Concept Architecture
Concept
Theoretically, a Life Table is a mathematical framework that describes the survival experience of a population by quantifying the probability of surviving, dying, or remaining alive across successive age intervals. Originating in actuarial science and demography, life tables provide the foundation for estimating life expectancy, survival distributions, and age-specific mortality. In health economics, life tables are widely used to represent background mortality within decision-analytic models, enabling estimates of survival independent of disease-specific risks.
Mathematically, a life table represents a discrete survival process in which a hypothetical cohort is exposed to age-specific mortality probabilities. The canonical framework uses age-specific probabilities of death to derive the number surviving, deaths, person-years lived, cumulative person-years remaining, and life expectancy. These quantities form a consistent set of recursive calculations describing survival across the lifetime of the cohort.
In practice, life tables are constructed from national mortality statistics or population registries. Health economic models incorporate life table mortality by applying age- and sex-specific mortality probabilities to simulated cohorts or individuals. Where disease-specific mortality is modelled separately, background mortality from life tables is combined with excess mortality using recognised methods appropriate to the modelling framework.
Purpose
Used to estimate background mortality, survival, remaining life expectancy, and person-years lived for populations within health economic evaluations and decision-analytic models.
Mathematical Formulae
Primary Formula
For age interval x,
l??? = l?(1 ? q?)
where:
- l? = number alive at age x
- q? = probability of dying between ages x and x + 1
Supporting Formulae
Probability of survival:
p? = 1 ? q?
Number of deaths:
d? = l?q?
Person-years lived (uniform distribution of deaths assumption):
L? = l??? + �d?
Total remaining person-years:
T? = �???? L?
Life expectancy:
e? = T?/l?
Related Mathematical Methods
- Survival analysis
- Kaplan-Meier estimation
- Hazard-to-probability conversion
- Multi-state life table modelling
- Markov modelling
- Microsimulation
Example
A national life table reports a one-year mortality probability of 0.020 for individuals aged 70 years.
Assuming 100,000 people are alive at age 70:
l?? = 100,000 ? (1 ? 0.020) = 98,000
Deaths during the year:
d?? = 100,000 ? 0.020 = 2,000
Person-years lived:
L?? = 98,000 + 2,000/2 = 99,000
These values provide the background mortality inputs for a cost-effectiveness model evaluating a new cardiovascular intervention.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Multiplication | =B2*(1-C2) | Calculate survivors at the next age interval |
| PRODUCT | =PRODUCT(1-C2:C11) | Calculate cumulative survival across multiple years |
| SUM | =SUM(E2:E101) | Calculate total remaining person-years |
| INDEX | =INDEX(Mortality!B:B,MATCH(A2,Mortality!A:A,0)) | Retrieve age-specific mortality probability from a reference life table |
| MATCH | =MATCH(A2,Mortality!A:A,0) | Locate the correct age row within the mortality table |
VBA (Optional)
Automate the import of national life tables and generate age-specific survival schedules for decision-analytic and microsimulation models.
Sources
- Briggs AH, Claxton K, Sculpher MJ. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
- NICE. Health Technology Evaluation Manual. National Institute for Health and Care Excellence.
- Preston SH, Heuveline P, Guillot M. Demography: Measuring and Modelling Population Processes. Blackwell Publishing.
- Chiang CL. The Life Table and Its Applications. Krieger Publishing.
Related Concepts (2)
Library
Publications
1
Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6 — Briggs, Weinstein, Fenwick, Karnon, Sculpher & Paltiel, Task Force Report 6 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on parameter estimation and the characterisation of uncertainty in decision models, covering probabilistic sensitivity analysis, distributional choices, and correlation between parameters.
Journal ArticleView source →
Frequently Asked Questions (6)
What is a life table?
A tabular record of a population's mortality experience, showing the probability of death at each age and the resulting survivors over time.
Source: Halley 1693
Where did the life table originate?
The life table has its origins in the seventeenth century, when John Graunt analysed London's bills of mortality to describe how many people survived to each age, and Edmond Halley later constructed a fuller table from birth and death records. Their work turned scattered mortality data into an orderly account of survival by age, which became the foundation of demography and actuarial science. The same structure is used in health models today. Graunt (1662) produced an early version.
Source: Graunt 1662
What does a life table show?
A life table shows, for each age, the probability of dying within the year, the number of survivors from an initial cohort reaching that age, the number of deaths, and derived quantities such as the expectation of life at each age. It summarises how mortality operates across the lifespan, tracing a cohort's attrition from birth or a starting age through to the oldest ages. From these columns, life expectancy and survival probabilities are read, making the life table a compact summary of mortality.
Source: Halley 1693
How is a life table constructed?
A life table is constructed by taking age-specific mortality rates for a population and applying them successively to a hypothetical cohort, usually starting at a round number such as 100,000 at birth or a given age. At each age, the mortality rate determines the deaths and the survivors passing to the next age, and this is repeated across all ages. Additional columns, such as life expectancy, are computed from the survivors. The result tabulates the cohort's mortality experience under the observed rates.
Source: Chiang 1984
How are life tables used in health economics?
In health economics, life tables provide the background, all-cause mortality applied to modelled patients, giving age-specific probabilities of death from population data. They supply the general mortality that patients face regardless of the disease modelled, onto which excess disease-specific mortality is added. Life tables also yield life expectancy, used in outcome measures. Because they capture how mortality rises with age, life tables are important for representing survival accurately in models with long horizons.
Source: Chiang 1984
What is the difference between a cohort and a period life table?
A cohort life table follows an actual birth cohort through their lives, using the mortality rates each experienced at successive ages over time, so it requires data spanning the cohort's lifespan. A period life table applies the mortality rates observed in a single period across all ages to a hypothetical cohort, giving a snapshot of current mortality conditions. Period life tables are more commonly used, since they reflect present rates without waiting for a cohort to age, though they assume current rates persist.
Source: Chiang 1984
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 9 Oct 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EM-MP-022
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