Model-based standardization using an outcome model with random effects

Model-based standardization uses a statistical outcome model or exposure model to estimate a population-average association that is unconfounded by selected covariates. With it, one can compare groups using a distribution of confounders identical in each group to that of a standard population. We develop an approach based on an outcome model, in which the mean of the outcome is modeled conditional on the exposure and the confounders. In our approach, there is a confounder that clusters the observations into a very large number of categories. We treat the parameters for the clusters as random effects. We use a between-within model to account for the association of the random effects not only with the exposure but also with the cluster population sizes. We review alternative approaches presented in the literature, and we compare the outcome-modeling approach to recently proposed exposure-modeling approaches incorporating random effects. To illustrate, we use 2014 to compare proportions of acute respiratory tract infection diagnoses with an antibiotic prescription for emergency department versus outpatient visits, adjusting for confounding by unmeasured patient level variables and measured diagnosis-level variables. We also present results of a simulation study.