Ranking hospitals when performance and risk factors are correlated: A simulation-based comparison of risk adjustment approaches for binary outcomes

Background: The conceptualization of hospital quality indicators usually includes some form of risk adjustment to account for hospital differences in case mix. For binary outcome variables like in-hospital mortality, frequently utilized risk adjusted measures include the standardized mortality ratio (SMR), the risk standardized mortality rate (RSMR), and excess risk (ER). All of these measures require the estimation of expected hospital mortality, which is often based on logistic regression models. In this context, an issue that is often neglected is correlation between hospital performance (e.g. care quality) and patient-specific risk factors. The objective of this study was to investigate the impact of such correlation on the adequacy of hospital rankings based on different measures and methods. Methods: Using Monte Carlo simulation, the impact of correlation between hospital care quality and patient-specific risk factors on the adequacy of hospital rankings was assessed for SMR/RSMR, and ER based on logistic regression and random effects logistic regression. As an alternative method, fixed effects logistic regression with Firth correction was considered. The adequacies of the resulting hospital rankings were assessed by the shares of hospitals correctly classified into quintiles according to their true (unobserved) care qualities. Results: The performance of risk adjustment approaches based on logistic regression and random effects logistic regression declined when correlation between care quality and a risk factor was induced. In contrast, fixed-effects-based estimations proved to be more robust. This was particularly true for fixed-effects-logistic-regression-based ER. In the absence of correlation between risk factors and care quality, all approaches showed similar performance. Conclusions: Correlation between risk factors and hospital performance may severely bias hospital rankings based on logistic regression and random effects logistic regression. ER based on fixed effects logistic regression with Firth correction should be considered as an alternative approach to assess hospital performance.