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 thirty 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 paper, 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.