An underappreciated peculiarity of late-life human mortality kinetics assessed through the lens of a generalization of the Gompertz-Makeham law.

Much attention in biogerontology is paid to the deceleration of mortality rate increase with age by the end of a species-specific lifespan, e.g. after ca. 90 years in humans. Being analyzed based on the Gompertz law µ(t)=µe^γt with its inbuilt linearity of the dependency of lnµ on t, this is commonly assumed to reflect the heterogeneity of populations where the frailer subjects die out earlier thus increasing the proportions of those whose dying out is slower and leading to decreases in the demographic rates of aging. Using Human Mortality Database data related to France, Sweden and Japan in five periods 1920, 1950, 1980, 2018 and 2020 and to the cohorts born in 1920, it is shown by LOESS smoothing of the lnµ-vs-t plots and constructing the first derivatives of the results that the late-life deceleration of the life-table aging rate (LAR) is preceded by an acceleration. It starts at about 65 years and makes LAR at about 85 years to become 30% higher than it was before the acceleration. Thereafter, LAR decreases and reaches the pre-acceleration level at ca. 90 years. This peculiarity cannot be explained by the predominant dying out of frailer subjects at earlier ages. Its plausible explanation may be the acceleration of the biological aging in humans at ages above 65-70 years, which conspicuously coincide with retirement. The decelerated biological aging may therefore contribute to the subsequent late-life LAR deceleration. The biological implications of these findings are discussed in terms of a generalized Gompertz-Makeham law µ(t) = C(t)+µe^f(t).