X-Ray Survival as Gompertz Growth in Number Killed

X-ray and age-dependent survival studies both involve increasing numbers of deaths in proportion to the destructive force implicit in the independent variable, which is radiation dose in the former and the ravages of time in the latter. Ordinarily modelled by entirely different but often unsatisfactory equations, these similar situations can both be represented by a Gompertz growth model in which the dependent variable is number dead rather than number of survivors. The present paper applies the model to X-ray survival curves. Two free parameters suffice for a curve in which the log survival terminates in a straight line. In those instances in which the slope of the log plot becomes increasingly steep, an exponential term is required to account for the disproportionate increase in X-ray sensitivity. Examples are shown of the fit to a variety of data.