Deprivation as an Earlier Entry onto the Mortality Trajectory: Modelling Life Years Lost from Gompertz–Makeham Age Shift

Abstract

Background: Deprivation is associated with shorter life expectancy, higher service use and substantial resource demands, particularly in inner‑city populations. However, clinical and policy responses often rest on qualitative notions of “accelerated ageing” and do not quantify deprivation as a reproducible structural change in mortality. Aim: To model deprivation as an earlier entry onto the standard mortality trajectory and estimate the resulting life‑years lost (LYL) for males and females across adult life. Model: Modelling study using national life‑table parameters and Gompertz–Makeham age‑shift scenarios. Methods: Age‑specific mortality was described by the Gompertz–Makeham law parameterised from Irish Life Table 17 for males and females, providing sex‑specific baseline life expectancy from ages 40–85 years. Deprivation was represented as a pure age shift on this trajectory, without altering the Gompertz slope: a 12‑year shift for males and a 9‑year shift for females. For each starting age, remaining life expectancy and LYL were calculated as the difference between baseline and deprivation life expectancy. To contextualise deprivation, we constructed proportional‑hazard reference curves with 2‑fold and 4‑fold constant excess hazards and compared their LYL profiles with the deprivation curves. Results: Under the male baseline, remaining life expectancy fell from about 35 years at age 40 to 8 years at age 85; a 12‑year age shift produced an average LYL penalty of approximately 8 years between ages 40 and 85, declining from 9.4 to 3.4 years. For females, a 9‑year age shift yielded an average LYL of about 6 years, with LYL decreasing from 7.6 to 3.8 years over the same age range. In both sexes, the deprivation LYL trajectories lay between the 2‑fold and 4‑fold hazard benchmarks, consistent with a stable excess hazard close to two‑fold across adult life. The implied standardized mortality ratio rose only slightly with age, from 2.04 to 2.20 in males and from 1.60 to 1.80 in females, approaching the theoretical Gompertz limits expected from the calibrated age shifts. Conclusion:  Deprivation is modelled as earlier entry onto the mortality trajectory without a need to assume altered acceleration constant of the Gompertz–Makeham equation. LYL trajectories lay somewhat above the 2‑fold hazard benchmark, but with a stable  and consistent excess hazard across adult life