Deprived Men and Women Age Differently: Insights from Gompertz–Makeham Modelling

Abstract

Background: Men and women differ in lifespan and health trajectories, but little work has translated those differences into structural patterns of life-years lost (LYL) on national life tables. Modelling deprivation as a simple age shift on sex-specific Gompertz–Makeham life tables provides a common framework within which the sequencing of remaining life years and derivatives can be compared between sexes. Aim: To examine whether deprived men and women age differently by analysing the sex-specific sequencing of remaining life expectancy  ​, proportional life-years lost, and their first and second derivatives across ages 40–85, using Irish Life Table 17 and a fixed Gompertz–Makeham age-shift model. Methods: Age-specific mortality was modelled separately for males and females using Gompertz–Makeham parameters derived from Irish Life Table 17. Deprivation was represented as an earlier entry onto the same mortality trajectory by fixed age shifts of +12 years in males and +9 years in females. For each sex, absolute LYL(x) and proportional LYL(x) were computed from ages 40 to 85 years, and the velocity and acceleration of proportional loss were approximated from finite differences in PropLYL(x). Results:  Deprivation produced substantial LYL in both sexes, but the sequencing of proportional loss and its derivatives differed markedly. In males, proportional LYL was strongly front-loaded, with a heavier penalty in early mid-life and a near-constant velocity of accumulation across most of the adult age range. In females, early proportional losses were smaller, but the velocity and acceleration of proportional LYL increased sharply after mid-life, producing a late-life catch-up in which the proportional penalty converged with and slightly exceeded the male value by age 85. Conclusion:  The Gompertz-Makeham age‑shift framework reveals that deprivation is not a uniform reduction in lifespan but a sex‑specific re‑timing of loss. In men, the penalty is advanced and broadly distributed across mid‑life; in women, it is deferred and then compressed into a high‑risk late‑life phase. This distinction in temporal structure, revealed by the derivatives of proportional life‑years lost, suggests that social disadvantage shapes male and female ageing through different kinetic pathways and provides a basis for future work on sex‑specific prevention and policy.