Bayesian Modelling for Spatially Misaligned Health Areal Data: A Multiple Membership Approach

Abstract

AbstractDiabetes prevalence is on the rise in the United Kingdom, and for public health strategy, estimation of relative disease risk and subsequent mapping is important. We consider an application to London data on diabetes prevalence and mortality. In order to improve the estimation of relative risks, we analyse jointly prevalence and mortality data to ensure borrowing strength over the two outcomes. The available data involve two spatial frameworks, areas (Middle Layer Super Output Areas, MSOAs) and general practices (GPs) recruiting patients from several areas. This raises a spatial misalignment issue that we deal with by employing the multiple membership principle. Specifically, we translate areal spatial effects to explain GP practice prevalence according to proportions of GP populations resident in different areas. A sparse implementation in RStan of both the multivariate conditional autoregressive (MCAR) and generalised MCAR (GMCAR) with multiple membership allows the comparison of these bivariate priors as well as exploring the different implications for the mapping patterns for both outcomes. The necessary causal precedence of diabetes prevalence over mortality allows a specific conditionality assumption in the GMCAR, not always present in the context of disease mapping. Additionally, an area-locality comparison is considered to locate high versus low relative risk clusters.