Concept Architecture
Concept
Theoretically, a Cure Model is a survival model that assumes a proportion of individuals become permanently free from the event of interest, while the remaining individuals continue to experience disease-related risk. It is founded on survival analysis, mixture modelling and long-term survival theory and exists to represent populations in which a genuine cure is possible. In health economics, cure models are used to estimate lifetime survival for interventions that achieve durable remission or cure, particularly in oncology and regenerative medicine.
Mathematically, cure models partition the study population into cured and uncured subgroups. Overall survival is represented as a weighted combination of the cure proportion and the survival distribution of uncured individuals. Model parameters are estimated simultaneously using maximum likelihood methods, allowing estimation of both the cure proportion and the survival function for patients who remain at risk.
In practice, cure models are estimated using long-term follow-up data from clinical trials, disease registries and observational studies. They are routinely applied in health technology assessment and cost-effectiveness analysis to extrapolate survival beyond observed follow-up, estimate lifetime QALYs and project long-term healthcare costs.
Purpose
Used to estimate long-term survival when a proportion of patients are effectively cured, improve survival extrapolation and generate lifetime estimates for health economic evaluation and health technology assessment.
Mathematical Formulae
Primary Formula
S(t) = � + (1 ? �) ? S?(t)
where:
- � = cure proportion
- S(t) = overall survival
- S?(t) = survival function for uncured individuals
Supporting Formulae
Long-term survival:
lim??� S(t) = �
Logistic model for the cure proportion:
� = exp(X?) � (1 + exp(X?))
Likelihood function:
L = ?S(t?)???? ? f(t?)??
where:
- �? = event indicator
- f(t?) = probability density function
- S(t?) = survival function
Related Mathematical Methods
- Mixture cure models
- Non-mixture cure models
- Parametric survival modelling
- Maximum likelihood estimation
- Relative survival modelling
- Flexible parametric survival models
Example
A health technology assessment evaluates a CAR-T therapy using a cure model. The model estimates that 45% of patients achieve long-term remission and thereafter experience background mortality, while the remaining 55% follow a Weibull survival distribution. The resulting survival projections are used to estimate lifetime QALYs and incremental cost-effectiveness.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Logistic Function | =EXP(B2)/(1+EXP(B2)) | Estimate the cure proportion from model coefficients. |
| Survival Function | =C2+(1-C2)*D2 | Calculate overall survival using a cure model. |
| EXP | =EXP(-(A2/$B$1)^$C$1) | Calculate Weibull survival for the uncured subgroup. |
VBA (Optional)
Automate estimation of cure model outputs and generate lifetime survival projections for economic evaluation.
Sources
- Boag JW. Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy. Journal of the Royal Statistical Society Series B. 1949;11(1):15?53.
- Berkson J, Gage RP. Survival Curve for Cancer Patients Following Treatment. Journal of the American Statistical Association. 1952;47:501?515.
- Lambert PC, Thompson JR, Weston CL, Dickman PW. Estimating and Modelling the Cure Fraction in Population-Based Cancer Survival Analysis. Biostatistics.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
2
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.
NICE DSU Technical Support Document 19: Partitioned survival analysis as a decision modelling tool — Woods, Sideris, Palmer, Latimer & Soares, TSD 19 ed., 2017 (NICE Decision Support Unit (University of Sheffield))
Guidance on the partitioned survival (area-under-the-curve) modelling approach widely used in oncology cost-effectiveness analysis, contrasting it with state-transition models and setting out its assumptions, strengths and limitations.
Frequently Asked Questions (6)
What is a cure model?
A survival model assuming a defined proportion of a population will never experience the event of interest, distinguishing this cured group from those still at risk.
Source: Boag 1949
What assumption defines a cure model?
A cure model is defined by the assumption that some fraction of patients will never experience the event of interest, no matter how long they are followed, and so are effectively cured. This differs from standard survival models, in which everyone eventually experiences the event given enough time. Building in a permanently event-free group changes the shape of projected survival, allowing a curve that levels off rather than declining to zero. The assumption must be clinically justified, since not every disease admits a cure. Lambert and colleagues (2007) discuss this.
Source: Lambert et al. 2007
How is a cure model structured?
A cure model is typically structured as a mixture of a cured fraction, who never experience the disease event, and an uncured fraction, whose time to event follows a survival distribution. The model estimates the proportion cured and the survival of the uncured. This mixture produces overall survival that declines as the uncured have events and then plateaus at the cured fraction. Non-mixture cure models are an alternative formulation, but both represent a subgroup that will not experience the event.
Source: Boag 1949
When are cure models used?
Cure models are used when a proportion of patients appear cured after treatment, so that disease-specific survival plateaus above zero and long-term survivors are seen, as in some cancers. Evidence of a plateau in the survival curve and of patients with no further events supports their use. They are important for extrapolation, since assuming cure versus eventual failure for all greatly affects long-term survival estimates. Where no cure occurs and all remain at risk, a standard survival model is used instead.
Source: Latimer 2013
Why do cure models matter for survival extrapolation?
Cure models matter for extrapolation because whether a fraction of patients are cured strongly affects projected long-term and mean survival: a cure model implies a survival plateau and long life for the cured, while a standard model implies eventual failure for all, giving very different tails. Because extrapolated survival drives cost-effectiveness in potentially curable conditions, using or omitting a cure component can markedly change the estimated benefit, so the choice is based on evidence of long-term cure and its uncertainty examined.
Source: Latimer 2013
What are the limitations of cure models?
Cure models require long follow-up to observe a plateau and confirm cure, so with short data the cure fraction is uncertain and may be confounded with slow progression. Estimates depend on the distribution assumed for the uncured and on background mortality, and whether cure genuinely occurs may be clinically debated. Overstating cure can substantially overstate survival benefit. These limitations mean cure models are applied where cure is clinically plausible and supported by data, with careful attention to the uncertainty in the cured fraction.
Source: Boag 1949
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 20 Oct 2025
Content version: 1.0.0
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- Persistent URI
- https://healtheconomics.wiki/concept/cure-model
- Term code
- HE-EM-SM-013
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