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With the recent explosion of ultrahigh-dimensional data, extensive work has been carried out for screening methods which can effectively reduce the dimensionality. However, censored survival data which often arise in clinical trials and genetic studies have been left greatly unexplored for ultrahigh-dimensional scenarios. A novel feature screening procedure is proposed for ultrahigh-dimensional survival data. Also established are the ranking consistency and the sure independent screening properties. Compared with the existing methods, the proposed screening procedure is invariant to the monotone transformation, known or unknown, of the response. Moreover, it can be readily applied to ultrahighdimensional complete data when the censoring rate is zero. Simulation studies demonstrate that the proposed procedure exhibits favorably in comparisons with the existing ones. As an illustration, the proposed method is applied to the mantle cell lymphoma study.

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To accommodate the heterogeneity that is often present in ultrahigh-dimensional data, we propose a conditional quantile screening method, which enables us to select features that contribute to the conditional quantile of the response given the covariates. The method can naturally handle censored data by incorporating a weighting scheme through redistribution of the mass to the right; moreover, it is invariant to monotone transformation of the response and requires substantially weaker conditions than do alternative methods. We establish sure independent screening properties for both the complete and the censored response cases. We also conduct simulations to evaluate the finite-sample performance of the proposed method, and compare it with existing approaches.

For complete ultrahigh-dimensional data, sure independent screening methods can effectively reduce the dimensionality while retaining all the active variables with high probability. However, limited screening methods have been developed for ultrahigh-dimensional survival data subject to censoring. We propose a censored cumulative residual independent screening method that is model-free and enjoys the sure independent screening property. Active variables tend to be ranked above the inactive ones in terms of their association with the survival times. Compared with several existing methods, our model-free screening method works well with general survival models, and it is invariant to the monotone transformation of the responses, as well as requiring substantially weaker moment conditions. Numerical studies demonstrate the usefulness of the censored cumulative residual independent screening method, and the new approach is illustrated with a gene expression data set.