Analysis of Receiver Operating Characteristic Curves for Cure Survival Data and Mismeasured Biomarkers

Cure models and receiver operating characteristic (ROC) curve estimation are two important issues in survival analysis and have received attention for many years. In the development of biostatistics, these two topics have been well discussed separately. However, a rare development in the estimation of the ROC curve has been made available based on survival data with the cure fraction. On the other hand, while a large body of estimation methods have been proposed, they rely on an implicit assumption that the variables are precisely measured. In applications, measurement errors are generally ubiquitous and ignoring measurement errors can cause unexpected bias for the estimator and lead to the wrong conclusion. In this paper, we study the estimation of the ROC curve and the area under curve (AUC) when variables or biomarkers are subject to measurement error. We propose a valid procedure to handle measurement error effects and estimate the parameters in the cure model, as well as the AUC. We also make an effort to establish the theoretical properties with rigorous justification.