Supercentenarians and the theory of heterogeneity

James W. Vaupel, Max Planck Institute for Demographic Research
Jutta Gampe, Max Planck Institute for Demographic Research

Statistical analysis of survival data on about 800 supercentenarians (age 110+) indicates that q, the annual probability of death, is constant at about 50% per year. Recent mathematical proofs indicate that this finding implies that at advanced ages the force of mortality for individuals increases exponentially at a rate of about .14, frailty is gamma distributed with variance about .2, and individuals differ in their level of mortality rather than the rate of increase, i.e., that the gamma-Gompertz model proposed by Vaupel et al. (1979) is valid at older ages and with parameters that are now known. Analysis of historical data for Sweden and other countries suggests that both today and in the past human mortality asymptotically approaches a plateau at q equal about .5. The results lead to a new strategy for closing out lifetables. Furthermore, the results shed light on the number and magnitude of genes affecting longevity.