On the accuracy of classifying hospitals on their performance measures

The evaluation, comparison, and public report of health care provider performance is essential to improving the quality of health care. Hospitals, as one type of provider, are often classified into quality tiers (e.g., top or suboptimal) based on their performance data for various purposes. However, potential misclassification might lead to detrimental effects for both consumers and payers. Although such risk has been highlighted by applied health services researchers, a systematic investigation of statistical approaches has been lacking. We assess and compare the expected accuracy of several commonly used classification methods: unadjusted hospital-level averages, shrinkage estimators under a random-effects model accommodating between-hospital variation, and two others based on posterior probabilities. Assuming that performance data follow a classic one-way random-effects model with unequal sample size per hospital, we derive accuracy formulae for these classification approaches and gain insight into how the misclassification might be affected by various factors such as reliability of the data, hospital-level sample size distribution, and cutoff values between quality tiers. The case of binary performance data is also explored using Monte Carlo simulation strategies. We apply the methods to real data and discuss the practical implications.