Observed to expected or logistic regression to identify hospitals with high or low 30-day mortality?

A common quality indicator for monitoring and comparing hospitals is based on death within 30 days of admission. An important use is to determine whether a hospital has higher or lower mortality than other hospitals. Thus, the ability to identify such outliers correctly is essential. Two approaches for detection are: 1) calculating the ratio of observed to expected number of deaths (OE) per hospital and 2) including all hospitals in a logistic regression (LR) comparing each hospital to a form of average over all hospitals. The aim of this study was to compare OE and LR with respect to correctly identifying 30-day mortality outliers. Modifications of the methods, i.e., variance corrected approach of OE (OE-Faris), bias corrected LR (LR-Firth), and trimmed mean variants of LR and LR-Firth were also studied.To study the properties of OE and LR and their variants, we performed a simulation study by generating patient data from hospitals with known outlier status (low mortality, high mortality, non-outlier). Data from simulated scenarios with varying number of hospitals, hospital volume, and mortality outlier status, were analysed by the different methods and compared by level of significance (ability to falsely claim an outlier) and power (ability to reveal an outlier). Moreover, administrative data for patients with acute myocardial infarction (AMI), stroke, and hip fracture from Norwegian hospitals for 2012-2014 were analysed.None of the methods achieved the nominal (test) level of significance for both low and high mortality outliers. For low mortality outliers, the levels of significance were increased four- to fivefold for OE and OE-Faris. For high mortality outliers, OE and OE-Faris, LR 25% trimmed and LR-Firth 10% and 25% trimmed maintained approximately the nominal level. The methods agreed with respect to outlier status for 94.1% of the AMI hospitals, 98.0% of the stroke, and 97.8% of the hip fracture hospitals.We recommend, on the balance, LR-Firth 10% or 25% trimmed for detection of both low and high mortality outliers.