Concept Architecture
Concept
Theoretically, Relative Survival is a population-based survival measure that estimates survival attributable to a disease by comparing the observed survival of patients with the survival expected in a comparable disease-free population. It represents disease-specific survival without requiring reliable cause-of-death information and is founded on excess mortality theory. Relative survival is widely used in cancer epidemiology and health economics to quantify the survival impact of disease independently of background mortality.
Mathematically, relative survival is represented as the ratio of observed survival to expected survival. Expected survival is obtained from general population life tables matched for characteristics such as age, sex and calendar year. The framework separates mortality attributable to the disease from mortality expected due to other causes through excess hazard modelling or non-parametric estimation.
In practice, relative survival is estimated by calculating observed survival using methods such as the Kaplan?Meier estimator and expected survival using life-table methods including the Ederer I, Ederer II or Hakulinen approaches. It is routinely applied in cancer registries, health technology assessment and survival modelling to estimate disease-specific outcomes and extrapolate long-term survival.
Purpose
Used to estimate disease-specific survival independently of cause-of-death information, quantify excess mortality, compare survival across populations and provide survival inputs for health economic evaluation.
Mathematical Formulae
Primary Formula
RS(t) = S?(t) / S?(t)
Where:
RS(t) = relative survival at time t
S?(t) = observed survival
S?(t) = expected survival in the comparable general population
Supporting Formulae
Observed hazard:
h?(t) = h?(t) + h?(t)
Where:
h?(t) = observed hazard
h?(t) = expected population hazard
h?(t) = excess hazard attributable to the disease
Excess hazard:
h?(t) = h?(t) ? h?(t)
Related Mathematical Methods
- Kaplan?Meier estimation
- Life-table estimation
- Excess hazard modelling
- Nelson?Aalen estimation
- Flexible parametric survival modelling
- Net survival estimation
Example
A cohort of patients with colorectal cancer has an observed five-year survival of 0.60. The expected five-year survival for an age- and sex-matched general population is 0.80.
Relative survival is calculated as:
RS = 0.60 � 0.80 = 0.75
The estimated relative survival is 75%, indicating that patients experience 75% of the survival expected in the absence of disease-related excess mortality.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
/ | =B2/C2 | Calculates relative survival as observed survival divided by expected survival. |
| LOOKUP | =XLOOKUP(A2,LifeTable[Age],LifeTable[ExpectedSurvival]) | Retrieves expected survival from population life tables. |
| IF | =IF(C2>0,B2/C2,"") | Prevents division by zero when calculating relative survival. |
| INDEX/MATCH | =INDEX(Expected,MATCH(A2,Age,0)) | Matches expected survival by demographic characteristics. |
VBA (Optional)
VBA can automate linkage to population life tables and calculate relative survival estimates for multiple patient cohorts.
Sources
Dickman PW, Coviello E. Estimating and modelling relative survival. The Stata Journal. 2015.
Pohar Perme M, Stare J, Est�ve J. On estimation in relative survival. Biometrics. 2012;68:113?120.
Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
NICE. Health Technology Evaluations: The Manual. National Institute for Health and Care Excellence; 2022.
Related Concepts (2)
Library
Publications
1
NICE DSU Technical Support Document 21: Flexible methods for survival analysis — Rutherford, Lambert, Sweeting, Pennington, Crowther, Abrams & Latimer, TSD 21 ed., 2020 (NICE Decision Support Unit (University of Sheffield))
Guidance extending standard survival analysis to flexible parametric methods — spline-based models, fractional polynomials, mixture and cure models, and relative-survival approaches — for capturing complex hazard functions in economic evaluation.
Frequently Asked Questions (6)
What is relative survival?
A survival measure comparing observed survival in a population to expected survival in a comparable general population, without needing cause-of-death data.
Source: Ederer, Axtell & Cutler 1961
Why is relative survival used in cancer registries?
Cancer registries follow large populations whose individual causes of death are often unrecorded or unreliable, yet they need to measure how much a cancer shortens life. Relative survival meets this by dividing the survival actually observed in the patient group by the survival expected in a matched general population, so the ratio reflects the excess mortality from the cancer without any death needing to be classified by cause. Its independence from cause-of-death coding is what makes it the registry standard. Rutherford and colleagues (2015) describe this use.
Source: Rutherford et al. 2015
How is relative survival calculated?
Relative survival is calculated as the ratio of the observed survival in the diseased population to the expected survival of a comparable group from the general population, matched for factors such as age, sex, and calendar period, with expected survival taken from population life tables. Dividing observed by expected survival gives the proportion surviving beyond what background mortality alone would produce, attributing the shortfall to the disease. This yields relative survival without requiring the cause of each death to be known.
Source: Ederer, Axtell & Cutler 1961
Why is relative survival useful?
Relative survival is useful because it isolates disease-related survival without needing cause-of-death information, which is often missing or unreliable in population data, and because it removes the effect of differing background mortality, making survival comparable across populations, periods, and age groups. This is valuable for comparing cancer survival between countries or over time, where general mortality differs. By contrasting observed with expected survival, relative survival provides a measure of disease-specific outcome not distorted by other-cause mortality or dependent on cause coding.
Source: Latimer 2013
How does relative survival avoid needing cause-of-death data?
Relative survival avoids needing cause-of-death data by comparing observed survival in the diseased population with the survival expected from general population mortality, rather than counting deaths by cause. The difference between observed and expected survival is attributed to the disease, so disease-specific mortality is inferred from the comparison with background rates rather than from classifying each death. This is advantageous where cause of death is unavailable or unreliable, allowing disease survival to be estimated from observed all-cause survival and population life tables.
Source: Ederer, Axtell & Cutler 1961
What are the limitations of relative survival?
Relative survival relies on the accuracy of the general population life tables used for expected survival and on the assumption that the diseased population's other-cause mortality matches the general population's, which may not hold if patients differ in other risks. It estimates a net, somewhat hypothetical measure of disease survival rather than the actual probability of dying from the disease amid competing causes. Its interpretation and estimation can be sensitive to method. These limitations mean relative survival is used as a comparative measure with its assumptions in mind.
Source: Latimer 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 23 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/relative-survival
- Term code
- HE-EM-SM-069
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