Gompertz mortality analysis: aging, longevity hormesis and toxicity.

The hazard function, denoted h(x), is the probability of death during an interval of time [Formula: see text], assuming survival to the beginning of the interval. Brues and Sacher provided both theoretical and experimental support for the assumption that h(x) is an exponential function of the mean intensity of physiologic injury for a homogeneous mammalian population provided an adequate diet, kept free of preventable disease and maintained under favorable, uniform conditions. Consequently, the Napierian logarithm of the hazard function, the 'Gompertzian', is proportional to the mean intensity of physiologic injury under the aforementioned conditions. Investigation of Gompertzian values therefore affords a simple and convenient measure of the mean population time course of aging, toxicity and beneficial life-enhancing effects (e.g., longevity hormesis and slowing of the aging process). (The word 'hormesis' has been applied to various forms of 'stimulation' elicited by low doses of otherwise toxic agents.) Using this method of analysis, reversible toxicity, reversible reduction in physiologic injury (longevity 'hormesis'), irreversible toxicity and irreversible reduction in aging (via caloric restriction) are all reviewed. It is demonstrated that these effects may superimpose upon one another, the most common combination following administration of mild to moderate doses of a toxic agent being irreversible toxicity combining with longevity hormesis.