Nonparametric estimation of time-dependent ROC curves conditional on a continuous covariate

• Published in: Statistics in medicine 2016-03, Vol.35 (7), p.1090-1102
• Main Authors: Rodríguez-Álvarez, María Xosé, Meira-Machado, Luís, Abu-Assi, Emad, Raposeiras-Roubín, Sergio
• Format: Article
• Language: English
• Subjects: acute coronary syndrome; Acute Coronary Syndrome - diagnosis; Biomarkers; Biomarkers - analysis; Biostatistics; Computer Simulation; Estimating techniques; False Positive Reactions; Humans; kernel-type smoothing; Medical diagnosis; Medical statistics; Models, Statistical; Predictive Value of Tests; ROC Curve; Statistics, Nonparametric; Survival Analysis; Time Factors; time-dependent ROC curve
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.6769

The receiver‐operating characteristic (ROC) curve is the most widely used measure for evaluating the performance of a diagnostic biomarker when predicting a binary disease outcome. The ROC curve displays the true positive rate (or sensitivity) and the false positive rate (or 1‐specificity) for different cut‐off values used to classify an individual as healthy or diseased. In time‐to‐event studies, however, the disease status (e.g. death or alive) of an individual is not a fixed characteristic, and it varies along the study. In such cases, when evaluating the performance of the biomarker, several issues should be taken into account: first, the time‐dependent nature of the disease status; and second, the presence of incomplete data (e.g. censored data typically present in survival studies). Accordingly, to assess the discrimination power of continuous biomarkers for time‐dependent disease outcomes, time‐dependent extensions of true positive rate, false positive rate, and ROC curve have been recently proposed. In this work, we present new nonparametric estimators of the cumulative/dynamic time‐dependent ROC curve that allow accounting for the possible modifying effect of current or past covariate measures on the discriminatory power of the biomarker. The proposed estimators can accommodate right‐censored data, as well as covariate‐dependent censoring. The behavior of the estimators proposed in this study will be explored through simulations and illustrated using data from a cohort of patients who suffered from acute coronary syndrome. Copyright © 2015 John Wiley & Sons, Ltd.