An Evolution-based Model of Causation that Accounts for the Gompertz Pattern of Mortality, Including Some New Results on the Asymptotic Behavior of the Minimum of Time-to-Event Random Variables
The most widely applied statistical model for mortality in demography and gerontology has been the Gompertz model, describing an exponential relation between age-specific mortality rates and age. However, there is no satisfactory account based on biological principles of its relatively good fit to human mortality data, for deaths occurring between about 10-15 and 90 years old. The evolutionary theory of aging currently provides the fundamental concepts about the biological aging process that have been lacking in most accounts of the Gompertz pattern of mortality. In this report, we first offer an account of the Gompertz pattern of mortality through the statistical theory of extreme values and biological evolution. This involves some original results on the asymptotic behavior of the minimum of time-to-event random variables. Second, we establish the boundaries on the extent to which the argument for Gompertzian mortality on evolutionary grounds is valid. These boundaries refer to the types of causes of death (excluding deaths caused by extrinsic or accidental factors) and the range of ages at death (excluding deaths occurring in neonatal and infant years as well as late life). Third, we consider departures from the Gompertz model, which lead us to the notion that the Gompertz equation reflects some underlying biological truth, but departures from the model emerge from the action of environmental factors. To address that, we finally develop the sufficient and component causes model of causation in epidemiology into an evolution-based model of causation. This model of causation will play an essential role in a following article in creating a framework and providing a motivation for a survival mixture model of the Gompertz and Weibull distributions for the description of human mortality, from which an index of aging-relatedness will naturally emerge.