Concept Architecture
Concept
Theoretically, Background Hazard is the underlying hazard of an event occurring in a reference population independently of the condition or intervention under study. It is a fundamental concept in survival analysis and epidemiology, representing the baseline risk arising from general population mortality or disease incidence. In health economics, background hazard is incorporated into survival models to distinguish disease-specific risk from the underlying risk experienced by the general population.
Mathematically, background hazard is represented as the hazard function for the reference population and is commonly combined with excess disease hazard within additive or relative survival models. The mathematical framework enables estimation of total event risk while accounting for age-, sex- and calendar-specific background mortality obtained from population life tables.
In practice, background hazard is estimated from national life tables, mortality registries or population statistics and incorporated into health economic models, survival extrapolations and decision models. It is routinely used when modelling long-term survival beyond clinical trial follow-up and when estimating life expectancy, QALYs and disease burden.
Purpose
Used to represent underlying population risk, adjust survival estimates for general population mortality, support relative survival modelling and improve long-term extrapolation in health economic evaluations.
Mathematical Formulae
Primary Formula
h(t) = h?(t)
Supporting Formulae
Total hazard under an additive hazards framework:
h?????(t) = h?(t) + h?(t)
Survival function:
S(t) = exp(???? h(u) du)
where:
- h?(t) or h?(t) = background hazard
- h?(t) = excess disease hazard
- h?????(t) = total hazard
- S(t) = survival probability
Related Mathematical Methods
- Survival analysis
- Relative survival modelling
- Excess hazard modelling
- Parametric survival modelling
- Life table analysis
Example
A 70-year-old individual has an annual background mortality hazard of 0.030 based on national life tables. A disease contributes an excess annual hazard of 0.050.
Total hazard:
h????? = 0.030 + 0.050 = 0.080
The patient's annual hazard is therefore 8%, comprising both background and disease-specific risk.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Addition | =B2+C2 | Calculate total hazard by combining background and excess hazards. |
| EXP | =EXP(-B2*C2) | Estimate survival probability assuming a constant hazard over a time interval. |
| XLOOKUP | =XLOOKUP(A2,LifeTable[Age],LifeTable[Hazard]) | Retrieve age-specific background hazards from life tables. |
VBA (Optional)
Automate retrieval of age- and sex-specific background hazards from life tables and apply them across cohort survival models.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Collett D. Modelling Survival Data in Medical Research. CRC Press.
- NICE. Health Technology Evaluation Manual.
- Dickman PW, Coviello E. Estimating and modelling relative survival.
- ISPOR Good Practice Reports.
Related Concepts (2)
Library
Publications
1
NICE DSU Technical Support Document 15: Cost-effectiveness modelling using patient-level simulation — Davis, Stevenson, Tappenden & Wailoo, TSD 15 ed., 2014 (NICE Decision Support Unit (University of Sheffield))
Guidance on individual patient-level (microsimulation) cost-effectiveness modelling — when to use it in preference to cohort models, how to structure it, and how to handle the associated computational and uncertainty challenges.
Frequently Asked Questions (6)
What is background hazard?
The rate of death from causes unrelated to the disease under study, applied to represent risk a patient would face regardless of the condition.
Source: Latimer 2013
What would omitting background hazard do to a survival estimate?
If an extrapolated survival curve reflected only the disease's own risk, it would let patients live far longer than people of their age actually do, because everyone also faces the ordinary risk of dying from unrelated causes. Adding a background hazard, taken from general population mortality, prevents this by ensuring modelled survival never exceeds what the wider population experiences. Without it, long-term projections overstate life expectancy and inflate a treatment's estimated benefit. It anchors the tail to reality. Latimer (2013) recommends its inclusion.
Source: Latimer 2013
Why is background hazard included in survival extrapolation?
Background hazard is included in survival extrapolation because, especially over long horizons, patients face the general population's rising mortality regardless of the disease, and extrapolated disease survival curves may otherwise imply implausibly long life by ignoring this. Adding background hazard ensures modelled survival does not exceed what general mortality allows, so the extrapolation remains plausible. It anchors long-term survival to population mortality, preventing the fitted curve from projecting survival beyond what age-related death from other causes would permit.
Source: Latimer 2013
How is background hazard applied?
Background hazard is applied by taking age- and sex-specific mortality rates from population life tables and imposing them as a minimum hazard on modelled patients, so that total mortality is at least the background rate, with disease-specific excess hazard added for affected patients. As the cohort ages, the background hazard rises, giving a time-varying risk. This ensures that extrapolated survival reflects both the disease and the general mortality patients face, keeping long-term projections consistent with population mortality.
Source: Chiang 1984
How does background hazard relate to disease-specific hazard?
Background hazard and disease-specific, or excess, hazard together make up the total hazard for affected patients: background hazard is the risk from causes unrelated to the disease, applying to everyone, while disease-specific hazard is the additional risk the condition adds. In a model, the two are combined, so patients with the disease face both. Separating them allows general mortality to be applied to all patients and the disease's excess added to those affected, capturing total mortality correctly in survival modelling.
Source: Latimer 2013
Why does background hazard matter for long-term survival estimates?
Background hazard matters for long-term survival estimates because over extended horizons the general risk of death rises with age and increasingly dominates, so ignoring it can make extrapolated survival implausibly long. Imposing background hazard ensures the estimated survival does not exceed what age-related mortality permits, keeping mean survival and life-year estimates realistic. Because survival benefits and cost-effectiveness depend on long-term survival, including background hazard is important for plausible extrapolation, particularly in models with lifetime horizons where general mortality strongly shapes the tail.
Source: Latimer 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 17 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/background-hazard
- Term code
- HE-EM-SM-003
Stable URI · Machine-readable · Resolvable · CC BY 4.0