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A covariate‐specific time‐dependent receiver operating characteristic curve for correlated survival data
Author(s) -
Meddis Alessandra,
Blanche Paul,
Bidard François C,
Latouche Aurélien
Publication year - 2020
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8550
Subject(s) - covariate , censoring (clinical trials) , receiver operating characteristic , estimator , breast cancer , nonparametric statistics , inverse probability weighting , statistics , survival analysis , medicine , oncology , computer science , cancer , mathematics
Several studies for the clinical validity of circulating tumor cells (CTCs) in metastatic breast cancer were conducted showing that it is a prognostic biomarker of overall survival. In this work, we consider an individual patient data meta‐analysis for nonmetastatic breast cancer to assess the discrimination of CTCs regarding the risk of death. Data are collected in several centers and present correlated failure times for subjects of the same center. However, although the covariate‐specific time‐dependent receiver operating characteristic (ROC) curve has been widely used for assessing the performance of a biomarker, there is no methodology yet that can handle this specific setting with clustered censored failure times. We propose an estimator for the covariate‐specific time‐dependent ROC curves and area under the ROC curve when clustered failure times are detected. We discuss the assumptions under which the estimators are consistent and their interpretations. We assume a shared frailty model for modeling the effect of the covariates and the biomarker on the outcome in order to account for the cluster effect. A simulation study was conducted and it shows negligible bias for the proposed estimator and a nonparametric one based on inverse probability censoring weighting, while a semiparametric estimator, ignoring the clustering, is markedly biased. Finally, in our application to breast cancer data, the estimation of the covariate‐specific area under the curves illustrates that the CTCs discriminate better patients with inflammatory tumor than patients with noninflammatory tumor, with respect to their risk of death.