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

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.

The research of L. Machado was financed by FEDER Funds through ‘Programa Operacional Factores de Competitividade - COMPETE’ and by Portuguese Funds through FCT - ‘Fundação para a Ciência e a Tecnologia’, in the form of grant PEst-OE/MAT/UI0013/2014. M.X. Rodríguez - Álvarez would like to express their gratitude for the support received in the form of the Spanish Ministry of Economy and Competitiveness grant MTM2014-55966-P and the Agrupamento INBIOMED from DXPCTSUG-FEDER unha maneira de facer Europa (2012/273). We are also grateful to the associate editor and the two peer referees for their valuable comments and suggestions, which served to make a substantial improvement to this paper.