Dependent stochastic block models for age-indexed sequences of directed causes-of-death networks

Death events commonly arise from complex interactions among interrelated causes, formally classified in reporting practices as underlying and contributing. Leveraging information from death certificates, these interactions can be naturally represented through a sequence of directed networks encoding co-occurrence strengths between pairs of underlying and contributing causes across ages. Although this perspective opens the avenues to learn informative age-specific block interactions among endogenous groups of underlying and contributing causes displaying similar co-occurrence patterns, there has been limited research along this direction in mortality modeling. This is mainly due to the lack of suitable stochastic block models for age-indexed sequences of directed networks. We cover this gap through a novel Bayesian formulation which crucially learns two separate group structures for underlying and contributing causes, while allowing both structures to change smoothly across ages via dependent random partition priors. As illustrated in simulations, this formulation outperforms state-of-the-art solutions that could be adapted to our motivating application. Moreover, when applied to USA mortality data, it unveils structures in the composition, evolution, and modular interactions among causes-of-death groups that were hidden to previous studies. Such findings could have relevant policy implications and contribute to an improved understanding of the recent "death of despair" phenomena in USA.