COVID-19 has led to excess deaths around the world, however it remains unclear how the mortality of other causes of death has changed during the pandemic. Aiming at understanding the wider impact of COVID-19 on other death causes, we study Italian data set that consists of monthly mortality counts of different causes from January 2015 to December 2020. Due to the high dimensional nature of the data, we develop a model which combines conventional Poisson regression with tensor train decomposition to explore the lower dimensional residual structure of the data. We take a Bayesian approach, impose priors on model parameters. Posterior inference is performed using an efficient Metropolis-Hastings within Gibbs algorithm. The validity of our approach is tested in simulation studies. Our method not only identifies differential effects of interventions on cause specific mortality rates through the Poisson regression component, but also offers informative interpretations of the relationship between COVID-19 and other causes of death as well as latent classes that underline demographic characteristics, temporal patterns and causes of death respectively.

翻译：COVID-19已在全球范围内导致超额死亡，然而疫情期间其他死因的死亡率如何变化仍不清楚。为探究COVID-19对其他死因的广泛影响，我们研究了意大利2015年1月至2020年12月期间每月不同死因死亡人数的数据集。鉴于数据的高维特性，我们构建了一个将传统泊松回归与张量列分解相结合的模型，以探索数据的低维残差结构。我们采用贝叶斯方法，对模型参数施加先验分布。后验推断通过一种高效的Gibbs内嵌Metropolis-Hastings算法实现。模拟研究验证了该方法的有效性。我们的方法不仅通过泊松回归组件识别了干预措施对特定死因死亡率的差异化影响，还提供了关于COVID-19与其他死因关系以及分别对应于人口统计特征、时间模式和死因的潜在类别的解释性见解。