Cumulative/Dynamic Time-Dependent ROC Analysis for Left-Truncated and Right-Censored Data: Estimators and Comparison

Time-dependent Receiver Operating Characteristics (ROC) analysis is a standard method to evaluate the discriminative performance of biomarkers or risk scores for time-to-event outcomes. Extensions of this useful method to left-truncated right-censored data have been understudied, with the exception of Li 2017. In this paper, we first extended the estimators in Li 2017 to several regression-type estimators that account for independent or covariate-induced dependent left truncation and right censoring. We further proposed novel inverse probability weighting estimators of cumulative sensitivity, dynamic specificity, and area under the ROC curve (AUC), where the weights simultaneously account for left truncation and right censoring, with or without adjusting for covariates. We demonstrated the proposed AUC estimators in simulation studies with different scenarios. We performed the proposed time-dependent ROC analysis to evaluate the predictive performance of two risk prediction models of heart failure by Chow et al. 2015 in five-year childhood cancer survivors using the St. Jude Lifetime Cohort Study.