Multivariate Bayesian models with flexible shared interactions for analyzing spatio-temporal patterns of rare cancers

Rare cancers affect millions of people worldwide each year. However, estimating incidence or mortality rates associated with rare cancers presents important difficulties and poses new statistical methodological challenges. In this paper, we expand the collection of multivariate spatio-temporal models by introducing adaptable shared spatio-temporal components to enable a comprehensive analysis of both incidence and cancer mortality in rare cancer cases. These models allow the modulation of spatio-temporal effects between incidence and mortality, allowing for changes in their relationship over time. The new models have been implemented in INLA using r-generic constructions. We conduct a simulation study to evaluate the performance of the new spatio-temporal models. Our results show that multivariate spatio-temporal models incorporating a flexible shared spatio-temporal term outperform conventional multivariate spatio-temporal models that include specific spatio-temporal effects for each health outcome. We use these models to analyze incidence and mortality data for pancreatic cancer and leukaemia among males across 142 administrative health care districts of Great Britain over a span of nine biennial periods (2002-2019).