Hierarchical Multivariate Directed Acyclic Graph Auto-Regressive (MDAGAR) models for spatial diseases mapping

TL;DR

This paper introduces MDAGAR models for multivariate spatial disease mapping, enabling disentanglement of inter-disease and spatial dependencies with flexible hierarchical structure and Bayesian model averaging.

Contribution

The paper develops a novel hierarchical multivariate DAG-based autoregressive model that captures spatial and inter-disease dependence, with Bayesian model selection to address ordering issues.

Findings

Demonstrates improved modeling of spatial and inter-disease relationships.

Shows effectiveness through simulation studies and real cancer data.

Provides interpretable insights into disease spatial patterns.

Abstract

Disease mapping is an important statistical tool used by epidemiologists to assess geographic variation in disease rates and identify lurking environmental risk factors from spatial patterns. Such maps rely upon spatial models for regionally aggregated data, where neighboring regions tend to exhibit similar outcomes than those farther apart. We contribute to the literature on multivariate disease mapping, which deals with measurements on multiple (two or more) diseases in each region. We aim to disentangle associations among the multiple diseases from spatial autocorrelation in each disease. We develop Multivariate Directed Acyclic Graphical Autoregression (MDAGAR) models to accommodate spatial and inter-disease dependence. The hierarchical construction imparts flexibility and richness, interpretability of spatial autocorrelation and inter-disease relationships, and computational ease, but depends upon the order in which the cancers are modeled. To obviate this, we demonstrate how Bayesian model selection and averaging across orders are easily achieved using bridge sampling. We compare our method with a competitor using simulation studies and present an application to multiple cancer mapping using data from the Surveillance, Epidemiology, and End Results (SEER) Program.