Joint models for cause-of-death mortality in multiple populations

We investigate jointly modeling Age-specific rates of various causes of death in a multinational setting. We apply Multi-Output Gaussian Processes (MOGP), a spatial machine learning method, to smooth and extrapolate multiple cause-of-death mortality rates across several countries and both genders. To maintain flexibility and scalability, we investigate MOGPs with Kronecker-structured kernels and latent factors. In particular, we develop a custom multi-level MOGP that leverages the gridded structure of mortality tables to efficiently capture heterogeneity and dependence across different factor inputs. Results are illustrated with datasets from the Human Cause-of-Death Database (HCD). We discuss a case study involving cancer variations in three European nations, and a US-based study that considers eight top-level causes and includes comparison to all-cause analysis. Our models provide insights into the commonality of cause-specific mortality trends and demonstrate the opportunities for respective data fusion. 1 Background and motivation In-depth modeling of the evolution of human mortality necessitates analysis of the prevalent causes of death. This is doubly so for making mortality forecasts into the future across different age groups, populations and genders. In this article we develop a methodology for probabilistic forecasting of cause-specific mortality in a multi-population (primarily interpreted as a multi-national) context. Thus, we simultaneously fit multiple cause-specific longevity surfaces via a spatio-temporal model that accounts for the complex dependencies across causes and countries and across the Age-Year dimensions. While there have been many works on modeling mortality across several populations (Dong et al. 2020, Enchev et al. 2017, Guibert et al. 2019, Hyndman et al. 2013, Kleinow 2015, Li and Lu 2017, Tsai and Zhang 2019), as well as an active literature on cause-of-death mortality, there are very few that do both simultaneously. As we detail below, there are many natural reasons for building such a joint model, and this gap is arguably driven by the underlying “Big Data” methodological challenge. Indeed, with dozens of mortality datasets that are indexed by countries, causes-of-death, genders, etc., developing a scalable approach is daunting. We demonstrate that this issue may be overcome by adapting machine learning approaches, specifically techniques from multi-task learning (Bonilla et al. 2008, Caruana 1997, Letham and Bakshy 2019, Williams et al. 2009). To this end, we employ multi-output Gaussian Processes (MOGP) combined with linear coregionalization. GPs are a kernel-based data-driven regression framework that translates mortality modeling into smoothing and extrapolating an input-output response surface based on noisy observations. It yields a full Department of Statistics and Applied Probability, University of California at Santa Barbara Department of Statistics and Applied Probability, University of California at Santa Barbara, ludkovski@pstat. ucsb.edu ar X iv :2 11 1. 06 63 1v 1 [ st at .A P] 1 2 N ov 2 02 1