Time-dependent AUC with right-censored data: a survey study <s> The cumulative dynamic AUC: AUC <s> Sensitivity, specificity, and area under the ROC curve (AUC) are often used to measure the ability of survival models to predict future risk. Estimation of these parameters is complicated by the fact that these parameters are time-dependent and by the fact that censoring affects their estimation just as it affects estimation of survival curves or coefficients of survival regression models. The authors present several estimators that overcome these complications. One approach is a recursive calculation over the ordered times of events, analogous to the Kaplan-Meier approach to survival function estimation. Another is to first apply Bayes' theorem to write the parameters of interest in terms of conditional survival functions that are then estimated by survival analysis methods. Simulation studies demonstrate that the proposed estimators perform well in practical situations, when compared with an estimator (c-statistic, from logistic regression) that ignores time. An illustration with data from a cardiovascular follow-up study is provided. <s> BIB001 </s> Time-dependent AUC with right-censored data: a survey study <s> The cumulative dynamic AUC: AUC <s> The performance of clinical tests for disease screening is often evaluated using the area under the receiver-operating characteristic (ROC) curve (AUC). Recent developments have extended the traditional setting to the AUC with binary time-varying failure status. Without considering covariates, our first theme is to propose a simple and easily computed nonparametric estimator for the time-dependent AUC. Moreover, we use generalized linear models with time-varying coefficients to characterize the time-dependent AUC as a function of covariate values. The corresponding estimation procedures are proposed to estimate the parameter functions of interest. The derived limiting Gaussian processes and the estimated asymptotic variances enable us to construct the approximated confidence regions for the AUCs. The finite sample properties of our proposed estimators and inference procedures are examined through extensive simulations. An analysis of the AIDS Clinical Trials Group (ACTG) 175 data is further presented to show the applicability of the proposed methods. The Canadian Journal of Statistics 38:8–26; 2010 © 2009 Statistical Society of Canada <s> BIB002 </s> Time-dependent AUC with right-censored data: a survey study <s> The cumulative dynamic AUC: AUC <s> Finding out biomarkers and building risk scores to predict the occurrence of survival outcomes is a major concern of clinical epidemiology, and so is the evaluation of prognostic models. In this paper, we are concerned with the estimation of the time-dependent AUC -- area under the receiver operating curve -- which naturally extends standard AUC to the setting of survival outcomes and enables to evaluate the discriminative power of prognostic models. We establish a simple and useful relation between the predictiveness curve and the time-dependent AUC -- AUC(t). This relation confirms that the predictiveness curve is the key concept for evaluating calibration and discrimination of prognostic models. It also highlights that accurate estimates of the conditional absolute risk function should yield accurate estimates for AUC(t). From this observation, we derive several estimators for AUC(t) relying on distinct estimators of the conditional absolute risk function. An empirical study was conducted to compare our estimators with existing ones and assess the effect of model misspecification -- when estimating the conditional absolute risk function-- on the AUC(t) estimation. We further illustrate the methodology on the Mayo PBC and the VA lung cancer data sets. <s> BIB003 </s> Time-dependent AUC with right-censored data: a survey study <s> The cumulative dynamic AUC: AUC <s> To quantify the ability of a marker to predict the onset of a clinical outcome in the future, time-dependent estimators of sensitivity, specificity, and ROC curve have been proposed accounting for censoring of the outcome. In this paper, we review these estimators, recall their assumptions about the censoring mechanism and highlight their relationships and properties. A simulation study shows that marker-dependent censoring can lead to important biases for the ROC estimators not adapted to this case. A slight modification of the inverse probability of censoring weighting estimators proposed by Uno et al. (2007) and Hung and Chiang (2010a) performs as well as the nearest neighbor estimator of Heagerty et al. (2000) in the simulation study and has interesting practical properties. Finally, the estimators were used to evaluate abilities of a marker combining age and a cognitive test to predict dementia in the elderly. Data were obtained from the French PAQUID cohort. The censoring appears clearly marker-dependent leading to appreciable differences between ROC curves estimated with the different methods. <s> BIB004
The setting of cumulative cases and dynamic controls may be regarded as the most natural choice for planning enrollment criteria in clinical trials or when specific evaluation times are of particular interest. It simply corresponds to defining cases at time t as subjects who experienced the event prior to time t, and controls at time t as patients who were still event-free at time t. In other words, it corresponds to setting . Cumulative true positive rates and dynamic false positive rates are then respectively defined as The cumulative/dynamic AUC at time t is then obtained by using these definitions of true and false positive rates in (1). Usually, however, 1I(T ≤ t) is not observed for all subjects due to the presence of censoring before time t and simple contingency tables can therefore not be used to return estimates of TPR C (c,t), FPR D (c,t) and To handle censoring, Bayes' theorem can be used to rewrite AUC C,D (t) as a function of the conditional survival function IP(T > t|X = x) (see paragraph 3.1.1 below). Other approaches rely on so-called Inverse Probability of Censoring Weighted (IPCW) estimates (see paragraph 3.1.2 below). Before describing these two approaches in more details below, we shall add that Chambless and Diao BIB001 developed an alternative method -which will not be described here -based on an idea similar to the one used to derive the Kaplan-Meier estimator of the cumulative distribution function in the presence of censoring. Among all these methods, only those relying on primary estimates of IP(T > t|X = x) (and a recent extension of IPCW estimates proposed in BIB004 ) may account for the dependence between censoring and the marker (since they basically only assume that T and C are independent given X and not that T and C are independent). We refer the reader to BIB004 BIB002 BIB003 for empirical comparisons and illustrations of these various methods.