Prior Smoothing for Multivariate Disease Mapping Models

TL;DR

This paper explores how different multivariate priors influence spatial smoothing in disease mapping models, providing theoretical and empirical insights into their effects on model departure from data fit.

Contribution

It extends univariate smoothing research to multivariate models, analyzing within and across prior smoothing effects with new metrics and real data applications.

Findings

Different priors induce varying degrees of smoothing.

Theoretical and empirical metrics reveal expected model departure.

Results guide prior choice to balance smoothing and data fit.

Abstract

To date, we have seen the emergence of a large literature on multivariate disease mapping. That is, incidence of (or mortality from) multiple diseases is recorded at the scale of areal units where incidence (mortality) across the diseases is expected to manifest dependence. The modeling involves a hierarchical structure: a Poisson model for disease counts (conditioning on the rates) at the first stage, and a specification of a function of the rates using spatial random effects at the second stage. These random effects are specified as a prior and introduce spatial smoothing to the rate (or risk) estimates. What we see in the literature is the amount of smoothing induced under a given prior across areal units compared with the observed/empirical risks. Our contribution here extends previous research on smoothing in univariate areal data models. Specifically, for three different choices of multivariate prior, we investigate both within prior smoothing according to hyperparameters and across prior smoothing. Its benefit to the user is to illuminate the expected nature of departure from perfect fit associated with these priors since model performance is not a question of goodness of fit. We propose both theoretical and empirical metrics for our investigation and illustrate with both simulated and real data.