Inference about time-dependent prognostic accuracy measures in the presence of competing risks

Addressing subject heterogeneity in time-dependent discrimination for biomarker evaluation

Accurate discrimination has been the central goal in identifying biomarkers for monitoring disease progression and early detection. Acknowledging the fact that discrimination accuracy of biomarkers for a time-to-event outcome often changes over time, local measures such as the time-dependent receiver operating characteristic curve and its area under the curve (AUC) are used to assess time-dependent predictive discrimination. However, such measures do not address subject heterogeneity, although the impact of covariates including demographics, disease-related characteristics, and other clinical information on the discriminatory performance of biomarkers needs to be investigated before their clinical use. We propose the covariate-specific time-dependent AUC, a measure for covariate-adjusted discrimination. We develop a regression model on the covariate-specific time-dependent AUC to understand how and in what magnitude the covariates influence biomarker performance. Then we construct a pseudo partial-likelihood for estimation and inference. This is followed by our establishing the asymptotic properties of the proposed estimators and provide variance estimation. The simulation studies and application to the AIDS Clinical Trials Group 175 data demonstrate that the proposed method offers an informative tool for inferring covariate-specific and time-dependent predictive discrimination.