Abstract: In the era of precision medicine, survival outcome data with high-throug-hput predictors are routinely collected. Models with an exceedingly large number of covariates are either infeasible to fit or likely to incur low predictability because of overfitting. Variable screening is crucial to identifying and removing irrelevant attributes. Although numerous screening methods have been proposed, most rely on some particular modeling assumptions. Motivated by a study on detecting gene signatures for the survival of patients with multiple myeloma, we propose a model-free Lq-norm learning procedure, which includes the well-known Cramér-von Mises and Kolmogorov criteria as two special cases. This work provides an integrative framework for detecting predictors with various levels of impact, such as short- or long-term impacts, on censored outcome data. The framework leads naturally to a scheme that combines results from different q to reduce false negatives, an aspect often overlooked by the current literature. We show that our method possesses sure screening properties. The utility of the proposed method is confirmed using simulation studies and an analysis of the multiple myeloma study.

Key words and phrases: Cramér-von Mises statistic, Kolmogorov statistic, Lq-norm learning, survival data, variable screening.