Cure Rate Model

Cure Rate Model in Health Technology Assessment

A "cure rate model" is any survival model that lets a share of patients, the cure rate or cure fraction, stop dying from their disease, so that their long-run mortality falls back to that of the general population. The name comes mainly from statistics; health technology assessment (HTA) guidance such as the NICE Decision Support Unit's TSD 21 calls the same models cure models. In an appraisal, the cure fraction and the survival of the uncured together set lifetime mean survival and most of the QALY gain. The choice matters because trials of immunotherapies, CAR T-cell therapies and other potentially curative treatments often end while many patients are still alive, and switching between a cure and a no-cure extrapolation has moved a published cost per QALY by a factor of almost three. The meaning of statistical cure has its own cure model page, and the parameter its own cure fraction page.

What "cure rate model" means in HTA and oncology practice

The phrase is used in the statistical literature on estimating cure rates from survival data; Tsodikov, Ibrahim and Yakovlev, for example, review cure rate estimation with the bounded cumulative hazard model as an alternative to the two-component mixture model. HTA documents call the same models cure models, and the term covers both families described below.

Cure here is a population statement, defined in TSD 21 as the cause-specific hazard falling to zero, so cure models are fitted to cause-specific survival or in an excess mortality (relative survival) framework. Latimer and Rutherford's HTA tutorial states that, for overall survival, every cure model estimates the cure fraction, the proportion who will not die from their disease, and survival for the uncured; for progression-free survival the fraction becomes the proportion who will neither progress nor die.

Mixture and non-mixture models in brief

Two families of cure rate model are in common use, and each has its own page. A mixture cure model treats the population as two latent groups, cured and uncured, and writes survival as a weighted sum of the two. A non-mixture cure model does not split the population; it bounds the cumulative hazard so that survival approaches the cure fraction as time tends to infinity. In the relative survival form, TSD 21 writes the mixture model as

$$S(t) = S^{*}(t)\,\bigl[\pi + (1-\pi)\,S_u(t)\bigr]$$

where $S(t)$ is all-cause survival at time $t$, $S^{*}(t)$ is expected survival in the matched general population, $\pi$ is the cure fraction and $S_u(t)$ is survival among the uncured. The non-mixture model replaces the bracket with $\pi^{F_z(t)}$, where $F_z(t)$ is a cumulative distribution function.

The families often agree on the fraction but differ in interpretation. In Othus and colleagues' analysis of progression-free survival under four Total Therapy regimens for multiple myeloma, Weibull mixture models estimated cured proportions of 10%, 16%, 29% and 60%, and non-mixture models 9%, 11%, 27% and 60%; the mixture model placed Total Therapy 3's gain over Total Therapy 1 in cure (odds ratio 20.23), not in progression-free survival of the uncured (hazard ratio 0.92, not significant).

How the cure assumption drives extrapolation and QALY gains

TSD 21 observes that follow-up is usually very short compared with the extrapolated period, and that survival models typically diverge there, often producing dramatically varying mean survival and cost-effectiveness estimates. A cure rate model fixes the shape of the tail. Once the uncured have died, the remaining hazard is background mortality, so each extra percentage point of cure fraction carries close to a full remaining lifetime into the model's life years and QALYs. The NICE manual (PMG36, section 4.6.25) names cure approaches among the flexible options for extrapolation and asks that the clinical plausibility of the underlying hazard functions be routinely assessed.

Published cases show how much rides on the assumption. In a mixture cure analysis of ipilimumab against gp100 in advanced melanoma, Othus and colleagues found that a conventional analysis gave ipilimumab a mean overall survival 8 months longer, while the cure model attributed the difference to the cured proportion, 21% against 6%; the ICER fell from USD 324,000 to USD 113,000 per QALY. Bullement and colleagues revisited NICE appraisal TA319 of ipilimumab with a later data cut. Fitted to 3-year data, only the appraisal's piecewise model and two mixture cure models predicted 5-year survival in the ipilimumab arm close to the 18.1% observed, while standard parametric, spline and non-cure mixture models predicted 10.1% to 13.2%.

