Time-dependent diagnostic accuracy analysis with censored outcome and censored predictor

We consider a unified approach for estimating time-dependent diagnostic accuracy measures, including time-dependent sensitivity, specificity, positive predictive value, negative predictive value, receiver operating characteristic (ROC) curve, area under the ROC curve (AUC) and integrated AUC across time. In particular, our estimation method incorporates the double censoring setting, i.e. a censored outcome and a censored marker. Our unified approach greatly broadens the application of time-dependent diagnostic measures and allows for comparison between event-type predictors and/or completely observed continuous markers. More specifically, we express these time-dependent diagnostic accuracy measures in terms of bivariate and univariate survival functions. Hence they can be estimated by simply plugging in the Kaplan–Meier estimator for univariate survival functions and the Dabrowska estimator for the bivariate survival function. Asymptotic properties for our proposed estimators and bootstrap validity are established by using empirical processes techniques. Our simulation studies show that our proposed estimators and test procedures perform well for samples of moderate size. We apply our methods to an econometric example as well as a diabetic study.