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Prognostic biomarkers for survival outcomes are widely used in clinical research and practice. Such biomarkers are often evaluated using a C-index as well as quantities based on time-dependent receiver operating characteristic curves. Existing methods for their evaluation generally assume that censoring is uninformative in the sense that the censoring time is independent of the failure time with or without conditioning on the biomarker under evaluation. With focus on the C-index and the area under a particular receiver operating characteristic curve, we describe and compare three estimation methods that account for informative censoring based on observed baseline covariates. Two of them are straightforward extensions of existing plug-in and inverse probability weighting methods for uninformative censoring. By appealing to semiparametric theory, we also develop a doubly robust, locally efficient method that is more robust than the plug-in and inverse probability weighting methods and typically more efficient than the inverse probability weighting method. The methods are evaluated and compared in a simulation study, and applied to real data from studies of breast cancer and heart failure.
Liu et al. (2024) studied this question.