Concept Architecture
Concept
Theoretically, a Cure Rate Model is a survival model that assumes a proportion of individuals are 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 rate models are used to estimate lifetime survival for interventions that achieve durable remission or cure, particularly in oncology and regenerative medicine.
Mathematically, cure rate 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 rate 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 gene therapy using a cure rate model. The model estimates that 42% of patients achieve permanent remission and thereafter experience only background mortality, while the remaining 58% follow a Weibull survival distribution. These estimates are used to project lifetime QALYs and costs.
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 rate model. |
| EXP | =EXP(-(A2/$B$1)^$C$1) | Calculate Weibull survival for the uncured subgroup. |
VBA (Optional)
Automate estimation of cure rate model outputs and generate lifetime survival projections for health economic decision models.
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 14: Survival analysis for economic evaluations alongside clinical trials – extrapolation with patient-level data — Nicholas R. Latimer, TSD 14 ed., 2013 (NICE Decision Support Unit (University of Sheffield))
The reference guidance on survival analysis for economic evaluation: fitting standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal) to censored trial data and extrapolating to estimate lifetime survival benefit, with a process guide for model selection and justification.
Frequently Asked Questions (6)
What is a cure rate model?
A statistical model estimating both the proportion of a population considered cured and the survival distribution governing the remaining uncured population.
Source: Boag 1949
What two quantities does a cure rate model produce?
A cure rate model yields two linked results, the proportion of the population considered cured, and the survival distribution describing how long the uncured take to experience the event. Together these determine the whole projected survival curve, its long-term plateau set by the cure proportion and its earlier decline set by the uncured distribution. Reporting both makes explicit what fraction is expected to be free of the disease and what awaits the rest. The two are estimated jointly from the data. Lambert and colleagues (2007) describe this output.
Source: Lambert et al. 2007
What does a cure rate model estimate?
A cure rate model estimates two things: the cure rate, the proportion of the population who will never experience the disease event and are effectively cured, and the survival distribution of the uncured, describing the timing of the event among those still at risk. From these, overall survival is obtained as a mixture. Estimating both allows the model to quantify how many patients are cured and how quickly the uncured have events, together determining the survival curve and its long-term plateau.
Source: Boag 1949
How does a cure rate model differ from a standard survival model?
A cure rate model differs from a standard survival model by including a proportion of patients who never experience the event, whereas a standard model assumes all individuals eventually have it, so survival declines to zero. The cure rate model produces a survival plateau at the cure rate, while a standard model does not. This allows the cure rate model to represent long-term survivors and curable conditions, capturing patterns that standard distributions, implying eventual failure for everyone, cannot reproduce.
Source: Latimer 2013
How is the cure rate estimated?
The cure rate is estimated by fitting the cure rate model to survival data, which requires sufficient follow-up to observe a plateau in the survival curve indicating the cured fraction. The model separates the influence of the cured, who contribute the plateau, from the uncured, whose events shape the earlier decline, estimating the cure rate and the uncured survival together. Because distinguishing cure from slow progression needs long follow-up, the cure rate estimate is more reliable with mature data and uncertain with short observation.
Source: Boag 1949
Why does the cure rate affect long-term survival estimates?
The cure rate affects long-term survival estimates because it determines the level at which survival plateaus: a higher cure rate implies more long-term survivors and greater mean survival, while a lower rate implies fewer. Since much of mean survival in curable conditions comes from the cured fraction living long, the cure rate strongly influences the estimated survival benefit and hence cost-effectiveness. This makes accurate estimation of the cure rate important, and its uncertainty, especially with limited follow-up, a key consideration in extrapolation.
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
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- Persistent URI
- https://healtheconomics.wiki/concept/cure-rate-model
- Term code
- HE-EM-SM-014
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