Confidence interval estimates of an index of quality performance based on logistic regression models

This paper considers an index of hospital quality performance defined as the ratio of the observed number deaths to the number predicted by a fitted logistic regression model. We study tests and confidence intervals under two different scenarios depending on the availability of an estimate of the covariance matrix of the coefficients from the fitted logistic regression model. We propose parametric as well as bootstrap-based confidence intervals. We apply the methods to an analysis of the performance of 27 intensive care units.