Heterogeneity, dependence among causes of death and gompertz

Heterogeneity in a population with respect to mortality, or variation in “frailty” among members of that population, which has been discussed extensively in the literature over the last decade and a half is essential to any realistic model of dependence among causes of death. The main problem then is the development of a mortality model incorporating heterogeneity and cause of death which is both realistic and of manageable proportions. In a recent paper (J. H. Pollard, 1991), it has been shown that many life table results are remarkably insensitive to the strict shape of the mortality curve, at least for more developed populations, and that accurate approximations can in many cases be obtained knowing only the mortality rates at two representative ages (e.g. 50 and 70). These results and the Gompertz “law” of mortality can be used to develop manageable approximate formulae for the expectation of life under heterogeneity and correlation among the causes of death. The formulae are confirmed by simulation. Numerical results indicate, somewhat surprisingly, that the effects of correlation among causes of death, even at quite high levels, on expectation of life and changes on expectation of life when particular causes of death are reduced or eliminated are relatively minor.