On the estimation of disability-free life expectancy: Sullivan's method and its extension

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.