A primer on using shrinkage to compare in-hospital mortality between centers

Outcomes of cardiothoracic surgery are usually compared among hospitals or physicians by reporting the frequency of in-hospital mortality. Although there is agreement that these frequencies should be adjusted for case mix, there remains uncertainty about the value of using a statistical model that represents hospitals as random effects as opposed to the conventional approach of fixed effects. For years, the Northern New England Cardiovascular Disease Study Group has compared in-hospital mortality after coronary artery bypass graft surgery among centers using a fixed effects approach. An alternative method using random effects has become increasingly popular, and is the method used by cardiothoracic surgery registries such as the Massachusetts Data Analysis Center. The purpose of this report is to provide a short background on fixed versus random effects modeling, describe the use of shrinkage estimators including empirical Bayes, and illustrate them using data from the Northern New England Cardiovascular Disease Study Group. We conclude that both are acceptable approaches to hospital profiling if done in combination with appropriate risk adjustment.