Time-Specific Life Tables Contrasted with Observed Survivorship

Abstract

In obtaining life tables for any group of individuals, biological or physical, there are two basically different types of observation which are commonly used. One of these consists in the classification of individuals at a fixed time into separate age groups and then in the recording of deaths for all the various ages simultaneously. The life table derived from this evidence is a time-specific or static life table because the deaths for all the ages are recorded at the same time. The second type of observations consists in following a group of individuals born at approximately the same time, from birth to the death of the longest-lived member of the group. In this case the survivorship curve is determined by direct observation. It has been called a generation or cohort or fluent life table [1]. The life tables resulting from these two different types of evidence on longevity will, except under unusual circumstances, be different in form, and in any case will be quite different in meaning. To consider an example of the two life tables, suppose we wish to study the present day survival of Ford automobiles. We may ask two different questions: what is the longevity of Fords at the current rates of survival, or what is the survival of the current model of Ford? That is, in one case we ask about current rates of cars existing at the present time and in the other about the present model and its future rates. To answer the first question we might get the date of manufacture (that is the age) of all the Fords registered on January 1, 1947, and during the following year get, by date of manufacture, the number of these cars irrevocably eliminated from service, that is, the deaths. Death in this case would be due to accidents, old age, or perhaps disease and malformations. From the age-specific death rates we could construct a survivorship curve for Fords for the year 1947. It would give us the way in which a group of Fords would survive if the 1947 rates pertained throughout their careers. The other life table could be obtained by following the 1947 models throughout their future existence to determine the number finally retired from service up to successive dates. This would give us the survivorship curve for the 1947 models, by direct subtraction. These two survivorship curves * Paper No. 233 from the Department of Biostatistics, School of Hygiene and Public Health, The Johns Hopkins University.