicare and Medicaid Services (CMS) star rating methodology for publicly evaluating hospitals uses a latent variable model that is based on the presumption of a single, but unobservable, hospital-specific quality factor shared across a group of performance measures. Performance measures are given higher weight if they statistically appear to be more strongly correlated with this hidden factor. We show how this approach, when applied to measures that are weakly or not correlated with each other, can effectively ignore measures and can exhibit “knife-edge” instability, so that even if hospitals improve relative to all other hospitals, they may nonetheless score lower overall because of weight shifting onto different measures than before. In contrast, we provide an approach to scoring and ranking hospitals that, under reasonable conditions, ensures that hospitals that improve relative to all other hospitals obtain higher scores, while also having the capability to autonomously adjust weights as measures are added or subtracted over time. Rather than exploit statistical correlation, we propose a conic optimization framework that offers a new integrated approach in data envelopment analysis for simultaneous efficiency analysis and performance evaluation. We develop theory that explains the behaviour of our approach, including various properties satisfied by hospital scores at optimality. Using data, we apply our approach to score and rank nearly every hospital in the United States and demonstrate the extent to which it agrees or disagrees with the existing approach to the CMS star ratings.