Concept Architecture
Concept
Theoretically, the Cure Fraction is the proportion of individuals within a population who are considered permanently free from the event of interest and therefore experience the same long-term risk as the general population. It is a fundamental concept in mixture cure modelling and survival analysis, recognising that some patients may be effectively cured rather than remaining indefinitely at risk. In health economics, cure fraction models are used to estimate long-term survival and lifetime benefits for interventions that produce durable treatment responses.
Mathematically, the cure fraction is represented within mixture cure models by partitioning the population into cured and uncured subgroups. Overall survival is expressed as a weighted combination of the survival of uncured individuals and the cured proportion, whose long-term survival approaches that of the background population. The cure fraction parameter is estimated simultaneously with the survival distribution of uncured patients.
In practice, the cure fraction is estimated using long-term follow-up data from clinical trials, registries and observational studies. It is widely applied in oncology and other therapeutic areas where treatments may achieve long-term remission, providing survival estimates for health technology assessment, cost-effectiveness analysis and lifetime decision modelling.
Purpose
Used to estimate the proportion of patients achieving long-term cure, model durable treatment effects and improve long-term survival extrapolation in health economic evaluations.
Mathematical Formulae
Primary Formula
S(t) = � + (1 ? �) ? S?(t)
where:
- � = cure fraction
- S(t) = overall survival function
- S?(t) = survival function for uncured individuals
Supporting Formulae
Long-term survival:
lim??� S(t) = �
Logistic model for estimating the cure fraction:
� = exp(X?) � (1 + exp(X?))
Related Mathematical Methods
- Mixture cure models
- Non-mixture cure models
- Parametric survival modelling
- Maximum likelihood estimation
- Relative survival modelling
Example
A cancer treatment is evaluated using a mixture cure model. The estimated cure fraction is 0.35, indicating that 35% of patients are expected to experience long-term survival comparable to the general population. The remaining 65% continue to follow the estimated disease-specific survival distribution used within the economic model.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Logistic Function | =EXP(B2)/(1+EXP(B2)) | Estimate the cure fraction from a logistic regression coefficient. |
| Survival Function | =C2+(1-C2)*D2 | Calculate overall survival using a mixture cure model. |
| EXP | =EXP(-B2*A2) | Estimate survival for the uncured subgroup under an exponential model. |
VBA (Optional)
Automate calculation of mixture cure model survival projections and lifetime survival estimates for economic evaluations.
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
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 a cure fraction?
The proportion of a population modelled as having no residual risk of the disease-specific event after successful treatment, effectively behaving as cured.
Source: Boag 1949
How is a cure fraction recognised in survival data?
A cure fraction shows up in survival data as a long-term levelling of the survival curve, where a portion of patients pass through the period of risk and then stop experiencing the disease-specific event, their curve flattening rather than continuing to fall. When the flat portion sits above zero and persists, it suggests a group effectively free of further disease risk. Recognising this pattern requires long follow-up, since a plateau cannot be distinguished from a slow decline early on. Othus and colleagues (2012) describe such patterns.
Source: Othus et al. 2012
What is a cure model?
A cure model is a survival model that represents a population as a mixture of a cured fraction, who have no residual risk of the disease-specific event, and an uncured fraction, who remain subject to the usual survival distribution. The model estimates both the proportion cured and the survival of the uncured. This structure suits diseases where a portion of patients are effectively cured after treatment, so that long-term survival plateaus, which standard survival distributions, implying eventual failure for all, cannot capture.
Source: Boag 1949
When are cure models appropriate?
Cure models are appropriate when a proportion of patients appear to be effectively cured after treatment, so that their survival, with respect to the disease, plateaus at a level above zero rather than declining to zero, a pattern seen in some cancers and other conditions with long-term survivors. Evidence of a plateau in the survival curve and of a subgroup with no further disease-specific events supports a cure model. Where all patients remain at risk, a standard survival model without a cure fraction is used instead.
Source: Latimer 2013
Why does the cure fraction matter for extrapolation?
The cure fraction matters for extrapolation because whether a proportion of patients are cured strongly affects long-term survival and hence mean survival estimates: a cure model with a substantial cured fraction implies a survival plateau and long life for the cured, while a standard model implies eventual failure for all. Because extrapolated survival drives cost-effectiveness in conditions with potential cure, using or omitting a cure fraction can markedly change the estimated benefit, so the choice is important and based on evidence of long-term cure.
Source: Latimer 2013
What are the challenges of estimating a cure fraction?
Estimating a cure fraction is challenging because distinguishing genuinely cured patients from those with slow progression requires long follow-up to observe a plateau, and short trials may not provide it, making the cure fraction uncertain. The estimate depends on the survival model assumed for the uncured and on the plausibility of cure, which may be clinically contested. Because the cure fraction strongly affects extrapolated survival, its uncertainty is important, so evidence of cure and sensitivity to the assumption are examined carefully.
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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