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

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.