Models for estimating empirical Gompertz mortality: With an application to evolution of the Gompertzian slope

Abstract

Using data from the human mortality database (HMD), and five different modeling approaches, we estimate Gompertz mortality parameters for 7,704 life tables. To gauge model fit, we predict life expectancy at age 40 from these parameters, and compare predicted to empirical values. Across a diversity of human populations, and both sexes, the overall best way to estimate Gompertz parameters is weighted least squares, although Poisson regression performs better in 996 cases for males and 1,027 cases for females, out of 3,852 populations per sex. We recommend against using unweighted least squares unless death counts (to use as weights or to allow Poisson estimation) are unavailable. We also recommend fitting to logged death rates. Over time in human populations, the Gompertz slope parameter has increased, indicating a more severe increase in mortality rates as age goes up. However, it is well‐known that the two parameters of the Gompertz model are very tightly (and negatively) correlated. When the slope goes up, the level goes down, and, overall, mortality rates are decreasing over time. An analysis of Gompertz parameters for all of the HMD countries shows a distinct pattern for males in the formerly socialist economies of Europe.

Life expectancy of parkinsonism patients in the general population

“…We calculated overall age-specific incidence rates for both transitions with Gompertz regression. Gompertz regression is a parametric proportional hazard regression with a Gompertz distribution, which is suitable for mortality data [12,13]. Subsequently, we multiplied the overall incidence rates with a weighing factor to obtain sex-specific incidence rates.…”

Social disadvantage, economic inequality, and life expectancy in nine Indian states

“…x = α × e βx , where x represents age in five-year groups starting at age 40, with the final age interval as 85+(Tai and Noymer, 2018). Source: Annual Health Survey 2010-2011.…”

Highlight in this issue

“…We are pleased to announce that we publish the special feature "Evolutionary demography: the dynamic and broad intersection of ecology and evolution" that consists of 14 papers (Anderson 2018;Colleran and Snopkowski 2018;DeLong and Luhring 2018;Gimenez and Gaillard 2018;Hartemink and Caswell 2018;Horvitz et al 2018;Kellett and Shefferson 2018;Morita 2018;Nakahashi et al 2018;Nicol-Harper et al 2018;Shefferson et al 2018;Shyu and Caswell 2018;Tai and Noymer 2018;. Although a special feature usually consists of 4-8 papers, either original or review articles, if the number of collected articles is large enough, an entire special issue, comprised of only those articles, would be considered (this is the case of this issue).…”