A new parametric model to assess delay and compression of mortality

Abstract

Background: A 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. Methods: This 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. Results: Applying 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. Conclusions: The 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.