A new parametric model to assess delay and compression of mortality

Abstract

BackgroundA decrease in mortality across all ages causes a shift of the age pattern of mortality, or mortality delay, while differences in the rate of decrease across ages cause a change in the shape of the age-at-death distribution, mortality compression or expansion. Evidence exists for both compression and delay of mortality. Existing parametric models to describe the full age pattern of mortality are not able to capture mortality delay versus mortality compression. More recent models that assess delay versus compression mostly focused on the adult or old ages alone and did not distinguish mortality compression below and above the modal age at death, although they represent different mechanisms.MethodsThis paper presents a new parametric model that describes the full age pattern of mortality and assesses compression – at different stages of life – and delay of mortality: the CoDe model. The model includes 10 parameters, of which five are constant over time. The five time-varying parameters reflect delay of mortality and compression of mortality in infancy, adolescence, young adulthood, late adulthood, and old age. The model describes infant and background mortality by two simple functions, uses a mixed logistic model with different slopes in adult, middle, and old age, and includes the modal age at death as a parameter to account for the delay in mortality.ResultsApplying the CoDe model to age-specific probabilities of death for Japanese, French, American, and Danish men and women between 1950 and 2010 showed a very good fit of the full age pattern of mortality. Delay of mortality explained about two-thirds of the increase in life expectancy at birth, whereas compression of mortality due to mortality declines in young age explained about one-third. No strong compression of mortality in late adulthood age was observed. Mortality compression in old age has had a small negative impact on life expectancy.ConclusionsThe CoDe model proved a valid instrument for describing the full age pattern of mortality and for disentangling the effects of mortality delay and compression – at different stages of life – on the increase in life expectancy.

Maximum human lifespan may increase to 125 years

“…Since Jeanne Calment survived to age 122 in women live in Japan. The logistic model is considered superior to the widely known Gompertz model 5,6,7,8,9,10 . Whereas the Gompertz model overestimates the acceleration of the increase in the death probabilities at the oldest ages, our logistic-type model describes this increase very accurately: R 2 = 99.97% (see Figure 1).…”

“…Given the declines in the death probabilities and the delay of mortality to older ages that occurred in the past 10 , it is, however, unlikely that the death probabilities will remain constant in the future. If we assume that survival to age 100 continues to improve at the same pace over the next 55 years as it did over the last 55 years, the number of centenarians will increase from 56 thousand in 2015 to 750 thousand in 2050.…”

Rotation of the age pattern of mortality improvements in the European Union

“…Further recent developments in this field include De Beer and Janssen (2016), who aim to model the distribution of the age at death by calendar year, and Li and Li (2017), who propose a sequential statistical testing procedure to determine the starting point of the longest plausible estimation base period where the two conditions of the linearity of the time series k t and the time-invariance of the parameters b x jointly hold, and find that for the majority of the 34 countries examined, this period starts somewhere between 1960 and 1990.…”

Projecting delay and compression of mortality

“…The modal age of French women is the highest among European populations and increased linearly from 1960 onward (Ouellette and Bourbeau 2011), whereas the modal age of American women was high in 1960 but decelerated in the 1980s and the 1990s. Japanese women have displayed the highest modal age since the beginning of the twenty-first century, along with the highest (non-linear) improvement rate in the world (de Beer et al 2017). Furthermore, for these countries, the CoDe model has been applied before (de Beer and Janssen 2016 and de Beer et al 2017).…”