The joint distribution of years lived in good and poor health

Incidence-based multistate models of population health are commonly applied to calculate state expectancies, such as a healthy life expectancy (HLE), or unhealthy life expectancy (UHE). These models also allow the computation of other summary indices, such as the distributions of healthy or unhealthy lifespans.

We aim to show how a multistate health model implies a multistate death distribution, giving joint information on years lived in good and poor health. We also propose three aggregate indices of joint health and mortality inequality.

We propose a double-accounting approach to increment-decrement life table methods to intuitively derive a multistate health distribution over age and cumulative duration spent in each state. We then define a variety of summary lifespan inequality indices based on different distance metrics, namely Euclidean, Chebyshev, and Manhattan distances.

We apply the method to multistate transition probabilities between health states based on the activities of daily living index for Italian women from the Survey of Health, Ageing and Retirement in Europe in 2015-2017. We demonstrate the added value of accounting for joint years lived in health states in multistate models for our understanding of the period health and mortality conditions from the perspective of health-specific lifespans of individuals.

Multivariate state distributions and summary indices derived from them give a holistic representation of population health inequality. We offer selected summary indices of the multivariate distribution with different demographic interpretations from the measures derived from univariate distributions. Although more theoretical and methodological work is required to motivate a single comprehensive population health inequality index, this direction is a promising path for a better understanding of population health dynamics and relationships between univariate statistics.