Detecting Interaction Between Random Region and Fixed Age Effects in Disease Mapping

Abstract

The purpose of this article is to draw attention to the possible need for inclusion of interaction effects between regions and age groups in mapping studies. We propose a simple model for including such an interaction in order to develop a test for its significance. The assumption of an absence of such interaction effects is a helpful simplifying one. The measure of relative risk related to a particular region becomes easily and neatly summarized. Indeed, such a test seems warranted because it is anticipated that the simple model, which ignores such interaction, as is in common use, may at times be adequate. The test proposed is a score test and hence only requires fitting the simpler model. We illustrate our approaches using mortality data from British Columbia, Canada, over the 5-year period 1985-1989. For this data, the interaction effect between age groups and regions is quite large and significant.

The Use of Score Tests for Inference on Variance Components

“…In this work a correlated mixed Poisson model and penalized quasilikelihood estimation for this model will be described. The model includes an interaction between random regions and fixed age effects (Dean, Ugarte and Militino, 2001). An analysis of mortality data from British Columbia (B.C.…”

A Gaussian random field model for similarity-based smoothing in Bayesian disease mapping

“…As mentioned by Waller and Carlin [84] DM refers to a collection of methods extending SAE to directly utilize the spatial setting and assumed positive spatial correlation between observations. The data used are aggregated or averaged values at the small area level, representing disease incidence, prevalence or mortality rates, frequently not coming from surveys but coming from counts of disease cases from hospital admissions [52,59]), counts of cancer cases or cancer deaths [9,47,82]), and mortality data [20,59,60]). In our motivating example we use counts of disease cases from a survey.…”

Smooth-CAR mixed models for spatial count data

“…This method led to simpler computations as in the P -splines case, both approaches are very attractive when data sets are large. The models presented by Dean et al (2001) and Militino et al (2001) are a reparametrization of Besag (1984), and allow for the determination of the relative weights between spatial and unstructured variation (these models have already been presented in the previous section). Finally, in the last few years, Congdon (2006) used a generalized additive form that allows regression to vary over regions, and Congdon (2007) considered continuous and discrete priors that account for risks that are discordant with those of neighbouring areas.…”