An Efficient Frontier Approach to Scoring and Ranking Hospital Performance

Forthcoming in Operations Research

55 Pages Posted: 25 Apr 2019 Last revised: 6 Dec 2019

See all articles by Daniel Adelman

Daniel Adelman

The University of Chicago Booth School of Business

Date Written: November 25, 2019


The Centers for Medicare and Medicaid Services (CMS) Star Ratings 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 due to weight shifting onto different measures than before.

In contrast, we provide an approach to scoring and ranking hospitals that, under reasonable conditions, ensures 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 (DEA) for simultaneous efficiency analysis and performance evaluation. We develop theory that explains the behavior 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.

Keywords: efficient frontier, ranking and scoring, hospital performance, data envelopment analysis

JEL Classification: I11, C60, C67

Suggested Citation

Adelman, Daniel, An Efficient Frontier Approach to Scoring and Ranking Hospital Performance (November 25, 2019). Forthcoming in Operations Research. Available at SSRN: or

Daniel Adelman (Contact Author)

The University of Chicago Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-834-2019 (Phone)

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