Hierarchical Models for Combining Ecological and Case–Control Data

Summary The ecological study design suffers from a broad range of biases that result from the loss of information regarding the joint distribution of individual‐level outcomes, exposures, and confounders. The consequent nonidentifiability of individual‐level models cannot be overcome without additional information; we combine ecological data with a sample of individual‐level case–control data. The focus of this article is hierarchical models to account for between‐group heterogeneity. Estimation and inference pose serious computational challenges. We present a Bayesian implementation based on a data augmentation scheme where the unobserved data are treated as auxiliary variables. The methods are illustrated with a dataset of county‐specific infant mortality data from the state of North Carolina.