Cure models are still relatively rarely relied upon in decisions. Latimer and Rutherford cite a 2020 review of 26 NICE immuno-oncology appraisals in which cure models were included in 8 and judged appropriate for decision-making in 3.

Discounting matters more because cure moves benefit far into the future. The reference case discounts at 3.5% a year (PMG36, section 4.5.1), and section 4.5.3 lets a committee consider 1.5% when a technology is for people who would otherwise die or have a very severely impaired life, is likely to restore them to full or near-full health, and has benefits likely to be sustained over a very long period.

Evidence a credible cure rate model needs

TSD 21 lists three assumptions behind any cure model, namely that the data are sufficient to estimate a cure fraction reliably, that a cure fraction exists and cure is reasonable at a given time point, and that the distribution chosen for the uncured is appropriate. Each turns into an evidence requirement.

Mature follow-up with patients still at risk. TSD 21 notes that a reliable cure fraction needs sufficient numbers at risk in the tail, which randomised trials often lack. Othus and colleagues observe that adequate follow-up varies by cancer, perhaps under five years for a high-mortality cancer while 20 years may not suffice for a low-mortality one, and that no formal test of adequacy exists. In a simulated case study by Grant and colleagues with a true progression-free cure fraction of 15%, a mixture cure model estimated 43% at 40 months and 15% at 153 months.

A plateau that is real, not an artefact of censoring. An apparent plateau in a short trial can come from heavy censoring and small numbers. When Othus and colleagues refitted mixture cure models to trials from SWOG's leukaemia committee after further follow-up, mean overall survival in one trial fell from 7.7 to 4.9 years and in another rose from 12.4 to 16.4 years; they judged the bias unpredictable.

External data on long-term mortality. Latimer and Rutherford fit cure models in a relative survival framework, with general population mortality from life tables for the right calendar year, by age and sex. Where survivors keep an excess risk, a standardised mortality ratio can be applied; recent NICE appraisals in ovarian and gastric cancer tested 1.4 to 1.8, based mainly on assumption and clinical opinion, and the authors favour registry data on long-term survivors. In the Bullement case study only models that used external information predicted 5-year survival accurately.

A justified distribution and cure time. TSD 21 cautions that the Akaike information criterion and BIC weight early follow-up, where events are dense, and give little weight to the tail that determines the cure fraction. Latimer and Rutherford add that different distributions for the uncured give very different cure fractions, so attention belongs on predicted survival over time, and that with a non-mixture model whose boundary knot (the cure time) was set at 5 years, hazards fell steeply at around 2 years. When cure is uncertain they recommend fitting both cure and non-cure models.

Worked example of how mean survival and QALYs move with the cure fraction

All numbers in this example are illustrative and chosen for simple arithmetic. Othus and colleagues note that mean survival in a population with a cure fraction is the weighted average of the mean survival of the cured and the uncured.

$$\bar{T}(\pi) = \pi\,E_B + (1-\pi)\,E_U$$

where $\bar{T}(\pi)$ is mean overall survival for cure fraction $\pi$, $E_B$ is mean survival under background mortality alone (the area under $S^{*}(t)$) and $E_U$ is mean survival of the uncured (the area under $S^{*}(t)S_u(t)$).

1. Set the inputs. Background mortality is a constant hazard of $\mu = 0.04$ a year, so $E_B = 1/0.04 = 25$ years; a real model would use life tables. Uncured patients carry an extra disease hazard of $\lambda = 0.46$ a year, so $E_U = 1/(0.04 + 0.46) = 2$ years.

2. Vary the cure fraction. Each unit of cure fraction adds $E_B - E_U$, or 23 years, so every 10 percentage points add 2.3 years.

3. Compare two treatments. A comparator has $\pi = 0.10$ and a new treatment $\pi = 0.25$, with identical survival among the uncured. Undiscounted, the new treatment adds 7.75 − 4.3 = 3.45 life years, all from the extra 15 percentage points of cure. With utilities of 0.80 for cured and 0.60 for uncured patients, mean QALYs are 0.10 × 25 × 0.80 + 0.90 × 2 × 0.60 = 3.08 and 0.25 × 25 × 0.80 + 0.75 × 2 × 0.60 = 5.9, a gain of 2.82 QALYs.

