How much can we trust life tables? Sensitivity of mortality measures to right-censoring treatment

Abstract

International organizations, research institutions, insurance companies, pension funds and health policymakers calculate human mortality measures from life tables. Life-table data, though, are usually right-censored; that is, the last open-end age group does not contain information about the exact ages at death of individuals there, and mortality measures are sensitive to the way censoring is addressed. The standard way of "closing" the life table assumes a constant hazard of death for the last age group. This might lead to erroneous conclusions about mortality measures, especially when the open-end age interval contains a large proportion of the study population. In this article, we propose, instead, fitting a parametric model that well describes human mortality patterns, the gamma-GompertzMakeham, accounting for censoring, and constructing model-based equivalents of five mortality measures: life expectancy, the modal age at death, life disparity, entropy and the Gini coefficient. We show that, in comparison to conventional life-table measures, modelbased measures are less sensitive to the age at censoring or, equivalently, to the proportion of censored individuals, and can be only slightly distorted even if the age at censoring is low. This study also compares life-table and model-based mortality measures for a non-human population with an underlying Gompertz mortality schedule in which a fixed proportion of the population is censored. Using model-based mortality measures is essential when studying the mortality of populations subjected to substantial censoring; for instance, many life tables for developing countries contain an open-end interval that contains more than 10% of the population. In this study, we show that life expectancy at birth for Brazilian females in 2007, calculated by standard life-table algebra, exceeds by almost 3 years the gamma-GompertzMakeham model-based life expectancy. This article might serve as a basis for recalculation of mortality measures for all populations subjected to substantial censoring.

Life expectancy versus lifespan inequality: A smudge or a clear relationship?

“…This could explain why the smudge in Fig 1A is much wider than in B, C and D: because e † is not a shape measure, as it depends on units of time (remaining life years left), whereas the other measures are scaled by life expectancy. Missov et al [ 25 ] compare life expectancy values in life tables based on the methods applied by the highest quality life-table databases. Life tables published in HMD, WHO and WPP databases use smoothing techniques for mortality rates at oldest-old ages in order to address right censoring adequately.…”

“…The HLD is a jumble of miscellaneous life tables from various sources, compiled from data of varying quality and estimated using various methods. Both the varying quality of the data in the four databases and the different methods used to estimate life tables [ 25 ] influence the scatter of points shown in the four Figures.…”

Expectation of life at old age: revisiting Horiuchi-Coale and reconciling with Mitra

“…The WHO and the HMD use an S-shaped model for extrapolating the death rates as alternative to the J-shaped Gompertz model used here. Indeed, logistic-type models were shown to better fit the deceleration of mortality at oldest old ages (Missov et al 2016 ; Thatcher et al 1998 ). However, our results for the younger open age intervals, where all mortality models fit closely to each other, suggest that the conclusion about the inferiority of extrapolation to the Horiuchi-Coale and Mitra methods is, in general, applicable to any mortality models other than the Gompertz model.…”

“…It builds upon age-specific death rates and produces various indicators of mortality, survival, and longevity for the age groups. A limitation of the model appears at the older ages where data scarcity or deficiency forces statisticians to disregard age details and aggregate the available data into a single “open age interval” (Missov et al 2016 ).…”

“…The classical approach is not the only one available for cases with age reporting problems. The most common alternative method to calculate the last “problematic” age range of the life table is extrapolation of death rates based on their change at younger ages in combination with a mortality model (Mathers and Ho 2014 ; Missov et al 2016 ; UN DESA/Population Division 1982 , 2017 ; Wilmoth et al 2007 ). The World Health Organization (WHO) (Mathers and Ho 2014 ) used to extrapolate the death rates above the age of 85 by assuming a logistic mortality model.…”