Integral differences among human survival distributions as a function of disease.

The mortality kinetics of white humans of the United States were examined for 25 different age-related causes of death (22 male, 21 female). The survivorship distributions for these diseases clustered into groups, as defined by their position on the time axis. When the survivorship curves were linearized, by plotting as log(-log S(t] vs. log t, this clustering was easily identified as well-defined intersections among the lines separated by 2-year intervals. The four largest groups had intersections at approximate time values of 101, 99, 95, and 93 years, with a small group having an intersection at 97 years. The distribution of diseases among the intersections was not random but was related to sex and disease type. The two-parameter Weibull and GDCP (Gamma Distribution raised to a Combinatoric Power) functions were fit to the individual cause of death survivorship curves and yielded parametric values for the shape (slope) and median time to death. These two parameters varied with disease type and exhibited a positive, linear regression. The regression slope between the shape (alpha) and time (tau m) parameters of the GDCP was also equal to approximately 2 years. This suggested to us that the 2-year intervals in the median times of death with integral changes in the shape parameter and the 2-year time interval between the survivorship clusters may both arise from a similar process involving integral numbers of discrete steps.