RANDOM WEIGHTING AND EDGEWORTH EXPANSION FOR THE NONPARAMETRIC TIME-DEPENDENT AUC ESTIMATOR

A confidence region for the time-dependent area under the receiver operating characteristic curve (AUC) can be constructed based on the asymptotic normality of a non-parametric estimator. In numerical studies, it was found that the performance of the normal approximated confidence interval is dramatically affected by small sample size and high censoring rate. To improve the accuracy of coverage probabilities as well as interval estimators, the random weighted bootstrap distribution and the Edgeworth expansion with remainder term o(n(-1/2)) are proposed to approximate the sampling distribution of the estimator. The asymptotic properties of random weighted bootstrap analogue and the one-term Edgeworth expansion are developed in this article. The usefulness of the proposed procedures are confirmed by a class of simulations with different sample sizes and censoring rates. Moreover, our methods are demonstrated using the ACTG 175 data.