Volume under the ROC surface for high-dimensional independent screening with ordinal competing risk outcomes

We propose a screening method for high-dimensional data with ordinal competing risk outcomes, which is time-dependent and model-free. Existing methods are designed for cause-specific variable screening and fail to evaluate how a biomarker is associated with multiple competing events simultaneously. The proposed method utilizes the Volume under the ROC surface (VUS), which measures the concordance between values of a biomarker and event status at certain time points and provides an overall evaluation of the discrimination capacity of a biomarker. We show that the VUS possesses the sure screening property, i.e., true important covariates can be retained with probability tending to one, and the size of the selected set can be bounded with high probability. The VUS appears to be a viable model-free screening metric as compared to some existing methods in simulation studies, and it is especially robust to data contamination. Through an analysis of breast-cancer gene-expression data, we illustrate the unique insights into the overall discriminatory capability provided by the VUS.