title: Bias and variance reduction in nonparametric estimation of time-dependent accuracy measures.
abstract: A new nonparametric approach is developed to estimate the time-dependent accuracy measure curves, which are defined on the cumulative cases and dynamic controls, for censored survival data. Based on an estimable survival process, the main intention of this study is to reduce the finite-sample biases of nearest neighbor estimators. The asymptotic variances of some retrospective accuracy measure estimators are further reduced by applying a smoothing technique to the underlying process of a marker. Meanwhile, practically feasible and theoretically valid procedures are proposed for bandwidth selection in the presented estimators. In addition, the proposed methodology can be reasonably extended to accommodate stratified survival data and survival data with multiple markers. As shown in the simulations, our new estimators outperform the nearest neighbor and inverse censoring weighted estimators. Data from the AIDS Clinical Trials Group study 175 and an angiographic coronary artery disease study are also used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Institute of Applied Mathematical Sciences, National Taiwan University, Taipei, Taiwan. chiangct@ntu.edu.tw.
authors.forename: Chin-Tsang
authors.initials: CT
authors.lastname: Chiang
authors.affiliation: Institute of Applied Mathematical Sciences, National Taiwan University, Taipei, Taiwan.
authors.forename: Ming-Yueh
authors.initials: MY
authors.lastname: Huang
authors.affiliation: Institute of Applied Mathematical Sciences, National Taiwan University, Taipei, Taiwan.
authors.forename: Shao-Hsuan
authors.initials: SH
authors.lastname: Wang
mesh_terms: D015982:Bias; D015415:Biomarkers; D003198:Computer Simulation; D003324:Coronary Artery Disease / Q000175:diagnosis; D006801:Humans; D015203:Reproducibility of Results; D012189:Retrospective Studies
chemical_list: D015415:Biomarkers
keywords: Gaussian process; U-statistic; bandwidth selection; conditional survival function; kernel function; marker-dependent censoring; positive/negative predictive value; receiver operating characteristic curve; true/false positive rate