Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates

Exploring Patterns of Human Mortality and Aging: A Reliability Theory Viewpoint

The most important manifestation of aging is an increased risk of death with advancing age, a mortality pattern characterized by empirical regularities known as mortality laws. We highlight three significant ones: the Gompertz law, compensation effect of mortality (CEM), and late-life mortality deceleration and describe new developments in this area. It is predicted that CEM should result in declining relative variability of mortality at older ages. The quiescent phase hypothesis of negligible actuarial aging at younger adult ages is tested and refuted by analyzing mortality of the most recent birth cohorts. To comprehend the aging mechanisms, it is crucial to explain the observed empirical mortality patterns. As an illustrative example of data-directed modeling and the insights it provides, we briefly describe two different reliability models applied to human mortality patterns. The explanation of aging using a reliability theory approach aligns with evolutionary theories of aging, including idea of chronic phenoptosis. This alignment stems from their focus on elucidating the process of organismal deterioration itself, rather than addressing the reasons why organisms are not designed for perpetual existence. This article is a part of a special issue of the journal that commemorates the legacy of the eminent Russian scientist Vladimir Petrovich Skulachev (1935-2023) and his bold ideas about evolution of biological aging and phenoptosis.

Using a penalized likelihood to detect mortality deceleration

We suggest a novel method for detecting mortality deceleration by adding a penalty to the log-likelihood function in a gamma-Gompertz setting. This is an alternative to traditional likelihood inference and hypothesis testing. The main advantage of the proposed method is that it does not involve using 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 method 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.

What have we learned about mortality patterns over the past 25 years?

In this paper, I examine progress in the field of mortality over the past 25 years. I argue that we have been most successful in taking advantage of an increasingly data-rich environment to improve aggregate mortality models and test pre-existing theories. Less progress has been made in relating our estimates of mortality risk at the individual level to broader mortality patterns at the population level while appropriately accounting for contextual differences and compositional change. Overall, I find that the field of mortality continues to be highly visible in demographic journals, including Population Studies. However much of what is published today in field journals could just as easily appear in neighbouring disciplinary journals, as disciplinary boundaries are shrinking.

Information measures and design issues in the study of mortality deceleration: findings for the gamma-Gompertz model

Mortality deceleration, or the slowing down of death rates at old ages, has been repeatedly investigated, but empirical studies of this phenomenon have produced mixed results. The scarcity of observations at the oldest ages complicates the statistical assessment of mortality deceleration, even in the parsimonious parametric framework of the gamma-Gompertz model considered here. The need for thorough verification of the ages at death can further limit the available data. As logistical constraints may only allow to validate survivors beyond a certain (high) age, samples may be restricted to a certain age range. If we can quantify the effects of the sample size and the age range on the assessment of mortality deceleration, we can make recommendations for study design. For that purpose, we propose applying the concept of the Fisher information and ideas from the theory of optimal design. We compute the Fisher information matrix in the gamma-Gompertz model, and derive information measures for comparing the performance of different study designs. We then discuss interpretations of these measures. The special case in which the frailty variance takes the value of zero and lies on the boundary of the parameter space is given particular attention. The changes in information related to varying sample sizes or age ranges are investigated for specific scenarios. The Fisher information also allows us to study the power of a likelihood ratio test to detect mortality deceleration depending on the study design. We illustrate these methods with a study of mortality among late nineteenth-century French-Canadian birth cohorts.

Comparative analysis of completeness of death registration, adult mortality and life expectancy at birth in Brazil at the subnational level

Background

Estimates of completeness of death registration are crucial to produce estimates of life tables and population projections and to estimate the burden of disease. They are an important step in assessing the quality of data. In the case of subnational data analysis in Brazil, it is important to consider spatial and temporal variation in the quality of mortality data. There are two main sources of data quality evaluation in Brazil, but there are few comparative studies and how they evolve over time. The aim of the paper is to compare and discuss alternative estimates of completeness of death registration, adult mortality (45q15) and life expectancy estimates produced by the National Statistics Office (IBGE), Institute for Health Metrics and Evaluation (IHME), and estimates presented in Queiroz et al. (2017) and Schmertmann and Gonzaga (2018), for 1980 and 2010.

Methods

We provide a descriptive and comparative analysis of aforementioned estimates from four (4) sources of estimates at subnational level (26 states and one Federal District) in Brazil from two different points in time.

Results

We found significant differences in estimates that affect both levels and trends of completeness of adult mortality in Brazil and states. IHME and Queiroz et al. (2017) estimates converge by 2010, but there are large differences when compared to estimates from the National Statistics Office (IBGE). Larger differences are observed for less developed states. We have showed that the quality of mortality data in Brazil has improved steadily overtime, but with large regional variations. However, we have observed that IBGE estimates show the lowest levels of completeness for the Northern of the country compared to other estimates. Choice of methods and approaches might lead to very unexpected results.

Conclusion

We produced a detailed comparative analysis of estimates of completeness of death registration from different sources and discuss the main results and possible explanations for these differences. We have also showed that new improved methods are still needed to study adult mortality in less developed countries and at a subnational level. More comparative studies are important in order to improve quality of estimates in Brazil.

New Trend in Old-Age Mortality: Gompertzialization of Mortality Trajectory

There is great interest among gerontologists, demographers, and actuaries in the question concerning the limits to human longevity. Attempts at getting answers to this important question have stimulated many studies on late-life mortality trajectories, often with opposing conclusions. One group of researchers believes that mortality stops growing with age at extreme old ages, and that hence there is no fixed limit to the human life span. Other studies found that mortality continues to grow with age up to extreme old ages. Our study suggests a possible solution to this controversy. We found that mortality deceleration is best observed when older, less accurate life span data are analyzed, while in the case of more recent and reliable data there is a persistent mortality growth with age. We compared the performance (goodness of fit) of two competing mortality models - the Gompertz model and the Kannisto ("mortality deceleration") model - at ages of 80-105 years using data for 1880-1899 single-year birth cohorts of US men and women. The mortality modeling approach suggests a transition from mortality deceleration to the Gompertzian mortality pattern over time for both men and women. These results are consistent with the hypothesis about disappearing mortality deceleration over time due to improvement in the accuracy of age reporting. In the case of more recent data, mortality continues to grow with age even at very old ages. This observation may lead to more conservative estimates of future human longevity records.

Late-life mortality is underestimated because of data errors

Knowledge of true mortality trajectory at extreme old ages is important for biologists who test their theories of aging with demographic data. Studies using both simulation and direct age validation found that longevity records for ages 105 years and older are often incorrect and may lead to spurious mortality deceleration and mortality plateau. After age 105 years, longevity claims should be considered as extraordinary claims that require extraordinary evidence. Traditional methods of data cleaning and data quality control are just not sufficient. New, more strict methodologies of data quality control need to be developed and tested. Before this happens, all mortality estimates for ages above 105 years should be treated with caution.

This Primer explores recent evidence that demographic data errors can explain away apparent late-life mortality plateaus, proposing that traditional methods of data quality control are insufficient, and that claims of human longevity greater than 105 years should be considered extraordinary and require extraordinary evidence.