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 interactions to enable a comprehensive analysis of both incidence and cancer mortality in rare cancer cases. These models allow the modulation of spatio-temporal interactions 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 in terms of sensitivity and specificity. Results show that multivariate spatio-temporal models with flexible shared interaction outperform conventional multivariate spatio-temporal models with independent interactions. We use these models to analyze incidence and mortality data for pancreatic cancer and leukaemia among males across 142 administrative healthcare districts of Great Britain over a span of nine biennial periods (2002-2019).

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