Hospital-level associations with 30-day patient mortality after cardiac surgery: a tutorial on the application and interpretation of marginal and multilevel logistic regression

The Australasian Society of Cardiac and Thoracic Surgeons (ASCTS) registry provided data on 32,354 patients undergoing cardiac surgery in 18 hospitals from 2001 to 2009. The logistic regression methods related 30-day mortality after surgery to hospital characteristics with concurrent adjustment for patient characteristics.Hospital-level mortality rates varied from 1.0% to 4.1% of patients. Ordinary, marginal and multilevel regression methods differed with regard to point estimates and conclusions on statistical significance for hospital-level risk factors; ordinary logistic regression giving inappropriately narrow confidence intervals. The median odds ratio, MOR, from the multilevel model was 1.2 whereas ORs for most patient-level characteristics were of greater magnitude suggesting that unexplained between-hospital variation was not as relevant as patient-level characteristics for understanding mortality rates. For hospital-level characteristics in the multilevel model, 80% interval ORs, IOR-80%, supplemented the usual ORs from the logistic regression. The IOR-80% was (0.8 to 1.8) for academic affiliation and (0.6 to 1.3) for the median annual number of cardiac surgery procedures. The width of these intervals reflected the unexplained variation between hospitals in mortality rates; the inclusion of one in each interval suggested an inability to add meaningfully to explaining variation in mortality rates.Marginal and multilevel models take different approaches to account for correlation between patients within hospitals and they lead to different interpretations for hospital-level odds ratios.Over the past two decades there has been a dramatic growth in the publication of cardiac surgery outcomes research. Many recent studies have examined the impact of hospital, physician, and process-related characteristics on outcomes for hospitalized patients who have undergone cardiac surgery [1-8]. By virtue of their observational design, these studies rely heavily on the use