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The quality of healthcare provided by hospitals is subject to considerable variability. Consequently, accurate measurements of hospital performance are essential for various decision-makers, including patients, hospital managers and health insurers. Hospital performance is assessed via the health outcomes of their patients. However, as the risk profiles of patients between hospitals vary, measuring hospital performance requires adjustment for patient risk. This task is formalized in the state-of-the-art procedure through a hierarchical generalized linear model, that isolates hospital fixed-effects from the effect of patient risk on health outcomes. Due to the linear nature of this approach, any non-linear relations or interaction terms between risk variables are neglected. In this work, we propose a novel method for measuring hospital performance adjusted for patient risk. This method captures non-linear relationships as well as interactions among patient risk variables, specifically the effect of co-occurring health conditions on health outcomes. For this purpose, we develop a tailored neural network architecture that is partially interpretable: a non-linear part is used to encode risk factors, while a linear structure models hospital fixed-effects, such that the risk-adjusted hospital performance can be estimated. We base our evaluation on more than 13 million patient admissions across almost 1,900 US hospitals as provided by the Nationwide Readmissions Database. Our model improves the ROC-AUC over the state-of-the-art by 4.1 percent. These findings demonstrate that a large portion of the variance in health outcomes can be attributed to non-linear relationships between patient risk variables and implicate that the current approach of measuring hospital performance should be expanded.