Questions: Multi-State Demography

Question 1

How does a multi-state life table differ from a standard (single-decrement) life table?

• A. A multi-state life table tracks multiple birth cohorts simultaneously, while a standard life table tracks only one
• B. A multi-state life table allows individuals to transition between multiple living states (not just alive-to-dead), with age-specific transition rates governing movement between states such as healthy, disabled, and deceased
• C. A multi-state life table uses different mortality rates for men and women, while a standard life table does not
• D. A multi-state life table is based on period data only, while a standard life table can use cohort data

Answer: (B)

A standard life table models a single decrement — the transition from alive to dead — using age-specific mortality rates. A multi-state life table generalizes this by defining multiple living states (e.g., healthy, mildly disabled, severely disabled) plus the absorbing state of death, with age-specific transition rates governing all possible movements between states, including recovery (disabled back to healthy). This allows calculation of state-specific life expectancies — such as how many years a person can expect to live disability-free — which a standard life table cannot provide.

Question 2

Multi-state models assume that transitions between states are irreversible, like the transition from alive to dead.

• T. True
• F. False

Answer: False

A key advantage of multi-state models is that they accommodate reversible transitions. While death is an absorbing state (irreversible), transitions between living states can go in both directions: a person can move from healthy to disabled and back to healthy, from married to divorced to remarried, or from employed to unemployed to employed. This reversibility is modeled through bidirectional transition rates and is what distinguishes increment-decrement life tables from the simpler multiple-decrement tables (which only model exits from a single state to various competing destinations without return).

Question 3

What is 'health expectancy' and how does multi-state demography make its calculation possible?

Model answer: Health expectancy (also called healthy life expectancy or disability-free life expectancy) is the expected number of years a person will live in a particular health state — typically 'good health' or 'without disability.' Multi-state demography makes this calculable by constructing a life table with multiple health states (e.g., healthy, disabled) plus death, with age-specific transition rates governing movement between all states. By tracking a synthetic cohort through these transitions, the model partitions total life expectancy into years spent in each health state. This is impossible with a standard life table, which can only compute total life expectancy without distinguishing quality of years lived.

Health expectancy has become one of the most policy-relevant demographic indicators. A country where rising life expectancy is accompanied by rising health expectancy faces a very different aging challenge than one where additional years of life are spent predominantly in disability. Sullivan's method provides a simplified calculation using prevalence data, but the full multi-state approach using transition rates is more accurate because it captures the dynamics of health deterioration and recovery rather than assuming a static prevalence distribution.

Question 4

Why is the Markov assumption important in multi-state demographic models, and when might it be violated?

Model answer: The Markov assumption states that transition rates depend only on the individual's current state and age, not on their history of previous states or duration in the current state. This assumption simplifies computation enormously — the entire system can be described by a matrix of age-specific transition rates. It may be violated when duration in a state matters (e.g., the probability of leaving unemployment depends on how long you have been unemployed — duration dependence) or when history matters (e.g., a person who has been disabled and recovered may face different re-disability rates than someone never disabled). When Markov assumptions are violated, semi-Markov models that incorporate duration dependence or expanded state spaces that encode relevant history are used.

The Markov assumption is a pragmatic simplification that makes multi-state models tractable. Most applied demographic work uses it because the data requirements for non-Markov models are severe — you need longitudinal data tracking individual trajectories, not just cross-sectional prevalence. However, awareness of when the assumption fails is critical for interpreting results. In health demography, ignoring duration dependence in disability can lead to underestimating the concentration of disability in a subset of the population who cycle repeatedly between health states.