Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach

Abstract

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...

Perturbation Analysis of Indices of Lifespan Variability

“…Indices of variability have been compared across populations to measure the rectangularity of the survival curve or degree of mortality compression for both human and and non-human populations (see for instance Eakin and Witten 1995;Edwards and Tuljapurkar 2005;Smits and Monden 2009;van Raalte et al 2011;Vaupel, Zhang and van Raalte 2011). They have also been employed above the modal age at death to examine whether old-age mortality is being compressed, or whether these deaths are shifting to higher ages (Brown et al 2012;Cheung et al 2005;Cheung and Robine 2007;Kannisto 2000;Ouellette and Bourbeau 2011;Thatcher et al 2010). The various indices of lifespan variation have been compared by Anand et al (2001); Cheung et al (2005); Kannisto (2000); Shkolnikov, Andreev and Begun (2003); Vaupel et al (2011) and Wilmoth and Horiuchi (1999).…”

The Gompertz force of mortality in terms of the modal age at death

“…The modal age of the life-table distribution of deaths has been suggested as an alternative to life expectancy in studying longevity (Kannisto 2001;Cheung et al 2005;Cheung and Robine 2007;Canudas-Romo 2008Ouellette and Bourbeau 2011;Horiuchi et al 2013). Life expectancy for Japanese females was estimated to be 86.4 years in 2012 (HMD 2014); most of the deaths in this population, however, will occur 6 years later around the modal age at death at about age 92 (HMD 2014).…”

Decomposing changes in life expectancy: Compression versus shifting mortality

“…In fact, the modal age at death has shown an accelerated pace of increase since the onset of the old-age mortality decline (Kannisto 2000;Wilmoth and Robine 2003;Canudas-Romo 2008). Since the beginning of the 21st century, this indicator has received increasing attention and has become a key indicator of lifespan, especially since longevity extension became determined by adult and old-age mortality (Kannisto 2000(Kannisto , 2001Bongaarts 2005;Cheung and Robine 2007;Canudas-Romo 2008Ouellette and Bourbeau 2011;Horiuchi et al 2013).…”