Bayesian Disease Mapping Beyond Aggregated Counts: A BYM2 Framework for Individual-Level Inference

Abstract

Bayesian disease mapping models are formulated for aggregated areal counts, although veterinary epidemiological studies commonly collect individual-level data from animals located in geographical units. Aggregating such data to the areal level may change the estimand and make individual-level interpretation inappropriate. This study extends the original Besag–York–Mollié 2 (BYM2) model to a multilevel modeling framework for individual-level binary outcomes by embedding a BYM2 random effect within a logistic regression model. The proposed model retains individual animals as the unit of analysis, estimates covariate associations, and accounts for residual structured and unstructured areal variation. We present the work as a practical guide, covering likelihood and priors specifications, BYM2 scaling, estimation algorithm, model diagnostics, posterior predictive checks, practical model comparison, sensitivity analysis, and interpretation of fixed and areal effects. The model is directly applicable to individual-level binary outcomes in a cross-sectional study or a cohort study with a fixed follow-up period, while we also demonstrated that the proposed model can estimate associations generated from an open cohort time-to-event process under appropriate sampling frameworks including probability proportional to size sampling and incidence density sampling. This paper provides a reproducible workflow for applying BYM2 disease mapping to individual-level epidemiological data and clarifies the study designs under which the proposed binary modeling framework can be appropriately used.