An adaptive spatio-temporal smoothing model for estimating trends and step changes in disease risk

Statistical models used to estimate the spatio-temporal pattern in disease risk from areal unit data often represent the risk surface for each time period in terms of known covariates and a set of spatially smooth random effects. The latter act as a proxy for unmeasured spatial confounding, whose spatial structure is often characterised by a spatially smooth evolution between some pairs of adjacent areal units while other pairs exhibit large step changes. This spatial heterogeneity is not consistent with a global smoothing model in which partial correlation exists between all pairs of adjacent spatial random effects, and a novel space-time disease model with an adaptive spatial smoothing specification that can identify step changes is therefore proposed. The new model is motivated by a new study of respiratory and circulatory disease risk across the set of Local Authorities in England, and is rigorously tested by simulation to assess its efficacy. Results from the England study show that the two diseases have similar spatial patterns in risk, and exhibit a number of common step changes in the unmeasured component of risk between neighbouring local authorities.