Marginal indirect standardization using latent clustering on multiple hospitals

A method was introduced in 2018 of performing indirect standardization for hospital profiling when only the marginal distributions of confounding variables are observed for the index hospital but the full joint covariate distribution is available for the reference hospitals (Wang et al, J Am Stat Assoc 2018; 114:662-630). The method constructs a synthetic comparison hospital using a weighted combination of reference hospitals, with weights assumed to follow a Dirichlet distribution with equal concentration parameters. In this article, we propose a novel method that improves upon the approach in a previous study (Wang et al, J Am Stat Assoc 2018; 114:662-630), by assuming the existence of latent classes among reference hospitals to allow for unequal Dirichlet concentration parameters. The latent class memberships, and thus the hospital weights, are informed by hospital-level characteristics. Our new method results in less biased point estimates and narrower uncertainty intervals for the standardized incidence ratio compared with the existing approach. We show the superiority of our novel methods in an application to a study on prevalence of high-radiation computed tomography exams, as well as in a simulation of the same medical context.