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.