Life Tables

A life table describes, in terms of various life table functions, the probability distribution of duration time in a tabular form. Duration time is the time interval from an initial time point to the occurrence of a point event such as death or incidence of disease. A point event is a transition from one state to another. For example, death is a transition from the alive state (a transient state) to the dead state (an absorbing state). If the initial time point is taken as birth and the point event as death, then the time interval from birth to deathiscalledthe life length or age-at-death, and the life table that describes the distribution of the age-atdeath is also called a mortality table (particularly by actuaries). In the case of period life tables, the life length random variable X is further decomposed into two random variables, current age A and future lifetime Y, and the distributions of all three random variables X, A, and Y are described in a period life table.

Construction of life tables has a long history, dating back to the 1662 Bills of Mortality by John Graunt and the famous 1693 mortality table constructed by Halley for the city of Breslau in what is now Poland. Construction of these two life tables, particularly Halley's table, can be regarded as marking the beginning of modern statistics and public health sciences. Modern life table methods are no longer limited to the study of human mortality and to their use in the calculation of life insurance premiums and annuities. They have been used to study the time to the first marriage and the duration of the marriage (as in the construction of nuptiality tables), the duration of intrauterine device use and birth control effectiveness (birth control life tables), labor force participation (working life tables), renewal of animal and plant populations (life cycles life tables), and so on. Epidemiologists are particularly interested in constructing life tables to measure the probabilities of disease incidence, remission, relapse, and death from competing causes as well as to study the expected duration of stay in healthy and morbid states. Morbidity and mortality life table functions can also be combined to measure the burden of diseases and injuries. These epidemiological uses involve many types of life tables, and constructing them requires considerable technical skills. As can be seen in the following descriptions, life table methods are more sophisticated than most other epidemiological methods.