Concept Architecture
Concept
Theoretically, the Life Table Method is a non-parametric survival analysis technique that estimates survival probabilities over predefined time intervals rather than at individual event times. It was developed to analyse time-to-event data when exact event times are unavailable or when observations are naturally grouped into intervals. In health economics, the life table method is used to estimate survival, mortality and transition probabilities that inform decision models, epidemiological studies and health technology assessments.
Mathematically, the life table method divides follow-up into consecutive intervals and estimates the conditional probability of surviving each interval using the number of individuals at risk, the number of events and the number censored within that interval. Overall survival is then obtained by multiplying the interval-specific survival probabilities, producing a stepwise estimate of the survival function.
In practice, the life table method is applied to grouped survival data using actuarial life tables or interval-based follow-up data. It is widely used in demographic analyses, epidemiology and health economics when exact event times are unavailable or unnecessary. Although the Kaplan-Meier method is preferred when precise event times are known, the life table method remains valuable for analysing interval-based survival data and estimating long-term outcomes.
Purpose
Used to estimate survival probabilities from interval-based time-to-event data, evaluate mortality patterns and generate survival estimates for epidemiological studies and health economic evaluation.
Mathematical Formulae
Primary Formula
p? = 1 ? d? / (n? ? w? / 2)
where:
- p? = conditional probability of surviving interval i
- d? = number of events during interval i
- n? = number at risk at the start of interval i
- w? = number censored during interval i
Supporting Formulae
Cumulative survival:
?(t) = ?p?
Interval probability of failure:
q? = 1 ? p?
Related Mathematical Methods
- Kaplan-Meier estimator
- Survival analysis
- Actuarial life tables
- Nelson-Aalen estimator
- Parametric survival modelling
- Mortality analysis
Example
A population-based study follows patients annually for five years. During the first year, 1,000 patients are at risk, 80 die and 40 are censored. The conditional survival probability for the first interval is:
p? = 1 ? 80 � (1000 ? 40 � 2) = 1 ? 80 � 980 = 0.918
This interval survival estimate is multiplied by those from subsequent years to estimate cumulative survival, which is then used to inform a cost-effectiveness model.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =1-(Deaths/(AtRisk-Censored/2)) | Calculate interval-specific survival probabilities. |
| PRODUCT | =PRODUCT(E$2:E2) | Calculate cumulative survival across intervals. |
| SUM | =SUM(C2:C20) | Calculate the total number of observed events. |
| COUNTIFS | =COUNTIFS(TimeRange,">="&A2,TimeRange,"<"&A3) | Count events occurring within each life table interval. |
VBA (Optional)
Automate construction of actuarial life tables, calculation of interval survival probabilities and generation of cumulative survival estimates for health economic analyses.
Sources
- Cutler SJ, Ederer F. Maximum Utilization of the Life Table Method in Analysing Survival.
- Klein JP, Moeschberger ML. Survival Analysis: Techniques for Censored and Truncated Data.
- Collett D. Modelling Survival Data in Medical Research.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
NICE DSU Technical Support Document 14: Survival analysis for economic evaluations alongside clinical trials – extrapolation with patient-level data — Nicholas R. Latimer, TSD 14 ed., 2013 (NICE Decision Support Unit (University of Sheffield))
The reference guidance on survival analysis for economic evaluation: fitting standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal) to censored trial data and extrapolating to estimate lifetime survival benefit, with a process guide for model selection and justification.
Frequently Asked Questions (6)
What is the life-table method?
A survival technique dividing follow-up into fixed intervals and calculating the proportion of at-risk patients surviving each, accounting for censoring.
Source: Cutler & Ederer 1958
Why does the life-table method assume censoring is spread across each interval?
Because the life-table method works with fixed intervals rather than exact event times, it cannot know when within an interval a censored patient was lost, so it conventionally assumes such losses are spread evenly through the interval. On this assumption a censored patient is treated as being at risk for, on average, half the interval, which adjusts the denominator used to estimate survival in that period. This handling lets grouped data be analysed without exact times. The assumption is reasonable when intervals are short. Collett (2015) describes it.
Source: Collett 2015
How does the life-table method work?
The life-table method works by dividing follow-up into fixed intervals and, for each, estimating the probability of surviving it as one minus the proportion of those at risk who have the event, where the number at risk is adjusted for censoring by assuming those lost during the interval were at risk for, on average, half of it. Multiplying these interval survival probabilities across intervals gives cumulative survival, producing a survival curve from grouped data with censoring accounted for.
Source: Cutler & Ederer 1958
How does the life-table method handle censoring?
The life-table method handles censoring within each interval by adjusting the number at risk: individuals lost to follow-up during an interval are assumed to have been at risk for, on average, half the interval, so the effective number at risk is those entering the interval minus half those censored in it. This accounts for their partial follow-up, allowing survival to be estimated from grouped data without discarding censored individuals, so that the interval survival probabilities reflect the at-risk population correctly.
Source: Cutler & Ederer 1958
How does the life-table method differ from Kaplan-Meier?
The life-table method estimates survival over fixed intervals, adjusting the number at risk for censoring within each, and suits grouped data, whereas the Kaplan-Meier method uses exact event times, recalculating survival at each event, and suits individual-level data. Kaplan-Meier steps down at each event time, while the life-table method gives survival by interval. Kaplan-Meier is preferred when exact times are available, while the life-table method is used for interval or grouped data where exact times are not recorded.
Source: Chiang 1984
Where is the life-table method used?
The life-table method is used to estimate survival when data are grouped into time intervals rather than recorded as exact event times, such as in older studies, large datasets, or where follow-up is reported periodically. It produces a survival curve accounting for censoring within intervals, and it underlies demographic and actuarial life tables. Although the Kaplan-Meier method is preferred for individual-level data with exact times, the life-table method remains appropriate and convenient for interval or grouped survival data.
Source: Cutler & Ederer 1958
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 21 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/life-table-method
- Term code
- HE-EM-SM-044
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