A note on life tables and nonlinear death processes

This note is viewing survival data of a natural cohort as being generated by a possibly nonlinear, nonhomogeneous death process. It proves that the usual conditional distributions of the number of survivors at a certain age are binomial if and only if the death process is linear. Thus the customary statistical methods for the analysis of life table data are, strictly speaking, invalid whenever the underlying death process is nonlinear. For example, if a contagious disease is the cause of some or all of the deaths, the deaths will not be independent and the death process, not linear. One should then base the statistical analysis on a model for the spread of the disease rather than the routine binomial model.