Multistate Life Table
Also known as: Increment-Decrement Life Table, Multiple-State Life Table, Multistate Demography, Çok Durumlu Yaşam Tablosu
The multistate life table, also called the increment-decrement life table, generalizes the ordinary life table to populations that move among several living states — such as healthy and disabled, married and unmarried, or employed and unemployed — as well as the absorbing state of death. Using age-specific transition rates organized in matrices, it tracks the flows of a synthetic cohort among states and yields state-specific expectancies, such as the years a person can expect to spend healthy versus disabled.
Key highlights
- Handles multiple living states and reversible transitions, far beyond the single alive-to-dead structure of the ordinary life table.
- Yields incidence-based, state-specific expectancies such as healthy or working life expectancy that partition total longevity.
- Built on observed transition rates, so it reflects the dynamics of movement rather than a static prevalence snapshot.
- Matrix formulation scales cleanly to many states and integrates with multistate projection and population-renewal models.
Intuition
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How it works
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When to use it
Use a multistate life table when individuals can occupy and move between several living states over the life course and you want expectancies broken down by state — for example healthy versus disabled years, or working versus retired years — derived from transition rates rather than from a single prevalence snapshot. It requires longitudinal data that observe transitions (incidence and recovery), and it assumes the process is Markovian: transition rates depend on current state and age but not on prior history or duration in state. It is the method of choice when transitions are reversible and incidence-based estimates are wanted. When only cross-sectional prevalence is available and the simpler one-state-partition question suffices, the Sullivan method is the pragmatic alternative; when duration dependence or unobserved heterogeneity is important, semi-Markov or frailty extensions are needed.
Strengths & limitations
- Handles multiple living states and reversible transitions, far beyond the single alive-to-dead structure of the ordinary life table.
- Yields incidence-based, state-specific expectancies such as healthy or working life expectancy that partition total longevity.
- Built on observed transition rates, so it reflects the dynamics of movement rather than a static prevalence snapshot.
- Matrix formulation scales cleanly to many states and integrates with multistate projection and population-renewal models.
- Requires longitudinal or multi-wave panel data on transitions, which are far more demanding to collect than cross-sectional prevalence.
- The Markov assumption ignores duration in state and prior history, which can bias expectancies when transition risk depends on them.
- Estimates become unstable when some transitions are rare and the cells of the rate matrices are sparse.
- Results are sensitive to the discrete approximation used to convert rates into transition probabilities, especially over wide age intervals.
Common pitfalls
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Applications
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Frequently asked
How does a multistate life table differ from the Sullivan method?
The Sullivan method partitions ordinary life-table person-years using an observed cross-sectional prevalence of states (e.g., the share disabled at each age), so it needs only a standard life table plus a single prevalence survey. The multistate life table instead uses observed transition rates between states and is incidence-based, capturing the actual dynamics of movement and recovery. Sullivan is simpler and less data-hungry but reflects historical prevalence; the multistate table is more demanding but yields genuine transition-based expectancies.
What is the increment-decrement terminology about?
In a classical life table the cohort only decrements — it can only lose members to death. In a multistate table a living state can also increment, gaining members who transition into it from other living states (for example, recovering from disability back to health). Tracking both increments and decrements for every state at every age is what the name 'increment-decrement life table' describes.
What data are needed to build one?
You need age-specific transition rates between all living states and state-specific mortality rates, estimated as transitions divided by person-years of exposure in the origin state. This in practice requires longitudinal data — panel surveys, registers, or multi-wave studies — that observe the same individuals over time so that movements between states can be counted, unlike the single-survey prevalence that the Sullivan method requires.
Sources
- 1.Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell.ISBN 9781557864512
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Cite this page
ScholarGate. (2026, June 22). Multistate Life Table. ScholarGate. https://scholargate.app/demography/multistate-life-table