Longer healthy life, but for how many? A stochastic analysis of healthy lifespan inequality.

Over the past 150 years, life expectancy doubled and healthy life expectancy increased. Expectations reveal nothing about variability, so we present a stochastic analysis to investigate changes over time, age and gender of variation, among individuals, in healthy lifespan, for different levels of country income. To complement health-adjusted life expectancy (HALE) data from the Global Burden of Disease Study, we use a stochastic model to compute the standard deviation of healthy life (SDHL). The model is a finite-state absorbing Markov chain with rewards. It includes stochastic survival, mortality, and loss of good health status. An individual surviving from one age to the next gains, as a "reward," a year of good health. This method provides all the moments of healthy longevity. The mean healthy longevity is exactly the HALE. As a measure of variation, here we focus on the standard deviation of healthy longevity. From 1990 to 2019, HALE increased, with greater increases at younger ages. At the same time, SDHL at younger ages decreased and at older ages increased. The most significant changes at birth occurred in low- and lower-middle-income countries. High- and upper-middle-income countries saw notable increases at old ages. Women generally have longer HALE and higher SDHL, but the overall HALE increase was greater for men. The reduction in SDHL over time suggests that more individuals benefit from increased longevity, particularly in low-income countries closing the gap with high-income countries. However, improvements in healthy survival at older ages appear unevenly distributed among individuals in high-income countries.