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.
Hirsch
H R
HR
Department of Physiology, College of Medicine, University of Kentucky, Lexington 40536-0084, USA.
D017677:Age Distribution; D006801:Humans; D016014:Linear Models; D009026:Mortality; D015996:Survival Rate