Estimating and comparing time‐dependent areas under receiver operating characteristic curves for censored event times with competing risks

TLDR

The area under the time‑dependent ROC curve quantifies a marker’s predictive ability for future clinical outcomes, and in survival analysis with competing risks, two alternative specificity definitions arise depending on how competing events are handled. The study proposes nonparametric inverse probability of censoring weighting estimators of the AUC for these two specificity definitions and investigates their asymptotic properties. The authors derive confidence intervals and test statistics for comparing AUCs, and conduct a simulation study to assess finite‑sample performance. Applied to the PAQUID cohort, the method compared two psychometric tests for predicting dementia onset while accounting for death as a competing risk, and the authors released the timeROC R package to facilitate use.

Abstract

The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The 'timeROC' R package is provided to make the methodology easily usable.