Intersections of mortality-rate and survival functions: model-independent considerations

In work reported previously (Hirsch, 1995), it was shown that families of straight lines intersect at a single point if and only if the slopes of the lines are linearly related to their intercepts. This slope-intercept relation was applied to several mathematical mortality models including the Gompertz-Makeham and the Weibull. In all cases, survival functions intersected at greater ages than the corresponding mortality-rate functions. It was further demonstrated that a common point of intersection can exist for members of a family of survival functions or for members of the corresponding family of mortality-rate functions but not for both. Here the same results are obtained with respect to intersections of general model-independent survival and mortality-rate functions. The generality of the results strengthens the conclusion reached earlier that these intersections imply only the existence of a valid slope-intercept relation and have little other significance with regard to the biology of aging.