Bayesian and frequentist approaches to assessing reliability and precision of health-care provider quality measures

Our purpose was to compare frequentist, empirical Bayes, and Bayesian hierarchical model approaches to estimating reliability of health care quality measures, including construction of credible intervals to quantify uncertainty in reliability estimates, using data on inpatient fall rates on hospital nursing units. Precision of reliability estimates and Bayesian approaches to estimating reliability are not well studied. We analyzed falls data from 2372 medical units; the rate of unassisted falls per 1000 inpatient days was the measure of interest. The Bayesian methods “shrunk” the observed fall rates and frequentist reliability estimates toward their posterior means. We examined the association between reliability and precision in fall rate rankings by plotting the length of a 90% credible interval for each unit’s percentile rank against the unit’s estimated reliability. Precision of rank estimates tended to increase as reliability increased but was limited even at higher reliability levels: Among units with reliability >0.8, only 5.5% had credible interval length <20; among units with reliability >0.9, only 31.9% had credible interval length <20. Thus, a high reliability estimate may not be sufficient to ensure precise differentiation among providers. Bayesian approaches allow for assessment of this precision.