4. Discount. Continuous discounting at $r = \ln(1.035)$, equivalent to 3.5% a year, turns each constant-hazard mean into one divided by the hazard plus $r$, giving 13.44 years for the cured and 1.871 for the uncured. Discounted QALYs become 2.086 and 3.530, so the gain shrinks to 1.444 QALYs, about half the undiscounted figure, because the cure gain arrives decades later. At 1.5% a year on the same basis the gain is 2.01 QALYs.

5. Interpretation. If neither arm had a real cured group, both would have mean survival of 2 years and the gain would be zero, against 3.45 life years under the cure model. The case rests on the 15-point difference in cure fraction, the quantity short follow-up supports least, so the cure assumption is a structural uncertainty tested by comparing cure and non-cure models in scenario analysis.

Relation to the other cure pages

The sibling pages deal with statistical cure, the cure fraction and each family's mathematics, while the concern for an appraisal is what the cure assumption does to its results. Latimer and Rutherford note that landmark-based piecewise models, which switch to general population mortality after a chosen time, give a cure-like tail without using the data to estimate the cure and can create discontinuities in the hazard.

Common misreadings of cure rate results

Most errors come from reading the cure fraction as something it is not. Two recur in appraisals and in the methods literature.

• A cure model applied where there is no cure flatters the treatment. TSD 21's simulations found substantial bias in mean overall survival when cure models were fitted where cure was not a reasonable assumption.
• Cure in progression-free survival is a different quantity. Othus and colleagues note that progression-free survival counts extra events, so it may underestimate a true cure fraction, and its use as a surrogate needs validation.

Sources

• Bullement A, Latimer NR, Bell Gorrod H. Survival extrapolation in cancer immunotherapy: a validation-based case study. Value in Health. 2019;22(3):276-283. https://doi.org/10.1016/j.jval.2018.10.007
• Grant TS, Burns D, Kiff C, Lee D. A case study examining the usefulness of cure modelling for the prediction of survival based on data maturity. PharmacoEconomics. 2020;38(4):385-395. https://doi.org/10.1007/s40273-019-00867-5
• Latimer NR, Rutherford MJ. Mixture and non-mixture cure models for health technology assessment: what you need to know. PharmacoEconomics. 2024;42(10):1073-1090. https://doi.org/10.1007/s40273-024-01406-7
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). 2022, last updated 13 October 2026. Sections 4.5.1, 4.5.3 and 4.6.25. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• Othus M, Barlogie B, LeBlanc ML, Crowley JJ. Cure models as a useful statistical tool for analyzing survival. Clinical Cancer Research. 2012;18(14):3731-3736. https://doi.org/10.1158/1078-0432.CCR-11-2859
• Othus M, Bansal A, Koepl L, Wagner S, Ramsey S. Accounting for cured patients in cost-effectiveness analysis. Value in Health. 2017;20(4):705-709. https://doi.org/10.1016/j.jval.2016.04.011
• Othus M, Bansal A, Erba H, Ramsey S. Bias in mean survival from fitting cure models with limited follow-up. Value in Health. 2020;23(8):1034-1039. https://doi.org/10.1016/j.jval.2020.02.015
• Rutherford MJ, Lambert PC, Sweeting MJ, Pennington B, Crowther MJ, Abrams KR, Latimer NR. NICE DSU Technical Support Document 21: Flexible methods for survival analysis. Sheffield: Decision Support Unit, ScHARR, University of Sheffield; 2020 (updated March 2022). Sections 2.1, 3.6 and 5.3.4. https://doi.org/10.15131/shef.data.33849118
• Tsodikov AD, Ibrahim JG, Yakovlev AY. Estimating cure rates from survival data: an alternative to two-component mixture models. Journal of the American Statistical Association. 2003;98(464):1063-1078. https://doi.org/10.1198/01622145030000001007