Restricted multivariate conditional autoregressive models for disease mapping

Abstract

Bayesian spatial and spatiotemporal models are widely used in disease mapping to stabilize rate estimates in sparse-count settings by pooling information across regions, subgroups, and time. Yet this pooling carries a risk: such models can end up reflecting their own structure more than the data. In other words, they exhibit unexpectedly high informativeness. This issue has already raised concern in the univariate conditional autoregressive (CAR) setting. This dissertation characterizes and mitigates this same risk in multivariate and spatiotemporal extensions of the CAR model, where added dependencies across outcomes, strata, and time further amplify it. The first contribution extends the informativeness framework to the multivariate CAR (MCAR) model for Poisson-distributed data, yielding a closed-form, outcome-specific informativeness measure that reduces to the univariate case when outcomes are modeled independently. Because directly restricting this measure requires awkward constraints on the between-outcome covariance matrix, we introduce a regression-based reparameterization of the MCAR model that preserves conjugacy and admits simple truncated full conditionals for enforcing the restriction. We illustrate this restricted MCAR model using county-level ischemic heart disease mortality data stratified by race and sex. The second contribution extends this framework to spatiotemporal disease mapping, treating repeated annual observations as the correlated dimension. We adopt a first-order antedependence (AD(1)) structure for the between-year covariance, which lets year-to-year correlation decay with lag while varying over time. The same regression-based reparameterization is especially well suited here, substantially reducing the number of parameters to estimate while maintaining computational efficiency. We demonstrate this restricted AD MCAR model using ten years of county-level heart disease mortality data from Texas, stratified by race and sex. The third contribution extends the framework from Poisson-distributed mortality data to binomially distributed survey data, whose prevalence estimates are natively modeled with a logit-normal prior. Using a delta-method approximation linking the logit-normal to a conjugate beta prior, we derive an analogous informativeness measure and extend it to the multivariate setting. This is especially relevant for survey data, where small sample sizes heighten both the benefits and risks of borrowing strength. We illustrate this framework with a spatiotemporal application to census-tract-level obesity prevalence, jointly modeled across survey years, race, sex, and age. Together, these three extensions provide researchers with practical tools for quantifying and controlling the informativeness of multivariate and spatiotemporal disease mapping models, allowing the benefits of borrowing strength across regions, outcomes, and time to be realized without sacrificing the integrity of the underlying data.