A local-EM algorithm for spatio-temporal disease mapping with aggregated data

Spatial data on disease incidence locations are often aggregated to regional counts to preserve privacy, and spatio-temporal modelling of such can be problematic when there are boundary changes over the study period. Here an inhomogeneous Poisson process with intensity depending on variations in population (known a priori) and a smoothly varying relative risk is estimated with a local-Expectation-Maximization (or local-EM) algorithm. Using incidence data for male bladder cancer in Nova Scotia, Canada, the question of whether the data are consistent with spatially varying but temporally constant relative risk is examined. Areas where there is evidence that relative risk is substantially greater than 1 are identified with the intention of assessing the possible presence of environmental risk factors. This paper extends existing work by incorporating a temporally varying risk surface and an explicit data structure which contains a mixture of point locations and locations aggregated to non-nested areas. This added flexibility allows the modelling of data amalgamated from different sources and collected over many years. While local-EM leads naturally to an Expectation-Maximization Smoothing algorithm, the extension to mixtures of aggregations leads to a modified algorithm that includes an additive term at every iteration to account for observed point locations. (C) 2017 Elsevier B.V. All rights reserved.