A general modelling framework for multivariate disease mapping

Abstract

This paper deals with multivariate disease mapping. We propose a novel framework that encompasses most of the models already proposed. Our framework starts with a simple identity, reformulating Kronecker products of covariance matrices as simple matrix products. This formula is computationally convenient, and its generalizations reproduce most of the proposals in the disease mapping literature. Use of the identity leads to a flexible, general and computationally convenient modelling framework, making it possible to combine spatial dependence structures and different relationships between diseases with limited effort. Moreover, as the proposed modelling framework covers most of the Gaussian Markov random field-based multivariate disease mapping models in the literature, it allows comparison of all these models in a common context, thus helping us to understand them better.