Correlation rank screening for ultrahigh-dimensional survival data

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 ultrahigh-dimensional 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.