Abstract
BackgroundIncreases in human longevity have made it critical to distinguish healthy longevity from longevity without regard to health. Current methods focus on expectations of healthy longevity, and are often limited to binary health outcomes (e.g., disabled vs. not disabled). We present a new matrix formulation for the statistics of healthy longevity, based on health prevalence data and Markov chain theory, applicable to any kind of health outcome and which provides variances and higher moments as well as expectations of healthy life.MethodThe model is based on a Markov chain description of the life course coupled with the moments of health outcomes (“rewards”) at each age or stage. As an example, we apply the method to nine European countries using the SHARE survey data on the binary outcome of disability as measured by activities of daily living, and the continuous health outcome of hand grip strength.ResultsWe provide analytical formulas for the mean, variance, coefficient of variation, skewness and other statistical properties of healthy longevity. The analysis is applicable to binary, categorical, ordinal, or interval scale health outcomes. The results are easily evaluated in any matrix-oriented software. The SHARE results reveal familiar patterns for the expectation of life and of healthy life: women live longer than men but spend less time in a healthy condition. New results on the variance shows that the standard deviation of remaining healthy life declines with age, but the coefficient of variation is nearly constant. Remaining grip strength years decrease with age more dramatically than healthy years but their variability pattern is similar to the pattern of healthy years. Patterns are similar across nine European countries.ConclusionsThe method extends, in several directions, current calculations of health expectancy (HE) and disability-adjusted life years (DALYs). It applies to both categorical and continuous health outcomes, to combinations of multiple outcomes (e.g., death and disability in the formulation of DALYs) and to age- or stage-classified models. It reveals previously unreported patterns of variation among individuals in the outcomes of healthy longevity.
Highlights
Increases in human longevity have made it critical to distinguish healthy longevity from longevity without regard to health
We show that healthy longevity can be analyzed by incorporating prevalence of health outcomes into a Markov chain with rewards
The Markov chain defines the transitions and survival between age classes; the rewards specify the moments of the health outcome at each age or stage
Summary
Increases in human longevity have made it critical to distinguish healthy longevity from longevity without regard to health. Driven by improvements in nutrition, public health, medical care, and medical technology have dramatically changed the prospects of future life, especially for the elderly. This has led to the need to distinguish healthy longevity from longevity without. Caswell and Zarulli Population Health Metrics (2018) 16:8 distinguished or even mutually exclusive on close examination” We are concerned with a class of health metrics that evaluate what we call healthy longevity. But not identical, to what Murray et al [3] call “summary measures of population health,” their usage leaves out important aspects
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