This paper examines and demonstrates the importance of the adult modal age at death (M) in longevity research. Unlike life expectancy at birth (e 0) and median age at death, M is determined solely by old-age mortality as far as mortality follows a bathtub curve. It represents the location of old-age death heap in the age distribution of deaths, and captures mortality shifts more accurately than conditional life expectancies such as e 65. Although M may not be directly determined from erratic mortality data, a recently developed method for deriving M from the P-spline-smoothed mortality curve based on penalised Poisson likelihood is highly effective in estimating M. Patterns of trends and differentials in M can be noticeably different from those in other lifespan measures, as indicated in some examples. In addition, major mathematical models of adult mortality such as the Gompertz, logistic and Weibull models can be reformulated using M, which plays a critical role as the mortality level parameter in those models.

References 618Appendix 623 A1 From B-splines to P-splines 623 A2 The penalized likelihood function for P-splines 624 A3 Smoothing mortality data with P-splines 625 A4 Comparison between HMD life table age-at-death distributions and P-spline smoothed density functions for Japan 626Demographic Research: Volume 25, Article 19 Research ArticleChanges in the age-at-death distribution in four low mortality countries: A nonparametric approach Nadine Ouellette 1 Robert Bourbeau 2 AbstractSince the beginning of the twentieth century, important transformations have occurred in the age-at-death distribution within human populations. We propose a flexible nonparametric smoothing approach based on P-splines to refine the monitoring of these changes. Using data from the Human Mortality Database for four low mortality countries, namely Canada (1921Canada ( -2007, France (1920( ), Japan (1947, and the USA , we find that the general scenario of compression of mortality no longer appropriately describes some of the recent adult mortality trends recorded. Indeed, reductions in the variability of age at death above the mode have stopped since the early 1990s in Japan and since the early 2000s for Canadian, US, and French women, while their respective modal age at death continued to increase. These findings provide additional support to the shifting mortality scenario, using an alternative method free from any assumption on the shape of the age-at-death distribution. Ouellette & Bourbeau: Changes in the age-at-death distribution in four low mortality countries IntroductionOver the course of the last century, we have witnessed major improvements in the level of mortality in regions all across the globe. This remarkable mortality decrease has also been characterized by important changes in the age-pattern of mortality, which inevitably led to substantial modifications in the shape of the distribution of age at death and the survival curve over time. Measuring transformations in the age-at-death distribution or in the survival curve quickly became a topic of great interest among researchers, as their implications on societies are profound. For example, with accurate historical trends on average lifespan and lifespan inequality in hand, governments and policymakers are in a better position to ensure sustainability of social security and health-care systems.Efforts to document such trends have indeed been made for several countries and regions: Canada ( Recently, Cheung et al. (2005) listed and reviewed more than 20 indicators used in these studies, each indicator aimed at quantifying either the central tendency or the dispersion (variability) of age at death across individuals. Since the computation of these indicators often involves the use of parametric statistical modelling techniques (e.g., quadratic model, normal model, or logistic model) that impose a predetermined structure on data, an exploration of nonparametric statistical methods, free from assumptions related to the structure of the data, is worth considering. Indeed, concer...

Recent outbreaks of H5, H7, and H9 influenza A viruses in humans have served as a vivid reminder of the potentially devastating effects that a novel pandemic could exert on the modern world. Those who have survived infections with influenza viruses in the past have been protected from subsequent antigenically similar pandemics through adaptive immunity. For example, during the 2009 H1N1 “swine flu” pandemic, those exposed to H1N1 viruses that circulated between 1918 and the 1940s were at a decreased risk for mortality as a result of their previous immunity. It is also generally thought that past exposures to antigenically dissimilar strains of influenza virus may also be beneficial due to cross-reactive cellular immunity. However, cohorts born during prior heterosubtypic pandemics have previously experienced elevated risk of death relative to surrounding cohorts of the same population. Indeed, individuals born during the 1890 H3Nx pandemic experienced the highest levels of excess mortality during the 1918 “Spanish flu.” Applying Serfling models to monthly mortality and influenza circulation data between October 1997 and July 2014 in the United States and Mexico, we show corresponding peaks in excess mortality during the 2009 H1N1 “swine flu” pandemic and during the resurgent 2013–2014 H1N1 outbreak for those born at the time of the 1957 H2N2 “Asian flu” pandemic. We suggest that the phenomenon observed in 1918 is not unique and points to exposure to pandemic influenza early in life as a risk factor for mortality during subsequent heterosubtypic pandemics.

We investigate a major turning point in mortality trends at adult ages that occurred for many low‐mortality countries in the late 1960s or early 1970s. We analyze patterns of total and cause‐specific mortality over the past 60 years using data from the Human Mortality Database and the World Health Organization. We focus on four broad categories of causes of death: heart diseases, cerebrovascular diseases, smoking‐related cancers, and all other cancers. We use a two‐slope regression model to assess the timing and magnitude of turning points in mortality trends over this era, making separate analyses by sex, age, and cause of death. The age pattern of temporal changes is given particular attention. Our results demonstrate convincingly that period‐based factors were very significant in the onset of the “cardiovascular revolution” in the years around 1970. In general, although cohort processes cannot be ruled out as a driver of mortality change in recent decades (especially for mortality due to smoking‐related cancers), the evidence reviewed here suggests that period factors have been the dominant force behind the mortality trends of high‐income countries during this era.

This study examines the roles of age, period, and cohort in influenza mortality trends over the years 1959–2016 in the United States. First, we use Lexis surfaces based on Serfling models to highlight influenza mortality patterns as well as to identify lingering effects of early-life exposure to specific influenza virus subtypes (e.g., H1N1, H3N2). Second, we use age-period-cohort (APC) methods to explore APC linear trends and identify changes in the slope of these trends (contrasts). Our analyses reveal a series of breakpoints where the magnitude and direction of birth cohort trends significantly change, mostly corresponding to years in which important antigenic drifts or shifts took place (i.e., 1947, 1957, 1968, and 1978). Whereas child, youth, and adult influenza mortality appear to be influenced by a combination of cohort- and period-specific factors, reflecting the interaction between the antigenic experience of the population and the evolution of the influenza virus itself, mortality patterns of the elderly appear to be molded by broader cohort factors. The latter would reflect the processes of physiological capital improvement in successive birth cohorts through secular changes in early-life conditions. Antigenic imprinting, cohort morbidity phenotype, and other mechanisms that can generate the observed cohort effects, including the baby boom, are discussed.Electronic supplementary materialThe online version of this article (10.1007/s13524-019-00809-y) contains supplementary material, which is available to authorized users.