Concept Architecture
Concept
Theoretically, Excess Hazard is the additional instantaneous risk of an event attributable to a specific disease or condition beyond the underlying risk experienced by the general population. It is a fundamental concept in relative survival analysis and excess mortality modelling, allowing disease-specific mortality to be estimated without requiring accurate cause-of-death information. In health economics, excess hazard is used to estimate disease-related mortality, extrapolate long-term survival and inform cost-effectiveness models.
Mathematically, excess hazard is represented as the difference between the total observed hazard and the expected background hazard derived from population life tables. This framework decomposes overall mortality into background mortality and disease-specific mortality, enabling estimation of the hazard directly attributable to the disease under investigation.
In practice, excess hazard is estimated using relative survival models that combine patient-level survival data with age-, sex- and calendar-specific population mortality rates. It is widely applied in oncology, rare diseases and chronic disease modelling to estimate long-term survival, project lifetime health outcomes and support health technology assessment.
Purpose
Used to quantify disease-specific mortality beyond background population risk, estimate relative survival, improve long-term survival extrapolation and provide mortality inputs for health economic evaluation.
Mathematical Formulae
Primary Formula
h?(t) = h?????(t) ? h?(t)
where:
- h?(t) = excess hazard
- h?????(t) = observed total hazard
- h?(t) = background hazard
Supporting Formulae
Total hazard:
h?????(t) = h?(t) + h?(t)
Relative survival:
RS(t) = S???(t) � S???(t)
where:
- RS(t) = relative survival
- S???(t) = observed survival
- S???(t) = expected survival from the general population
Related Mathematical Methods
- Relative survival modelling
- Excess hazard modelling
- Flexible parametric survival models
- Cure models
- Parametric survival modelling
- Maximum likelihood estimation
Example
Patients with a particular cancer have an observed annual hazard of 0.090. Age- and sex-matched life tables indicate a background annual hazard of 0.025.
Excess hazard:
h? = 0.090 ? 0.025 = 0.065
The disease therefore contributes an additional annual hazard of 6.5% beyond normal population mortality.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Subtraction | =B2-C2 | Calculate excess hazard by subtracting background hazard from observed hazard. |
| XLOOKUP | =XLOOKUP(A2,LifeTable[Age],LifeTable[Hazard]) | Retrieve background hazards from population life tables. |
| EXP | =EXP(-B2*A2) | Estimate survival probability from the fitted excess hazard model. |
VBA (Optional)
Automate calculation of excess hazards by combining observed survival data with population life tables and generate inputs for relative survival models.
Sources
- Dickman PW, Coviello E. Estimating and Modelling Relative Survival. The Stata Journal.
- Lambert PC, Royston P. Further Development of Flexible Parametric Models for Survival Analysis. The Stata Journal.
- Nelson CP, Lambert PC, Squire IB, Jones DR. Flexible Parametric Models for Relative Survival. Statistics in Medicine.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
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 excess hazard?
The additional death risk attributable specifically to the disease studied, the difference between total observed hazard and the background hazard in a comparable population.
Source: Latimer 2013
How does excess hazard separate disease risk from ordinary risk?
Excess hazard is found by subtracting the background mortality expected in a matched general population from the total mortality observed in the diseased group, leaving the risk attributable to the disease itself. This separation is useful when the cause of each death is not reliably recorded, since it needs only overall mortality and population life tables rather than accurate cause-of-death coding. The survival implied by the excess hazard alone is known as relative survival. It isolates the disease's toll without cause data. Rutherford and colleagues (2015) describe this approach.
Source: Rutherford et al. 2015
How is excess hazard calculated?
Excess hazard is calculated as the total hazard observed in the diseased population minus the background hazard expected in a comparable general population, matched for factors such as age and sex. The remainder is the hazard attributable to the disease. This decomposition, central to relative survival, estimates disease-related mortality without needing cause-of-death information, since it compares the observed mortality with that expected from background rates, attributing the excess to the condition.
Source: Latimer 2013
How does excess hazard relate to background hazard?
Excess hazard and background hazard together make up the total hazard for a diseased individual: background hazard is the general risk of death unrelated to the disease, applying to everyone, and excess hazard is the additional risk the disease adds. Total hazard is the sum of the two. In modelling, background hazard is taken from population life tables and excess hazard estimated or modelled for the disease, so that survival reflects both the general and the disease-specific mortality.
Source: Chiang 1984
Why is excess hazard useful in survival modelling?
Excess hazard is useful because it isolates the disease-related mortality, allowing survival attributable to the condition to be estimated and extrapolated separately from background mortality, which is important over long horizons where general mortality dominates. Modelling excess hazard, added to background mortality from life tables, keeps long-term survival plausible and captures the disease's specific contribution. It also avoids reliance on cause-of-death coding, since it is derived by comparison with expected background rates, making it valuable in relative survival analysis and extrapolation.
Source: Latimer 2013
What is relative survival and how does it use excess hazard?
Relative survival is the ratio of the observed survival in a diseased population to the survival expected in a comparable general population, and it corresponds to survival governed by the excess hazard. It measures survival attributable to the disease by comparing observed with expected mortality, without needing cause-of-death information. The excess hazard is the hazard underlying relative survival, so modelling excess hazard produces relative survival estimates. This framework is widely used in population-based cancer survival and in extrapolation that separates disease-related from background mortality.
Source: Latimer 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 20 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/excess-hazard
- Term code
- HE-EM-SM-017
Stable URI · Machine-readable · Resolvable · CC BY 4.0