Revival: Biological Effects of Low Level Exposures to Chemical and Radiation (1992)

CHAPTER 1

Hypotheses on Mammalian Aging, Toxicity, and

Longevity Hormesis: Explication by a

Generalized Gompertz Function

Harold Boxenbaum, Marion Merrell Dow, Cincinnati, Ohio

INTRODUCTION

I work all day, and get half-drunk at night.

Waking at four to soundless dark, I stare.

In time the curtain-edges will grow light.

Till then I see what’s really always there:

Unresting death, a whole day nearer now...

Philip Larkin

The triune concepts of aging, toxicity, and longevity hormesis are best
integrated through analysis of mortality kinetic data. Consequently, the
initial part of this introduction will review basic, relevant concepts in this
area.
Assuming an organism has survived to the onset (x) of a time interval (x

• Ax), the probability of dying over that interval is termed the age-specific
  mortality rate, and the time associated with that probability is usually taken
  as the midtime of the interval. When Ax becomes dx, the age-specific mor­
  tality rate assumes a theoretical designation, namely, the hazard function,
  h(x). The hazard function is also termed the instantaneous mortality rate,
  force of mortality, and conditional mortality rate. It is defined by the
  following relationship:

( 1 )

where h(x)

S(x)

N(x)

the hazard function at time x

the fraction of individuals surviving to time x

the number of individuals surviving to time x

The Napierian logarithm of the hazard function is termed the Gompertz
function, Gompertz transform or transformation, or simply the Gompert-

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