Date Published: June 4, 2018
Publisher: Public Library of Science
Author(s): László Németh, Trifon I. Missov, Hafiz T.A. Khan.
Mortality information of populations is aggregated in life tables that serve as a basis for calculation of life expectancy and various life disparity measures. Conventional life-table methods address right-censoring inadequately by assuming a constant hazard in the last open-ended age group. As a result, life expectancy can be substantially distorted, especially in the case when the last age group in a life table contains a large proportion of the population. Previous research suggests addressing censoring in a gamma-Gompertz-Makeham model setting as this framework incorporates all major features of adult mortality. In this article, we quantify the difference between gamma-Gompertz-Makeham life expectancy values and those published in the largest publicly available high-quality life-table databases for human populations, drawing attention to populations for which life expectancy values should be reconsidered. We also advocate the use of gamma-Gompertz-Makeham life expectancy for three reasons. First, model-based life-expectancy calculation successfully handles the problem of data quality or availability, resulting in severe censoring due to the unification of a substantial number of deaths in the last open-end age group. Second, model-based life expectancies are preferable in the case of data scarcity, i.e. when data contain numerous age groups with zero death counts: here, we provide an example of hunter-gatherer populations. Third, gamma-Gompertz-Makeham-based life expectancy values are almost identical to the ones provided by the major high-quality human mortality databases that use more complicated procedures. Applying a gamma-Gompertz-Makeham model to adult mortality data can be used to revise life-expectancy trends for historical populations that usually serve as input for mortality forecasts.
Mortality of populations is summarized in life tables. The latter contain certain measures of mortality (e.g. remaining life expectancy, survival probability at age x), but researchers also calculate other characteristics of the distribution of deaths based on life-table information (e.g. Gini coefficient, Human Development Index, etc.) to use them as input in public and health policy making, insurance and investments.
The most commonly used procedure for life tables in the open-ended age group is to assume that the average number of person-years lived by the individuals dying in this age group equals the reciprocal of the death rate in this age group . Suppose that xc is the censoring age for a life table and above this age age-specific information is aggregated. Using standard life-table algebra with a constant-hazard assumption, remaining life expectancy for this open-ended age group is given by
where mxc is the death rate corresponding to this age group.
For four hunter-gatherer populations presented in Fig 1 (data source: [25–28]), conventional life-table calculation overestimates the average length of life by 5.3 years (with a standard deviation of σ = 5.52 years). ΓGM estimates are closer to the ones of a Siler model (applied by the authors in ) that also assumes exponentially increasing adult mortality . Note that mortality deceleration is not captured by the Siler model, which might be adequate for hunter-gatherer populations, but not for contemporary populations. This is the reason why we do not compare ΓGM and Siler life expectancies for human populations.
Reconstructing adult human mortality within the ΓGM framework is essential for life tables in which a substantial proportion of the population are censored. Life tables that do not address censoring appropriately, distort life-expectancy values and other dispersion measures of mortality based on them, e.g. life disparity , Keyfitz’s entropy , the Gini coefficient , and the coefficient of variation (see e.g. ). In this article, we find such evidence for human (e.g. Bangladesh, females, 1974; Malta, males, 2007, etc.) and hunter-gatherer populations.