USE OF THE RECURSION FORMULA OF THE GOMPERTZ SURVIVAL FUNCTION TO EVALUATE LIFE-TABLE DATA

The recursion formula of the Gompertz function is an established metho d for the analysis of growth processes. In the present study the recur sion formula of the Gompertz survival function In S(t + s) = a + b x I n S(t) is introduced for the analysis of survival data, where S(t) is the survival fraction at age t, a is the constant age increment betwee n two consecutive measurements of the survival fraction and a and b ar e parameters. With the help of this method-and provided stroboscopical measurements of rates of survival are available-the Gompertz survival function, instead of the corresponding mortality function, can be det ermined directly using linear regression analysis. The application of the present algorithm is demonstrated by analysing two sets of data ta ken from the literature (survival of Drosophila imagoes and of female centenarians) using linear regression analysis to fit survival or mort ality rates to the corresponding models. In both cases the quality of fit was superior by using the algorithm presently introduced. Moreover , survival functions calculated from the fits to the mortality law onl y poorly predict the survival data. On the contrary, the results of th e present method not only fit to the measurements, but, for both sets of data the mortality parameters calculated by the present method are essentially identical to those obtained by a corresponding application of a non-linear Marquardt-Levenberg algorithm to fit the same sets of data to the explicit form of the Gompertz survival function. Taking i nto consideration the advantages of using a linear fit (goodness-of-fi t test and efficient statistical comparison of survival patterns) the method of the recursion formula of the Gompertz survival function is t he most preferable method to fit survival data to the Gompertz functio n.