PSC Working Paper Series

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Working Paper

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Fishman, Ezra. 2015. "Variance Estimation for a Complex Life Table Quantity: Disease-free Life Expectancy." PSC Working Paper Series, WPS 15-2,


Background: In the last decade, adult mortality in the United States has continued its long-run decline, while diabetes prevalence has increased. It is unknown whether the additional person-years lived in the adult population have mostly been spent in a diseased or a disease-free state. Furthermore, although illness and death are stochastic processes, little is known about the variance in diabetes-free life expectancy (DFLE) when compared across ages. More generally, methods of obtaining the variance of complex life table quantities are under-explored.

Objective: Estimate DFLE and its variance in the United States in 2000 and 2010.

Methods: Data on diabetes prevalence for ages 20+ come from the National Health and Nutrition Examination Surveys (NHANES), 1999-2000 (n=4,205) and 2009-2010 (n=5,752). Diabetes prevalence was defined as HbA1c at least 6.5% or taking diabetes medication. Deaths and population counts by age and sex come from the Human Mortality Database, covering the entire U.S. population. DFLE was estimated using Sullivan’s method. Three methods of estimating variance in DFLE were explained and compared: the delta method, Monte Carlo simulation, and bootstrapping.

Results: Although life expectancy at age 20 rose by approximately 3 years for both males and females between 2000 and 2010, DFLE at age 20 did not change during this decade. At age 70, life expectancy rose by 2.5 years for males and 2.7 years for females, but DFLE rose only 0.7 years for males and 0.8 years for females. For all methods, both sexes and in both years, variance in DFLE was larger at younger ages (males, 2000, age 20, delta method: 0.020) than at older ages (males, 2000, age 70, delta method: 0.012). For any given age/sex/year, the delta method produced the smallest estimates of variance of DFLE, followed by Monte Carlo. Bootstrapping produced variance estimates that were by far the largest, often ten times larger than the Monte Carlo variances. Differences across methods in the variance in estimated diabetes prevalence accounted for most of the differences across methods in the variance of DFLE.

Conclusions: The vast majority of the person-years of life gained by the U.S. adult population between 2000 and 2010 were spent with diabetes. Variance in DFLE arises mostly from variance in estimated disease prevalence. The variance of life-table quantities can be obtained using multiple methods, and the appropriate method for a given research problem will vary.


Diabetes, Life Expectancy, Sullivan Method, National Health and Nutrition Examination Survey (NHANES), Statistical Demography



Date Posted: 08 May 2015