Volume 35 - Article 15 | Pages 399–454 Author has provided data and code for replicating results

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

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Date received:21 Apr 2015
Date published:23 Aug 2016
Word count:5696
Keywords:Chiang method, delta method, health expectancy, life expectancy, life table, mortality, overdispersion, standard error, variance
Additional files:readme.35-15 (text file, 1 kB)
 demographic-research.35-15 (zip file, 149 kB)


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

Ernest Lo - Institut National de Santé Publique du Québec (INSPQ), Canada [Email]
Dan Vatnik - McGill University, Canada [Email]
Andrea Benedetti - McGill University, Canada [Email]
Robert Bourbeau - Université de Montréal, Canada [Email]

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

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