Comparing a multivariate response Bayesian random effects logistic regression model with a latent variable item response theory model for provider profiling on multiple binary indicators simultaneously

Provider profiling entails comparing the performance of hospitals on indicators of quality of care. Many common indicators of healthcare quality are binary (eg, short‐term mortality, use of appropriate medications). Typically, provider profiling examines the variation in each indicator in isolation across hospitals. We developed Bayesian multivariate response random effects logistic regression models that allow one to simultaneously examine variation and covariation in multiple binary indicators across hospitals. Use of this model allows for (i) determining the probability that a hospital has poor performance on a single indicator; (ii) determining the probability that a hospital has poor performance on multiple indicators simultaneously; (iii) determining, by using the Mahalanobis distance, how far the performance of a given hospital is from that of an average hospital. We illustrate the utility of the method by applying it to 10 881 patients hospitalized with acute myocardial infarction at 102 hospitals. We considered six binary patient‐level indicators of quality of care: use of reperfusion, assessment of left ventricular ejection fraction, measurement of cardiac troponins, use of acetylsalicylic acid within 6 hours of hospital arrival, use of beta‐blockers within 12 hours of hospital arrival, and survival to 30 days after hospital admission. When considering the five measures evaluating processes of care, we found that there was a strong correlation between a hospital's performance on one indicator and its performance on a second indicator for five of the 10 possible comparisons. We compared inferences made using this approach with those obtained using a latent variable item response theory model.