Spatial disaggregation for relative risks, with an application to drug-related problems in North East England

Recent cross-scale models for spatial disaggregation have likelihoods at region level, but the main model at neighbourhood level, where data are missing, with the object of predicting neighbourhood outcomes. In existing studies, the neighbourhood model involves a single latent indicator, and includes a regression and spatial error, but does not account for demographic variability in risk of the outcome. We instead propose methods for neighbourhood outcomes in the form of age-standardized relative risks. We propose further novel extensions: to borrow strength from comorbid indicators which are observed for neighbourhoods; to pool information on health need or risk from multiple target indicator regressions; and to spatio-temporal specifications for changing relative risk. We therefore provide a comprehensive approach to applying disaggregation to spatial morbidity profiling. We consider two data analyses. One involves cross-validation to assess recoverability of neighbourhood data, and the substantive plausibility of cross-scale neighbourhood models. We demonstrate over 90% recoverability of neighbourhood data. The second application where neighbourhood data are latent involves three target indicators, and investigates drug-related problems for 342 neighbourhoods in North East England, where the observed data are for 12 local authorities. We include a cross-scale trend analysis for drug mortality.