Cure Models in Survival Analysis

Amico, Maïlis; Keilegom, Ingrid Van

doi:10.1146/annurev-statistics-031017-100101

Cited by 120 publications

(115 citation statements)

References 87 publications

(162 reference statements)

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“…The possible reason for the large bias and MSE observed in the AUC estimates when using the misspecified Cox working model, in this case, can be explained by the bias in estimating the survival function for data with a cure fraction. This was well documented in Amico and Van Keilegom (). In their paper, when comparing the MCM and Cox model in a simulation study, the authors concluded that “not taking into account the presence of a cure fraction in survival data has important consequences that may lead to wrong conclusions.” In our simulations study, we also investigated the case when the data are generated for the classical Cox model (without cure) and the AUC is estimated using either the Cox or the mixture cure working model.…”

Section: Simulationssupporting

confidence: 72%

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On the validity of time‐dependent AUC estimation in the presence of cure fraction

2019

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During the last decades, several approaches have been proposed to estimate the timedependent area under the receiver operating characteristic curve (AUC) of risk tools derived from survival data. The validity of these estimators relies on some regularity assumptions among which a survival function being proper. In practice, this assumption is not always satisfied because a fraction of the population may not be susceptible to experience the event of interest even for long follow-up. Studying the sensitivity of the proposed estimators to the violation of this assumption is of substantial interest. In this paper, we investigate the performance of a nonparametric simple estimator, developed for classical survival data, in the case when the population exhibits a cure fraction. Motivated from the current practice of deriving risk tools in oncology and cardiovascular disease prevention, we also assess the loss, in terms of predictive performance, when deriving risk tools from survival models that do not acknowledge the presence of cure. The simulation results show that the investigated method is valid even under the presence of cure. They also show that risk tools derived from survival models that ignore the presence of cure have smaller AUC compared to those derived from survival models that acknowledge the presence of cure. This was also attested with a real data analysis from a breast cancer study. K E Y W O R D SCox model, mixture cure models, promotion time models, risk tools, time-dependent AUC 1430

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Section: Simulationssupporting

confidence: 72%

“…During the last decades, different methods for modeling survival data with cure fraction that yield valid regression coefficient estimates and inferences were proposed. For a recent review on cure models, see, for example, Amico and Van Keilegom () and Taweab and Ibrahim ().…”

Section: Introductionmentioning

confidence: 99%

On the validity of time‐dependent AUC estimation in the presence of cure fraction

2019

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“…Related to this, we aim at also expanding the Poly-Weibull model by implementing a version that allows the inclusion of covariates on the ancillary parameters as well as on the location. This effort is also part of a wider plan to bring into survHE more models based on mixtures, e.g., in the form of cure models (Amico and Van Keilegom 2018). This may result in an efficient way of accounting for the underlying complexity of the data generating process, as well as extrapolating the survival curves, potentially including external data.…”

Section: Limitations and Current/future Developments Of Survhementioning

confidence: 99%

survHE: Survival Analysis for Health Economic Evaluation and Cost-Effectiveness Modeling

Baio¹

2020

J. Stat. Soft.

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Survival analysis features heavily as an important part of health economic evaluation, an increasingly important component of medical research. In this setting, it is important to estimate the mean time to the survival endpoint using limited information (typically from randomized trials) and thus it is useful to consider parametric survival models. In this paper, we review the features of the R package survHE, specifically designed to wrap several tools to perform survival analysis for economic evaluation. In particular, survHE embeds both a standard, frequentist analysis (through the R package flexsurv) and a Bayesian approach, based on Hamiltonian Monte Carlo (via the R package rstan) or integrated nested Laplace approximation (with the R package INLA). Using this composite approach, we obtain maximum flexibility and are able to pre-compile a wide range of parametric models, with a view of simplifying the modelers' work and allowing them to move away from non-optimal work flows, including spreadsheets (e.g., Microsoft Excel).

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“…The cure rate can be treated as a risk score to make treatment decisions in clinical practice, and is a powerful statistic tool for prognostic studies. To identify the existence of a cure subgroup, one common approach is to look at whether there is a long and stable nonzero plateau in the tail of the survival curve 11,12 …”

Section: Introductionmentioning

confidence: 99%

Evaluating thetime‐dependentpredictive accuracy forevent‐to‐timeoutcome with a cure fraction

Wang

2020

Pharmaceutical Statistics

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Summary In medical studies, it is often observed that a portion of subjects will never experience the event of interest and thus can be treated as cured or long‐term survivors. Many populations of early‐stage cancer patients contain both uncured and cured individuals that should be modeled using cure models. In prognostic studies, the cure status (uncure or cure) is an issue of interest for medical practitioners, and the disease status (death or alive) of an individual is not a fixed characteristic and it varies along the time. These statuses are usually predicted by a prognostic risk score. The time‐dependent receiver operating characteristic (ROC) curve is a powerful tool to evaluate these predicting performances dynamically. In the context with a cure fraction, quantifying and estimating the predictive performances of the risk score is a challenge since the disease status and cure status are both unknown among individuals who are censored. In this paper, to assess the predictive accuracy for the survival outcome with a cure fraction, we propose a time‐dependent ROC curve semi‐parametric estimator based on the sieve maximum likelihood (ML) estimation under the mixture cure model. We also apply a Bernstein‐based smoothing method in the estimation procedure, and this estimator can lead to substantial gain in efficiency. In addition, we derive the time‐dependent area under the ROC curve (AUC) to summarize the discriminatory capacity of the risk score globally. Finally, we evaluate the finite sample performance of the proposed methods by extensive simulations and illustrate the estimation using two real data sets, one from a melanoma study and the other from stomach cancer.

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Cure Models in Survival Analysis

Cited by 120 publications

References 87 publications

On the validity of time‐dependent AUC estimation in the presence of cure fraction

On the validity of time‐dependent AUC estimation in the presence of cure fraction

survHE: Survival Analysis for Health Economic Evaluation and Cost-Effectiveness Modeling

Evaluating thetime‐dependentpredictive accuracy forevent‐to‐timeoutcome with a cure fraction

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