  Comparing outcomes across hospitals, often to identify underperforming
hospitals, is a critical task in health services research. However, naive
comparisons of average outcomes, such as surgery complication rates, can be
misleading because hospital case mixes differ -- a hospital's overall
complication rate may be lower due to more effective treatments or simply
because the hospital serves a healthier population overall. In this paper, we
develop a method of ``direct standardization'' where we re-weight each hospital
patient population to be representative of the overall population and then
compare the weighted averages across hospitals. Adapting methods from survey
sampling and causal inference, we find weights that directly control for
imbalance between the hospital patient mix and the target population, even
across many patient attributes. Critically, these balancing weights can also be
tuned to preserve sample size for more precise estimates. We also derive
principled measures of statistical precision, and use outcome modeling and
Bayesian shrinkage to increase precision and account for variation in hospital
size. We demonstrate these methods using claims data from Pennsylvania,
Florida, and New York, estimating standardized hospital complication rates for
general surgery patients. We conclude with a discussion of how to detect low
performing hospitals.
