• Disease mapping;
  • Kernel smoothing;
  • Local-EM;
  • Local likelihood;
  • Nonparametric inference;
  • Spatial statistics

Summary Mapping disease risk often involves working with data that have been spatially aggregated to census regions or postal regions, either for administrative reasons or confidentiality. When studying rare diseases, data must be collected over a long time period in order to accumulate a meaningful number of cases. These long time periods can result in spatial boundaries of the census regions changing over time, as is the case with the motivating example of exploring the spatial structure of mesothelioma lung cancer risk in Lambton County and Middlesex County of southwestern Ontario, Canada. This article presents a local-EM kernel smoothing algorithm that allows for the combining of data from different spatial maps, being capable of modeling risk for spatially aggregated data with time-varying boundaries. Inference and uncertainty estimates are carried out with parametric bootstrap procedures, and cross-validation is used for bandwidth selection. Results for the lung cancer study are shown and discussed.