Multi-output Gaussian processes for multi-population longevity modelling

We investigate joint modelling of longevity trends using the spatial statistical framework of Gaussian process (GP) regression. Our analysis is motivated by the Human Mortality Database (HMD) that provides unified raw mortality tables for nearly 40 countries. Yet few stochastic models exist for handling more than two populations at a time. To bridge this gap, we leverage a spatial covariance framework from machine learning that treats populations as distinct levels of a factor covariate, explicitly capturing the cross-population dependence. The proposed multi-output GP models straightforwardly scale up to a dozen populations and moreover intrinsically generate coherent joint longevity scenarios. In our numerous case studies, we investigate predictive gains from aggregating mortality experience across nations and genders, including by borrowing the most recently available “foreign” data. We show that in our approach, information fusion leads to more precise (and statistically more credible) forecasts. We implement our models in R, as well as a Bayesian version in Stan that provides further uncertainty quantification regarding the estimated mortality covariance structure. All examples utilise public HMD datasets.

Gender specific excess mortality in Italy during the COVID-19 pandemic accounting for age

Since the beginning of the COVID-19 pandemic, data have been accumulated to examine excess mortality in the first half of 2020. Mortality in the preceding year or years is used to calculate the expected number of deaths, which is then compared with the actual number of deaths in 2020. We calculated weekly age- and sex-specific mortality rates for 93.1% of the Italian municipalities for the years 2015–2019 and for the first 26 weeks in 2020. We assumed the mortality experience during 2015–2019 as the reference period to calculate standardised mortality ratios. Furthermore, in order to compare the mortality experience of males and females, we calculated sex- and age- specific weekly direct standardised mortality rates and differences between the observed and expected number of deaths. We observed considerable changes in the demographics in the Italian population between the years 2015 and 2020, particularly among people 60 years and older and among males. The population is aging and the proportion of elderly males has increased, which was not reflected adequately in previous estimates of excess mortality. Standardized excess mortality results show that in Italy between the 8th and 26th weeks in 2020, there were 33,035 excess deaths, which is only 643 fewer deaths than the official COVID-19 death toll for this time period. A comparative increase in the mortality rates was observed in March among both sexes, but particularly for males. Comparisons with recently published data show considerably higher excess deaths, but these data were either not covering the complete country or did not account for age and sex. Neglecting the demographic changes in a region, even over a short time span, can result in biased estimates.

On Estimate of Malaysian Mortality Rates Using Interpolation Methods

Life table is a table that shows mortality experience of a nation. However, in Malaysia, the information in this table is provided in the five-year age groups (abridged) instead of every one-year age. Hence, this study aims to estimate the one-year age mortality rates from the abridged mortality rates using several interpolation methods. We applied Kostaki method and the Akima spline method to five sets of Malaysian group mortality rates ranging from period of 2012 to 2016. The results were then compared with the one-year mortality rates. We found that the method by Akima is the best method for the Malaysian mortality experience as it gives the least minimum of sum of square errors. The method does not only provide a good fit but also, shows a smooth mortality curve.

Life table—a summary of mortality experience

A complete description of the construction and interpretation of life table mortality patterns of the total US 2010 population. Also included is a contrast of a British 17th century life table and the US 20th century life table.