Time-dependent AUC with right-censored data: a survey study <s> whereŜ(t) is the Kaplan-Meier estimator of IP(T > t). <s> ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. <s> BIB001 </s> Time-dependent AUC with right-censored data: a survey study <s> whereŜ(t) is the Kaplan-Meier estimator of IP(T > t). <s> Suppose that we are interested in establishing simple but reliable rules for predicting future t-year survivors through censored regression models. In this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models, we derive consistent estimators for the above measures through substitution and cross-validation estimation procedures. Furthermore, we provide large-sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All of the proposals are illustrated with real examples, and their finite-sample properties are evaluated through a simulation study. <s> BIB002 </s> Time-dependent AUC with right-censored data: a survey study <s> whereŜ(t) is the Kaplan-Meier estimator of IP(T > t). <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> BIB003 </s> Time-dependent AUC with right-censored data: a survey study <s> whereŜ(t) is the Kaplan-Meier estimator of IP(T > t). <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
Theoretical guarantees for these estimators can be found in BIB003 and BIB002 . These estimators are in a sense more flexible than those presented in paragraph 3.1.1 above: they are model-free and they do not rely on any bandwidth selection (unlike the estimator of Heagerty et al. BIB001 for instance, which is based on a local version of the Kaplan-Meier estimator). However, when censoring may depend on marker X, quantities like the conditional survival function of C given the marker X, S C (·|X), have to be estimated BIB004 , which implies either to work under some (semi-)parametric model or the selection of some parameter if nonparametric estimation is prefered.