Concept Architecture
Concept
Theoretically, the Relative Survival Model is a statistical survival model that estimates disease-specific survival by separating mortality attributable to a disease from expected background mortality in the general population. It is founded on excess hazard theory and population survival modelling, allowing estimation of survival without requiring accurate cause-of-death information. Relative survival models are widely applied in cancer epidemiology and health economics to quantify disease-attributable mortality and extrapolate long-term survival.
Mathematically, a relative survival model represents the observed hazard as the sum of the expected population hazard and the excess hazard associated with the disease. The expected hazard is obtained from population life tables matched on characteristics such as age, sex and calendar year, while the excess hazard is estimated using regression or flexible parametric modelling techniques. The resulting framework permits estimation of relative survival, excess mortality and net survival.
In practice, relative survival models are estimated using registry or clinical trial data together with national life tables. Flexible parametric, Poisson and excess hazard regression models are commonly employed to estimate disease-specific survival, evaluate prognostic factors and generate long-term survival projections for health technology assessment and economic evaluation.
Purpose
Used to estimate disease-specific survival independently of cause-of-death information, quantify excess mortality, extrapolate long-term survival and generate survival estimates for health economic decision models.
Mathematical Formulae
Primary Formula
h?(t) = h?(t) + h?(t)
Where:
h?(t) = observed hazard
h?(t) = expected population hazard
h?(t) = excess hazard attributable to the disease
Supporting Formulae
Relative survival:
RS(t) = S?(t) / S?(t)
Excess hazard:
h?(t) = h?(t) ? h?(t)
Related Mathematical Methods
- Excess hazard regression
- Relative survival estimation
- Flexible parametric survival modelling
- Royston?Parmar modelling
- Poisson regression
- Net survival estimation
Example
A five-year cancer registry study reports an observed survival of 0.55. Population life tables indicate an expected survival of 0.79 for individuals of the same age and sex.
Relative survival is:
RS = 0.55 � 0.79 = 0.696
The model estimates that approximately 69.6% of expected survival remains after accounting for excess mortality associated with the disease.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
/ | =B2/C2 | Calculates relative survival from observed and expected survival. |
| XLOOKUP | =XLOOKUP(A2,LifeTable[Age],LifeTable[ExpectedHazard]) | Retrieves expected mortality from population life tables. |
| IF | =IF(C2>0,B2/C2,"") | Prevents division by zero when calculating relative survival. |
| EXP | =EXP(-D2) | Converts cumulative hazards to survival probabilities where appropriate. |
VBA (Optional)
VBA can automate linkage to national life tables, estimate excess hazards and generate relative survival summaries 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.
Nelson CP, Lambert PC, Squire IB, Jones DR. Flexible parametric models for relative survival. Statistics in Medicine. 2007.
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
Tools & Resources
1
survHE — Survival Analysis for Health Economic Evaluation (R package) — Gianluca Baio, R package ed., 2023 (CRAN)
An R package for fitting and comparing parametric survival models for health economic evaluation, including Bayesian estimation, and for extrapolating time-to-event data to inform cost-effectiveness models.
Software (R package)View source →
Frequently Asked Questions (6)
What is a relative survival model?
A statistical model estimating disease-specific survival by comparing observed survival against expected general population survival, without individual cause-of-death data.
Source: Ederer, Axtell & Cutler 1961
How does a relative survival model separate disease and background mortality?
A relative survival model treats the total mortality observed in a patient group as the sum of two parts, the background rate expected in a matched general population, taken from life tables, and an excess rate attributable to the disease. By fixing the background component from external data, the model estimates the excess, disease-related mortality without needing to know the cause of any individual death. This decomposition is what lets it isolate the disease's effect. It assumes the chosen life tables represent the patients' background risk. Rutherford and colleagues (2015) describe it.
Source: Rutherford et al. 2015
How does a relative survival model work?
A relative survival model works by expressing the total hazard as the sum of a known background hazard, taken from population life tables matched for age, sex, and period, and an excess hazard attributable to the disease, which the model estimates. By modelling the excess hazard, it estimates relative, or net, survival, the survival due to the disease alone. This uses observed all-cause survival and expected background mortality, so disease-specific survival is estimated without classifying deaths by cause.
Source: Ederer, Axtell & Cutler 1961
Why use a relative survival model?
A relative survival model is used to estimate disease-specific survival when cause-of-death data are unavailable or unreliable, as often in population-based studies, and to remove the effect of differing background mortality so that survival is comparable across populations and over time. By modelling the excess hazard against background rates, it isolates the disease's contribution to mortality. This makes relative survival models valuable for cancer registry analyses and for comparing survival where cause coding cannot be relied upon or background mortality differs.
Source: Latimer 2013
What does a relative survival model estimate?
A relative survival model estimates the excess hazard due to the disease and, from it, relative or net survival, the survival a population would have if the disease were the only cause of death. It can also estimate how the excess hazard depends on covariates, giving disease-specific effects. By separating background and excess mortality, the model quantifies the disease's contribution to mortality and its survival impact, without needing cause-of-death information, providing measures comparable across populations and periods.
Source: Ederer, Axtell & Cutler 1961
What are the assumptions of relative survival models?
Relative survival models assume that the background mortality from the general population life tables accurately represents the other-cause mortality of the diseased population, so that any excess is attributable to the disease, and that the life tables are appropriately matched. If the diseased population has different other-cause risks, this assumption fails and estimates may be biased. The models also depend on the excess hazard being correctly specified. These assumptions mean relative survival estimates are interpreted with attention to the suitability of the background rates.
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
- Term code
- HE-EM-SM-070
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