Sample size estimation for time-dependent receiver operating characteristic

In contrast to the usual ROC analysis with a contemporaneous reference standard, the time-dependent setting introduces the possibility that the reference standard refers to an event at a future time and may not be known for every patient due to censoring. The goal of this research is to determine the sample size required for a study design to address the question of the accuracy of a diagnostic test using the area under the curve in time-dependent ROC analysis. We adapt a previously published estimator of the time-dependent area under the ROC curve, which is a function of the expected conditional survival functions. This estimator accommodates censored data. The estimation of the required sample size is based on approximations of the expected conditional survival functions and their variances, derived under parametric assumptions of an exponential failure time and an exponential censoring time. We also consider different patient enrollment strategies. The proposed method can provide an adequate sample size to ensure that the test's accuracy is estimated to a prespecified precision. We present results of a simulation study to assess the accuracy of the method and its robustness to departures from the parametric assumptions. We apply the proposed method to design of a study of positron emission tomography as predictor of disease free survival in women undergoing therapy for cervical cancer.