The analysis of survival (mortality) data: Fitting Gompertz, Weibull, and logistic functions

Abstract

Survival functions are fitted to survival data from several large populations. The Gompertz survival function corresponds to exponential mortality rate increases with time. The Weibull survival function corresponds to mortality rates that increase as a power function of time. A two-parameter, logistic survival function is introduced, and corresponds to mortality rates that increase, and then decrease, with time. A three-parameter logistic-mortality function also is examined. It reflects mortality rates that rise, and then plateau, with age. Data are from published studies of medflies, Drosophila, house flies, flour beetles, and humans. Some survival data are better fit by a logistic survival function than by the more traditionally used Gompertz or Weibull functions. Gompertz, Weibull, or logistic survival functions often fit the survival of 95+% of a population, and the ‘tails’ of the survival curves usually appear to fall between the values predicted by the three functions. For some populations, such ‘tails’ appear to be too complex to be fit well by any simple function. Survival data for males and females in some populations are best fit by different functions. Populations of 100 or more are needed to distinguish among the functions. When testing effects of environmental or genetic manipulations on survival, it has been common to determine the changes in parameter values for a given function, such as Gompertz. It may be equally important to determine whether the best-fit function has changed as well.