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).

翻译：罕见癌症每年影响全球数百万人。然而，估计罕见癌症的发病率或死亡率面临重大困难，并带来新的统计方法学挑战。本文通过引入可调整的共享交互作用，扩展了多元时空模型的集合，从而实现对罕见癌症病例中发病率和癌症死亡率的综合分析。这些模型允许调控发病率与死亡率之间的时空交互作用，使其关系随时间动态变化。新模型已通过R语言通用构造在INLA中实现。我们开展模拟研究，从敏感性和特异性角度评估新时空模型的性能。结果表明，采用灵活共享交互的多元时空模型优于传统独立交互的多元时空模型。我们应用这些模型分析了2002-2019年九个双年周期内英国142个行政医疗区男性胰腺癌和白血病的发病率和死亡率数据。