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

Abstract

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

Time-dependent receiver operating characteristic curve estimator for correlated right-censored time-to-event data

“…] I(Y ≤ t) which coincides with the formula given in. 5,7,9,12 Using the same approach, the theoretical formula for the time-dependent ROC curve given in equation ( 4) can be written as…”

“…It uses the popular Beran (also called weighted Kaplan–Meier) estimator 31 to estimate the conditional survival probability, S false( . | M false), which is a key component of their ROC and AUC estimators. We chose the Beran-based estimator because it is well-studied (see, for example, 5,9,12 ) and has been shown to have good performance than most existing methods proposed for right-censored data.…”

“…Several researchers, such as Heagerty et al, 2 Heagerty and Zheng, 3 Etzioni et al, 4 and others, have proposed various definitions and extensions to adapt classical methodologies for handling time-to-event data in prognostic studies. In literature, taking various censoring mechanisms into account, several time-dependent ROC curve and AUC estimation methods have been proposed; see, for example, Heagerty et al, 2 Heagerty and Zheng, 3 Li et al, 5 Blanche et al, 6 Martìnez-Camblor et al, 7 Martìnez-Camblor and Pardo- Fernández, 8 Beyene et al, 9 Díaz-Coto, 10 Wu and Cook, 11 Beyene and El Ghouch 12,13 and the references given in these papers.…”

Time‐dependent ROC curve estimation for interval‐censored data

“…By far, the most studied case in the literature is the case of right censoring where some results are only known to be at least as large as the reported value. In this case, several methods were proposed, like, for example, the work of Heagerty et al (2000), Heagerty and Zheng (2005), Martínez-Camblor et al (2016), Martínez-Camblor andPardo-Fernández (2018), Beyene et al (2019), andLi et al (2018), to cite just a few.…”

“…(2016), Martínez‐Camblor and Pardo‐Fernández (2018), Beyene et al. (2019), and Li et al. (2018), to cite just a few.…”