Volume 35 - Article 15 | Pages 399–454  

Variance models of the last age interval and their impact on life expectancy at subnational scales

By Ernest Lo, Dan Vatnik, Andrea Benedetti, Robert Bourbeau

Abstract

Background: The Chiang method is the most widely accepted standard for estimating life expectancy (LE) at subnational scales; it is the only method that provides an equation for the LE variance. However, the Chiang variance formula incorrectly omits the contribution of the last age interval. This error is largely unknown to practitioners, and its impact has not been rigorously assessed.

Objective: We aim to demonstrate the potentially substantial role of the last age interval on LE variance. We further aim to provide formulae and tools for corrected variance estimation.

Methods: The delta method is used to derive variance formulae for a range of variance models of the last age interval. Corrected variances are tested on 291 empirical, abridged life tables drawn from Canadian data (2004-2008) spanning provincial, regional, and intra-regional scales.

Results: The last age interval death count can contribute substantially to the LE variance, leading to overestimates of precision and false positives in statistical tests when using the uncorrected Chiang variance. Overdispersion amplifies the contribution while error in population counts has minimal impact.

Conclusions: Use of corrected variance formulae is essential for studies that use the Chiang LE. The important role of the last age interval , and hence the life table closure method, on LE variance is demonstrated. These findings extend to other LE-derived metrics such as health expectancy.

Contribution: We demonstrate that the last age interval death count can contribute substantially to the LE variance, thus resolving an ambiguity in the scientific literature. We provide heretofore-unavailable formulae for correcting the Chiang LE variance equation.

Author's Affiliation

Other articles by the same author/authors in Demographic Research

Insight on 'typical' longevity: An analysis of the modal lifespan by leading causes of death in Canada
Volume 35 - Article 17

Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach
Volume 25 - Article 19

Does the recent evolution of Canadian mortality agree with the epidemiologic transition theory?
Volume 18 - Article 19

Mortality statistics for the oldest-old: an evaluation of Canadian data
Volume 2 - Article 2

Most recent similar articles in Demographic Research

A Bayesian model for age at death with cohort effects
Volume 51 - Article 33    | Keywords: age at death, Bayesian approach, cohort effects, Italy, mortality

The impact of the COVID-19 pandemic on mortality in Uruguay from 2020 to 2022
Volume 51 - Article 29    | Keywords: COVID-19, excess mortality, life expectancy, Uruguay

On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy
Volume 51 - Article 24    | Keywords: Gompertz law, life expectancy, lifespan variation, longevity, mode, mortality

The role of sex and age in seasonal mortality – the case of Poland
Volume 51 - Article 17    | Keywords: mortality, Poland, seasonality, sex differences

Data errors in mortality estimation: Formal demographic analysis of under-registration, under-enumeration, and age misreporting
Volume 51 - Article 9    | Keywords: age misreporting, data errors, formal demography, mortality