Microsimulation Paper No. 4
Stochastic Modeling of Active Life and Its Expectancy
Douglas A. Wolf and Sarah B. Laditka
Abstract: The concept of active (or disability-free) life, and its average value, has proven to be a useful index of public health and of quality of life for populations. A question of great interest in recent years is whether recent trends towards longer life expectancy have been accompanied by comparable increases in active life expectancy.
Past research on patterns and trends of active and inactive life has focused almost exclusively on the expectancy--or, the average value--of years spent with and without disability. This measure is useful for actuarial calculations, for example analysis of the insurance value of programs that provide long-term care services. However, when considering broader issues of equity and efficiency in the financing and provision of services, or of targeting of programmatic resources, it is also useful to analyze the full frequency distribution of time spent in each activity status, in addition to the average values of each. Nevertheless, to our knowledge no past research has attempted to trace out the frequency distribution that underlies the calculations of Active Life Expectancy (ALE). Similarly, the uncertainty (or, the margin of error) in our calculations of active life expectancy traceable to sampling error has received little attention.
This paper addresses two related phenomena: variability in active life, which is to say the relative likelihood that someone will spend an additional 0, 1, 2, ... or more of his or her years in various functional statuses such as active or inactive; and uncertainty about the average value of additional years spent in each such status. Our concern with both phenomena leads us to present our findings in the form of intervals, or measures of dispersion, as well in the more conventional form of point estimates. Linking the two areas of analysis is a recognition of several sources of randomness, or stochasticity, that are inevitably present when analyzing the dynamics of functional status. In general, we find that the variability in years of active life is substantial. This variability is obscured in analyses that address only the expected value of active life. In contrast, uncertainly related to sampling error appears to be quite small, at least for the combination of survey data and model specification employed here.
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