Modelling life tables with advanced ages: An extreme value theory approach

A Mixture Model Incorporating Individual Heterogeneity in Human Lifetimes

“…We briefly recap the extreme value theory approach adopted to analyse the Netherlands data 9 . We reproduce in Figure 1 the empirical mortality rates (conditional probability of dying in the next year, given survival to the des-ignated age) for the complete dataset (231,129 females and 73,788 males, totaling 304,917 persons).…”

“…An innovative feature of the model, not present in earlier models, is that a smooth transition in hazard rates between ages less than and greater than the threshold age N is enforced. The resulting “smooth threshold life table” (STLT) model 9 was fitted to the Netherlands data by maximum likelihood, producing the estimates of γ and θ in Table 1 for each sex × year-of-birth cohort.…”

“…In each of the 16 cohorts of the Netherlands data analysed 9 , and for both females and males, the estimated γ was significantly negative (Table 1). So the data and the model strongly suggest a finite upper limit to individuals’ lifetimes.…”

“…Huang, Maller and Ning 9 analysed a high-quality Netherlands dataset, based on the Human Mortality Database 10 (HMD), augmented with a dataset from the Centraal Bureau voor de Statistiek of the Netherlands, to construct lifetables separately for females and males aged 65+ born in 1-year cohorts from 1893 to 1908. The data extends to 112 years of age for females and 110 years for males (maxima over all cohorts) and contains a substantial number of individuals aged 95 years or more at death.…”

“…In the next two sections we show how these ideas can be implemented. In later sections we review published discussions relating to the possible existence of an upper limit to human lifetimes, and discuss how advanced age mortality “acceleration and deceleration” effects are included in the Huang et al 9 model, and how the “three laws of biodemography” are satisfied by it.…”