Abridged Life Table

A complete life table uses single years of age, while an abridged table uses broad intervals — typically under 1, 1-4, and five-year groups up to an open oldest interval. The methods are identical in logic; the abridged table simply works on grouped ages, which makes it far more stable when single-year death or population counts are small. For most population-health and cross-national work the abridged table is preferred, and Chiang and Preston, Heuveline and Guillot both present it as the standard form.

Because survivorship is built by multiplying probabilities of surviving each interval, and a rate is not a probability. A rate has person-years in its denominator and can take values that a probability cannot. Chiang's conversion uses nax, the average years lived in the interval by those who die, to translate the central rate into the conditional probability of dying given survival to the start of the interval. Skipping this step and treating nMx as nqx biases the table, most severely in high-mortality intervals like infancy and old age.

The oldest interval has no upper bound, so the usual person-years formula does not apply. The standard solution, given in Preston, Heuveline and Guillot, sets the person-years in the open interval equal to the survivors entering it divided by the mortality rate prevailing there. This is equivalent to assuming a constant hazard above the cutoff. Because old-age death and population data are often unreliable, results in this interval — and therefore e0 to a small degree — are sensitive to this assumption and to data quality.