How do we age? A decomposition of Gompertz law

A strong regularity of human life is Gompertz's law, which predicts a near-perfect exponential increase in mortality with age. In this paper, we take into account that chronological age is not a cause of death and decompose Gompertz's law into two equally strong laws: (i) an exponential increase in health deficits as measured by the frailty index, and (ii) a power law association between the frailty index and the mortality rate. We show how the increase in the frailty index can be derived from the feature of self-productivity of health deficits. We explore the robustness of the Gompertz decomposition across countries, sex, and over time and show how information about mortality rates can be used to infer the state of health of an age-structured population. Finally, we use this method to infer the biological ages of past populations, such as Australians in 1940 and Swedes in 1770.