Mixture Cure Models in Oncology: A Tutorial and Practical Guidance

Abstract

Novel cancer therapies are associated with survival patterns that differ from established therapies, which may include survival curves that plateau after a certain follow-up time point. A fraction of the patient population is then considered statistically cured and subject to the same mortality experience as the cancer-free general population. Mixture cure models have been developed to account for this characteristic. As compared to standard survival analysis, mixture cure models can often lead to profoundly different estimates of long-term survival, required for health economic evaluations. This tutorial is designed as a practical introduction to mixture cure models. Step-by-step instructions are provided for the entire implementation workflow, i.e., from gathering and combining data from different sources to fitting models using maximum likelihood estimation and model results interpretation. Two mixture cure models were developed to illustrate (1) an "uninformed" approach where the cure fraction is estimated from trial data and (2) an "informed" approach where the cure fraction is obtained from an external source (e.g., real-world data) used as an input to the model. These models were implemented in the statistical software R, with the freely available code on GitHub. The cure fraction can be estimated as an output from ("uninformed" approach) or used as an input to ("informed" approach) a mixture cure model. Mixture cure models suggest presumed estimates of long-term survival proportions, especially in instances where some fraction of patients is expected to be statistically cured. While this type of model may initially seem complex, it is straightforward to use and interpret. Mixture cure models have the potential to improve the accuracy of survival estimates for treatments associated with statistical cure, and the present tutorial outlines the interpretation and implementation of mixture cure models in R. This type of model will likely become more widely used in health economic analyses as novel cancer therapies enter the market.

Fig. 1

Implementation workflow

Fig. 2

Different approaches on using and obtaining the cure fraction. The cure fraction can be obtained as an output or be used as an input to the model, based on real-world data, expert opinion or the literature

Fig. 3

Different background survival by country and sex, illustrated for Italy, Russia, and the USA. Data from the Human Mortality Database [26]

Fig. 4

Survival curves for different model specifications using simulated BRIM-3 trial data—intervention arm. The KM (black dashed line) shows a plateau; hence, the spectrum of extrapolations with different functions is relatively narrow. BRIM-3 BRAF Inhibitor in Melanoma 3, exponential exponential distribution, gamma gamma distribution, gengamma generalized gamma distribution, gompertz Gompertz distribution, KM Kaplan-Meier curve, llogis log-logistic distribution, lognormal lognormal distribution, weibull Weibull distribution

Fig. 5

Survival curves for different model specifications using simulated coBRIM trial data—control arm. The KM (solid dashed line) does not show a plateau; hence, the spectrum of possible extrapolations is wide. Exponential exponential distribution, gamma gamma distribution, gengamma generalized gamma distribution, gompertz Gompertz distribution, KM Kaplan–sMeier curve, llogis log-logistic distribution, lognormal lognormal distribution, weibull Weibull distribution