Volume 45 - Article 13 | Pages 397–452  

Healthy longevity from incidence-based models: More kinds of health than stars in the sky

By Hal Caswell, Silke van Daalen

Abstract

Background: Healthy longevity (HL) is an important measure of the prospects for quality of life in ageing societies. Incidence-based (cf. prevalence-based) models describe transitions among age classes and health stages. Despite the probabilistic nature of those transitions, analyses of healthy longevity have focused persistently on means (``health expectancy''), neglecting variances and higher moments.

Objective: Our goal is a comprehensive methodology to analyze HL in terms of any combination of health stages and age classes, or of transitions among health stages, or of values (e.g., quality of life) associated with health stages or transitions.

Methods: We construct multistate Markov chains for individuals classified by age and health stage and use Markov chains with rewards to compute all moments of HL.

Results: We present a new and straightforward algorithm to create the multistate reward matrices for occupancy, transitions, or values associated with occupancy or transitions. As an example, we analyze a published model for colorectal cancer. The possible definitions of HL in this simple model outnumber the stars in the visible universe. Our method can analyze any of them; we show four examples: longevity without abnormal cells, cancer-free longevity, and longevity with cancer before or after a critical age.

Contribution: Our methods make it possible to analyze any incidence-based model,with any number of health stages, any pattern of transitions, and any kind of values assigned to stages. It is easily computable, requires no simulations, provides all the moments of healthy longevity, and solves the inhomogeneity problem.

Author's Affiliation

Other articles by the same author/authors in Demographic Research

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
Volume 33 - Article 20

The formal demography of kinship VI: Demographic stochasticity and variance in the kinship network
Volume 51 - Article 39

The formal demography of kinship V: Kin loss, bereavement, and causes of death
Volume 49 - Article 41

The contributions of stochastic demography and social inequality to lifespan variability
Volume 49 - Article 13

How does the demographic transition affect kinship networks?
Volume 48 - Article 32

The formal demography of kinship IV: Two-sex models and their approximations
Volume 47 - Article 13

The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16

The formal demography of kinship II: Multistate models, parity, and sibship
Volume 42 - Article 38

The formal demography of kinship: A matrix formulation
Volume 41 - Article 24

The sensitivity analysis of population projections
Volume 33 - Article 28

Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19

A matrix approach to the statistics of longevity in heterogeneous frailty models
Volume 31 - Article 19

Why do lifespan variability trends for the young and old diverge? A perturbation analysis
Volume 30 - Article 48

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates
Volume 23 - Article 19

Perturbation analysis of nonlinear matrix population models
Volume 18 - Article 3

Most recent similar articles in Demographic Research

The formal demography of kinship VI: Demographic stochasticity and variance in the kinship network
Volume 51 - Article 39    | Keywords: dependency ratios, kinship, matrix models, multitype branching processes, prevalence, stochastic models

The influence of parental cancer on the mental health of children and young adults: Evidence from Norwegian register data on healthcare consultations
Volume 50 - Article 27    | Keywords: cancer, children, fixed effects, longitudinal, mental health, parents registers

Insight on 'typical' longevity: An analysis of the modal lifespan by leading causes of death in Canada
Volume 35 - Article 17    | Keywords: age-at-death distribution, Canada, cancer, cardiovascular diseases, cause of death, longevity, modal age at death, old-age mortality, Poisson P-splines, smoothing

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
Volume 33 - Article 20    | Keywords: fertility, fertility transition, individual stochasticity, lifetime reproduction, Markov chains

Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19    | Keywords: individual stochasticity, lifetime consumption, lifetime deficit, lifetime income, Markov chains, national transfer accounts (NTA)