Matrix Methods in Health Demography: A New Approach to the Stochastic Analysis of Healthy Longevity

Hal Caswell, University of Amsterdam
Virginia Zarulli, University of Southern Denmark

Current methods for distinguishing healthy longevity from longevity without regard to health focus on binary (e.g., disabled or not disabled) or categorical health outcomes (e.g. in good, poor, or very bad health), and report only expectations of healthy longevity. We present a new matrix formulation for the statistics of healthy longevity, based on health prevalence data and Markov chain theory. It provides the mean, variance, coefficient of variation, skewness and other statistical properties of healthy longevity, and is applicable to binary, categorical, ordinal, or interval scale health outcomes. The method also extends calculations of disability-adjusted life years (DALYs), which require accounting for combinations of multiple outcomes (e.g., death and disability) and applies to age-, stage-, or multistate classified models. The results are easily computed in any matrix-oriented software.

As an example, we apply the method to 9 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. The SHARE examples 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 9 European countries.

Presented in Session 1173: Health, Wellbeing, and Morbidity