Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models

In a Gompertz mortality model with constant yearly improvements at all ages, linear increases in period life expectancy correspond to linear increases in the respective cohort life expectancy. The link between the two measures can be given by a simple approximate relationship.cohort life expectancy, Gompertz mortality, Linear Shift Models, period life expectancy

Using a Penalized Likelihood to Detect Mortality Deceleration

In this paper, we suggest a novel method for detecting mortality deceleration. We focus on the gamma-Gompertz frailty model and suggest the subtraction of a penalty in the log-likelihood function as an alternative to traditional likelihood inference and hypothesis testing. Over existing methods, our method offers advantages, such as avoiding the use of a p-value, hypothesis testing, and asymptotic distributions. We evaluate the performance of our approach by comparing it with traditional likelihood inference on both simulated and real mortality data. Results have shown that our approach is more accurate in detecting mortality deceleration and provides more reliable estimates of the underlying parameters. The proposed method is a significant contribution to the literature as it offers a powerful tool for analyzing mortality patterns

Makeham Mortality Models as Mixtures

Mortality modeling is crucial to understanding the complex nature of population aging and projecting future trends. The Makeham term is a commonly used constant additive hazard in mortality modeling to capture background mortality unrelated to aging. In this manuscript, we propose representing Makeham mortality models as mixtures that describe lifetimes in a competing-risk framework: an individual dies either according to a baseline mortality mechanism or an exponential distribution, whatever strikes first. The baseline can describe mortality at all ages or just mortality due to aging. By using this approach, we can estimate the share of non-senescent mortality at each adult age, which is an essential contribution to the study of premature and senescent mortality. Our results allow for a better understanding of the underlying mechanisms of mortality and provide a more accurate picture of mortality dynamics in populations

Improvements in Age-Specific Mortality at the Oldest Ages

Age-specific mortality improvements are non-uniform, neither across ages nor across time. We propose a two-step procedure to estimate the rates of mortality improvement (RMI) in age-specific death rates (ASDR) at ages 85 and above for ten European countries from 1950 to 2019. In the first step, we smooth the raw death counts and estimate ASDR using four different methods: one parametric (gamma-Gompertz-Makeham), two non-parametric (P-splines and PCLM), and a novel Bayesian procedure to handle fluctuations resulting from ages with zero death counts. We compare the goodness of fit of the four smoothing methods and calculate the year-to-year ASDR differences according to the best-fitting one. We fit a piecewise linear function to these differences in the second step. The slope in each linear segment captures the average RMI in the respective year range. For each age, we calculate the goodness of fit in the last linear segment to assess how informative the estimated RMI of current mortality change is. The estimated rates of mortality improvement or deterioration (RMI) can be used to make short-term social, health, and social planning, as well as more precise mortality forecasts

Quantifying impacts of the COVID-19 pandemic through life-expectancy losses: a population-level study of 29 countries.

BACKGROUND: Variations in the age patterns and magnitudes of excess deaths, as well as differences in population sizes and age structures, make cross-national comparisons of the cumulative mortality impacts of the COVID-19 pandemic challenging. Life expectancy is a widely used indicator that provides a clear and cross-nationally comparable picture of the population-level impacts of the pandemic on mortality. METHODS: Life tables by sex were calculated for 29 countries, including most European countries, Chile and the USA, for 2015-2020. Life expectancy at birth and at age 60 years for 2020 were contextualized against recent trends between 2015 and 2019. Using decomposition techniques, we examined which specific age groups contributed to reductions in life expectancy in 2020 and to what extent reductions were attributable to official COVID-19 deaths. RESULTS: Life expectancy at birth declined from 2019 to 2020 in 27 out of 29 countries. Males in the USA and Lithuania experienced the largest losses in life expectancy at birth during 2020 (2.2 and 1.7 years, respectively), but reductions of more than an entire year were documented in 11 countries for males and 8 among females. Reductions were mostly attributable to increased mortality above age 60 years and to official COVID-19 deaths. CONCLUSIONS: The COVID-19 pandemic triggered significant mortality increases in 2020 of a magnitude not witnessed since World War II in Western Europe or the breakup of the Soviet Union in Eastern Europe. Females from 15 countries and males from 10 ended up with lower life expectancy at birth in 2020 than in 2015

Adequate life-expectancy reconstruction for adult human mortality data.

Mortality information of populations is aggregated in life tables that serve as a basis for calculation of life expectancy and various life disparity measures. Conventional life-table methods address right-censoring inadequately by assuming a constant hazard in the last open-ended age group. As a result, life expectancy can be substantially distorted, especially in the case when the last age group in a life table contains a large proportion of the population. Previous research suggests addressing censoring in a gamma-Gompertz-Makeham model setting as this framework incorporates all major features of adult mortality. In this article, we quantify the difference between gamma-Gompertz-Makeham life expectancy values and those published in the largest publicly available high-quality life-table databases for human populations, drawing attention to populations for which life expectancy values should be reconsidered. We also advocate the use of gamma-Gompertz-Makeham life expectancy for three reasons. First, model-based life-expectancy calculation successfully handles the problem of data quality or availability, resulting in severe censoring due to the unification of a substantial number of deaths in the last open-end age group. Second, model-based life expectancies are preferable in the case of data scarcity, i.e. when data contain numerous age groups with zero death counts: here, we provide an example of hunter-gatherer populations. Third, gamma-Gompertz-Makeham-based life expectancy values are almost identical to the ones provided by the major high-quality human mortality databases that use more complicated procedures. Applying a gamma-Gompertz-Makeham model to adult mortality data can be used to revise life-expectancy trends for historical populations that usually serve as input for mortality forecasts

Admissible mixing distributions for a general class of mixture survival models with known asymptotics

Statistical analysis of data on the longest living humans leaves room for speculation whether the human force of mortality is actually leveling o®. Based on this uncertainty, we study a mixture failure model, introduced by Finkelstein and Esaulova (2006) that generalizes, among others, the proportional hazards and accelerated failure time models. In this paper we, first, extend the Abelian theorem of these authors to mixing distributions, whose densities are functions of regular variation. In addition, taking into account the asymptotic behavior of the mixture hazard rate prescribed by this Abelian theorem, we prove three Tauberian-type theorems that describe the class of admissible mixing distributions. We illustrate our findings with examples of popular mixing distributions that are used to model unobserved heterogeneity.mortality

Lee Carter forecast for historical Bangladesh female data.

<p>Life-table data for year 2003 is designated by green squares. Forecasts based on the constant-hazard assumption and the ΓGM model are denoted by the red and blue curves, corresponding 95% confidence intervals with red and blue shaded areas, respectively.</p