Bayesian Models for Multivariate Difference Boundary Detection in Areal Data

TL;DR

This paper introduces a Bayesian multivariate model using Dirichlet processes to detect difference boundaries in spatial health data, accounting for multiple correlated diseases across regions.

Contribution

It develops a novel multivariate areally-referenced Dirichlet process model for boundary detection in multivariate spatial data, capturing dependence among diseases and regions.

Findings

Successfully detects difference boundaries in simulated data.

Identifies boundaries for multiple cancers in SEER data.

Demonstrates improved boundary detection over existing methods.

Abstract

Regional aggregates of health outcomes over delineated administrative units (e.g., states, counties, zip codes), or areal units, are widely used by epidemiologists to map mortality or incidence rates and capture geographic variation. To capture health disparities over regions, we seek "difference boundaries" that separate neighboring regions with significantly different spatial effects. Matters are more challenging with multiple outcomes over each unit, where we capture dependence among diseases as well as across the areal units. Here, we address multivariate difference boundary detection for correlated diseases. We formulate the problem in terms of Bayesian pairwise multiple comparisons and seek the posterior probabilities of neighboring spatial effects being different. To achieve this, we endow the spatial random effects with a discrete probability law using a class of multivariate areally-referenced Dirichlet process (MARDP) models that accommodate spatial and inter-disease dependence. We evaluate our method through simulation studies and detect difference boundaries for multiple cancers using data from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute.