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. 2007 Fall;102(480):1199-1211.
doi: 10.1198/016214507000000040.

On the Estimation of Disability-Free Life Expectancy: Sullivan' Method and Its Extension

Kosuke Imai  1 , Samir Soneji  1
Affiliations

On the Estimation of Disability-Free Life Expectancy: Sullivan' Method and Its Extension

Kosuke Imai et al. J Am Stat Assoc. 2007 Fall.

Abstract

A rapidly aging population, such as the United States today, is characterized by the increased prevalence of chronic impairment. Robust estimation of disability-free life expectancy (DFLE), or healthy life expectancy, is essential for examining whether additional years of life are spent in good health and whether life expectancy is increasing faster than the decline of disability rates. Over 30 years since its publication, Sullivan's method remains the most widely used method to estimate DFLE. Therefore, it is surprising to note that Sullivan did not provide any formal justification of his method. Debates in the literature have centered around the properties of Sullivan's method and have yielded conflicting results regarding the assumptions required for Sullivan's method. In this article we establish a statistical foundation of Sullivan's method. We prove that, under stationarity assumptions, Sullivan's estimator is unbiased and consistent. This resolves the debate in the literature, which has generally concluded that additional assumptions are necessary. We also show that the standard variance estimator is consistent and approximately unbiased. Finally, we demonstrate that Sullivan's method can be extended to estimate DFLE without stationarity assumptions. Such an extension is possible whenever a cohort life table and either consecutive cross-sectional disability surveys or a longitudinal survey are available. Our empirical analysis of the 1907 and 1912 U.S. birth cohorts suggests that while mortality rates remain approximately stationary, disability rates decline during this time period.

Keywords: Aggregate data; Demography; Healthy life expectancy; Life tables; Morbidity; Mortality; Stationarity.

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Figures

Figure 1
Figure 1
Estimated bounds of disability-free life expectancy (DFLE) and proportion of life spent disability-free for the 1907 and 1912 U.S. birth cohorts. The upper left (right) panel shows the estimated bounds of DFLE along with life expectancy for the 1907 (1912) birth cohort from age 81 (76) to 90 (90). The lower panels show the estimated bounds of the proportion of remaining life spent disability-free. The 95% confidence intervals are shown as dashed lines. For the 1907 (1912) birth cohort, DFLE and proportion of remaining life spent disability-free are calculated using the monotonicity assumption for ages from 81 (76) to 83 (78).
Figure 2
Figure 2
Comparison between the 1991 period and 1907 U.S. birth cohorts. The upper, middle, and lower panels compare the difference in life expectancy, DFLE, and the proportion or remaining life spent disability-free (i.e., 1991 period minus 1907 birth cohort). The estimated bounds of the differences are shown. The 95% balanced confidence intervals are calculated from the bootstrap method and shown as dashed lines.
Figure 3
Figure 3
Comparison of the 1991 period cohort with the 1907 birth cohort. The left panel compares the 1991 period cohort mortality rate (vertical axis) with the 1907 birth cohort mortality rate (horizontal axis) from age 81 to 95. The right panel compares the 1991 period disability prevalence (vertical axis) with the 1907 birth cohort disability prevalence (horizontal axis) from age 84 to 95. The 45° solid line represents equality.
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References

    1. Albarran I, Ayuso M, Guillen M, Monteverde M. A Multiple State Model for Disability Using the Decomposition of Death Probabilities and Cross-Sectional Data. Communications in Statistics, Part A—Theory and Methods. 2005;34:2063–2075.
    1. Arias E. United States Life Table, 2002. National Vital Statistics Reports. 2002;53:6. - PubMed
    1. Barendregt J, Bonneux L, Van der Maas P. Health Expectancy: An Indicator for Change? Journal of Epidemiology and Community Health. 1994;48:482–487. - PMC - PubMed
    1. Barendregt J, Bonneux L, Van der Maas P. Health Expectancy: An Indicator for Change? Journal of Epidemiology and Community Health. 1995;49:330–332. - PMC - PubMed
    1. Beran R. Balanced Simultaneous Confidence Sets. Journal of the American Statistical Association. 1988;83:679–686.

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