Tianyu Shen

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.

Many studies have compared individual measures of health expectancy across older populations by time-invariant characteristics. However, very few have included time-varying variables when calculating health expectancy. Even among older adults, socioeconomic and demographic characteristics are likely to change over the life course, and these changes may have substantial implications for health outcomes. This paper proposes a multiple multistate method (MMM) that situates the multistate model within the broader family of vector autoregressive models. Our approach allows the incorporation of the coevolution of multiple life course factors and provides a flexible yet simple way to model two or more time-varying variables with the multistate model. We demonstrate the MMM in two empirical applications, showing the flexibility of the approach to explore health expectancies with complex state spaces.

Multistate modeling is a commonly used method to compute healthy life expectancy. However, there is currently no analytical method to decompose the components of differentials in summary measures calculated from multistate models. In this research note, we propose a derivative-based method to decompose the differentials in population-based health expectancies estimated via a multistate model into two main components: the proportion resulting from differences in initial health structure and the proportion resulting from differences in health transitions. We illustrate the method using data on activities of daily living from the U.S. Health and Retirement Study to decompose the sex differential in disability-free life expectancy (HLE) among older Americans. Our results suggest that the sex gap in HLE results primarily from differences in transition rates between disability states rather than from the initial health distribution of female and male populations. The methods introduced here will enable researchers, including those working in fields other than health, to decompose the relative contribution of initial population structure and transition probabilities to differences in state-specific life expectancies from multistate models.

A substantial body of prior research has explored patterns of disability-free and morbidity-free life expectancy among older populations. However, these distinct facets of later-life health are almost always studied in isolation, even though they are very likely to be related. Using data from the US Health and Retirement Study and a multistate life table approach, this paper explores the interactions between disability, morbidity, and mortality by sex and education among four successive US birth cohorts, born from 1914 to 1923 to 1944–1953 and compared in the periods 1998–2008 and 2008–2018. We find little compression of disability but a marked expansion of morbidity across cohorts. However, disability-free life expectancy (DFLE) among those living with chronic morbidities has increased, even though at the population-level DFLE is largely unchanged. Broadly, these patterns suggest that successive cohorts of older populations in the US are experiencing a dynamic equilibrium, where the link between chronic morbidities and disability has weakened over successive cohorts. Investigating patterns by educational attainment, we find marked disparities where the least educated individuals not only live significantly fewer years free of disabilities or chronic morbidities but also have experienced an expansion in morbidity and disability. Our findings suggest that the future trajectory of disability-free life expectancy in the US is increasingly contingent on efforts to improve disease management and control the severe consequences of chronic morbidities.

The demographic balance equation relates the population growth rate with crude rates of fertility, mortality, and net migration. All these rates refer to changes occurring between two time points, say, t and t + h. However, this fundamental balance equation overlooks the contribution of historical fertility, mortality, and migration in explaining these population counts. Because of this, the balance equation only partially explains a change in growth rate between time t and t + h as it does not include the contribution of historical population trends in shaping the population at time t. The overall population growth rate can also be expressed as the weighted average of age-specific growth rates. In this article, we develop a method to decompose the historical drivers of current population growth by recursively employing the variable-r method on the population’s average age-specific growth rates. We illustrate our method by identifying the unique contributions of survival progress, migration change, and fertility decline for current population growth in Denmark, England and Wales, France, and the United States. Our results show that survival progress is mainly having an effect on population growth at older ages, although accounting for indirect historical effects illuminates additional contributions at younger ages. Migration is particularly important in Denmark and England and Wales. Finally, we find that across all populations studied, historical fertility decline plays the largest role in shaping recent reductions in population growth rates.