The Kinetics of Deprivation: Unifying Early Life with the Gompertz-Makeham Law of Mortality

Abstract

Background: Socio-economic deprivation is associated with higher mortality. In a previous adult life-table analysis, deprivation-related loss of life years was represented by an approximately fixed horizontal age shift in mortality risk: 12 years in males and 9 years in females across ages 40–85. Within the Gompertz component, this was associated with approximately constant standardised mortality ratios. Childhood studies have reported associations between social adversity and early-life biological differences, including altered leukocyte telomere dynamics. The relation between these early-life observations and the approximately fixed adult mortality shift is uncertain. Aim: To develop an illustrative life-course model showing how an age shift emerging in early life could travel from zero at birth to the approximately fixed adult displacement used in the mortality analysis, and to examine the resulting rate and acceleration profile. Methods: A continuous sigmoidal function was used to represent accumulation of the modelled age shift,  ), from zero at birth towards the sex-specific adult shifts. The trajectory was specified to increase gradually in early life, more rapidly through childhood and adolescence, and then decelerate as it approached the adult level. The adult shifts were 12 years in males and 9 years in females. Rates of change and acceleration were examined as properties of the illustrative function. Results:  A linear transition from childhood to the adult age shift produced an abrupt change in slope. In contrast, the sigmoidal function generated a smooth trajectory, with a low initial rate of accumulation, more rapid change through later childhood and adolescence, and progressive deceleration thereafter. The modelled trajectory was close to its adult level by the mid-thirties. In the adult life-table analysis, the resulting fixed shifts produced absolute annual mortality-risk differences that increased with age, despite the approximately constant relative mortality effect within the Gompertz component. Conclusion:  A simple continuous function can provide a mathematical illustration of how early-life divergence could approach the approximately fixed age shift observed in mature adult mortality.  at birth is used as a mathematical starting condition consistent with the adult boundary, not as a claim that biological divergence begins at birth, and the modelled timings depend on the calibration anchors chosen. The model does not identify an underlying biological mechanism or estimate the timing of real-world biological change. It provides a conceptual framework for considering how disadvantage across the life course may be related to later mortality inequalities.