Modeling Disability-Free Life Expectancy With Duration Dependence: A Research Note on the Bias in the Markov Assumption.

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Demographic studies on healthy life expectancy often rely on the Markov assumption, which fails to consider the duration of exposure to risk. To address this limitation, models like the duration-dependent multistate life table (DDMSLT) have been developed. However, these models cannot be directly applied to left-censored survey data, as they require knowledge of the time spent in the initial state, which is rarely known because of survey design. This research note presents a flexible approach for utilizing this type of survey data within the DDMSLT framework to estimate multistate life expectancies. The approach involves partially dropping left-censored observations and truncating the duration length after which duration dependence is assumed to be minimal. Utilizing the U.S. Health and Retirement Study, we apply this approach to compute disability-free/healthy life expectancy (HLE) among older adults in the United States and compare duration-dependent models to the typical multistate model with the Markov assumption. Findings suggest that while duration dependence is present in transition probabilities, its effect on HLE is averaged out. As a result, the bias in this case is minimal, and the Markov assumption provides a plausible and parsimonious estimate of HLE.