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Approximate method for elimination of a risk of death in current life table calculations

An approximate, short-cut method to produce the calculations for a current life table with the elimination of a cause of death is presented and illustrated. The method is to perform the usual calculations for a current life table using the schedule of rates obtained by subtracting the age-specific death rate for the cause to be eliminated from the corresponding death rate for all causes. When the risk of death for the cause of interest is not too large, the life table produced is comparable to that obtained from the theoretical development of Chiang [1968], involving the recalculation of the conditional probabilities of death in each age group to remove the effect of a particular risk of death. The mean value theorem for integrals provides the basis for the approximation; therefore, the approximation will be better with shorter age bands. This application of the theorem is equivalent to assuming exponential survivorship within each age band. For causes of death that are not too common and utilizing five year age bands, the method provides a good approximation to Chiang's approach to the recalculating of the conditional probabilities of death. An example is provided that demonstrates very reasonable approximation of the revised, age-specific probabilities of death and subsequently calculated age-specific life expectancies. *This research was completed under an Intergovernmental Personnel Act appointment while MJS was on leave from the Department of Biostatistics, School of Public Health, University of North Carolina at Chapel Hill, N.C. 27514