  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.
