Mixture Cure Model
Mixture Cure Model (Cure Fraction Model) · Also known as: cure fraction model, cure rate model, bounded cumulative hazard model, İyileşme Modeli (Mixture Cure Model)
The mixture cure model, first proposed by Boag in 1949 for cancer survival data, is a parametric survival model that explicitly accounts for a fraction of subjects who will never experience the event of interest — the so-called cured or immune fraction. It is the appropriate tool whenever the Kaplan-Meier curve levels off into a long, stable plateau rather than continuing to decline, indicating that a proportion of subjects are permanently event-free.
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When to use it
Use the mixture cure model when (1) time-to-event data show a pronounced plateau in the Kaplan-Meier curve, suggesting that a non-trivial fraction of subjects will never experience the event; (2) domain knowledge supports the existence of a cured or immune subgroup; and (3) follow-up is long enough that the plateau is clearly observable. The model requires at least 50 subjects and assumes that the cure fraction can be linked to covariates via a logistic model, while the uncured subjects follow a Cox or Weibull survival process. It is not appropriate when the Kaplan-Meier curve continues to decline to the end of follow-up, in which case standard Cox regression is preferable.
Strengths & limitations
- Directly models the cure fraction as a scientifically meaningful quantity rather than treating it as a nuisance.
- Separates covariate effects on the probability of cure (incidence) from effects on the timing of the event among uncured subjects (latency), providing richer inference than a single-equation model.
- Produces valid long-term survival predictions in populations where a cure fraction exists, avoiding the downward bias that standard models impose on the surviving tail.
- Applicable to both cross-sectional and longitudinal study designs with right-censored continuous and binary covariate data.
- Requires sufficiently long follow-up to identify the plateau; if the curve is still declining at study end, the cure fraction is not estimable.
- A minimum sample of around 50 events is needed for both sub-models to converge; in smaller samples the model often fails to identify π and S_u(t) separately.
- Model identifiability depends on the correctness of both the incidence and latency sub-model specifications; misspecification of either biases all estimates.
- Computationally more demanding than standard Cox regression; the EM algorithm may converge slowly with moderate samples.
Frequently asked
How do I know whether a cure model is appropriate for my data?
Examine the Kaplan-Meier curve. If it levels off to a stable, non-zero plateau well before the end of follow-up, and domain knowledge supports the existence of permanently event-free subjects, a cure model is warranted. If the curve continues to decline steadily to the last observation, the data do not support a cure fraction and standard Cox regression should be used instead.
What is the difference between the incidence and latency sub-models?
The incidence sub-model (logistic regression) estimates the probability that a subject belongs to the cured fraction — it answers the question 'will this subject ever experience the event?' The latency sub-model (Cox or Weibull) estimates the distribution of event times among those who will eventually experience the event — it answers 'when will the event occur for the uncured?' The two sub-models may include the same or different sets of covariates.
Can I use the mixture cure model with small samples?
The model requires a minimum of approximately 50 subjects (and typically more events) for both sub-models to converge reliably. With smaller samples the EM algorithm frequently fails to separate the cure fraction from the latency distribution, producing unreliable estimates with very wide confidence intervals. In such cases Kaplan-Meier is the safer descriptive tool.
How does the cure model differ from a standard Cox regression?
Standard Cox regression assumes that all subjects will eventually experience the event given sufficient follow-up. The mixture cure model relaxes this assumption by allowing a fraction π of subjects to be permanently event-free. This makes the Cox model a special case (π = 0). When a true cure fraction exists, standard Cox estimates are biased in the tail; when no cure fraction exists, forcing π > 0 introduces unnecessary model complexity.
Sources
- Boag, J. W. (1949). Maximum Likelihood Estimates of the Proportion of Patients Cured. Journal of the Royal Statistical Society B, 11(1), 15–53. link ↗
How to cite this page
ScholarGate. (2026, June 1). Mixture Cure Model (Cure Fraction Model). ScholarGate. https://scholargate.app/en/survival/cure-model
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