Multilevel Zero-One Inflated Beta Regression Model for the Analysis of the Relationship between Exogenous Health Variables and Technical Efficiency in the Spanish National Health System Hospitals

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Abstract
Background: This article proposes a methodological innovation in health economics for the second stage analysis of technical efficiency in hospitals. It investigates the relationship between the installed capacity in regions and hospitals and their ownership structure. Methods: A multilevel zero-one inflated beta regression model is employed to model pure technical efficiency more adequately than other models frequently used in econometrics. Results: Compared to publicly managed hospitals, the mean efficiency index of hospitals with public-private partnership (PPP) formulas was 4.27-fold. This figure was 1.90-fold for private hospitals. Concerning the efficiency frontier, the odds ratio (OR) of PPP models vs. public hospitals was 42.06. The OR of private hospitals vs. public hospitals was 8.17. A one standard deviation increase in the percentage of beds in intensive care units increases the odds of being situated on the efficiency frontier by 50%. Conclusions: The proportion of hospital beds in intensive care units relates to a higher chance of being on the efficiency frontier. Hospital ownership structure is related to the mean efficiency index of Spanish National Health Service hospitals, as well as the odds of being situated on the efficiency frontier.

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