Level‐adjusted funnel plots based on predicted marginal expectations: an application to prophylactic antibiotics in gallstone surgery

Funnel plots are widely used to visualize grouped data, for example, in institutional comparison. This paper extends the concept to a multi‐level setting, displaying one level at a time, adjusted for the other levels, as well as for covariates at all levels. These level‐adjusted funnel plots are based on a Markov chain Monte Carlo fit of a random effects model, translating the estimated model parameters to predicted marginal expectations. Working within the estimation framework, we accommodate outlying institutions using heavy‐tailed random effects distributions. We also develop computer‐efficient methods to compute predicted probabilities in the case of dichotomous outcome data and various random effect distributions. We apply the method to a data set on prophylactic antibiotics in gallstone surgery. Copyright © 2014 John Wiley & Sons, Ltd.