Feature screening with large-scale and high-dimensional survival data.

Data with a huge size present great challenges in modeling, inferences, and computation. In handling big data, much attention has been directed to settings with "large p small n", and relatively less work has been done to address problems with p and n being both large, though data with such a feature have now become more accessible than before, where p represents the number of variables and n stands for the sample size. The big volume of data does not automatically ensure good quality of inferences because a large number of unimportant variables may be collected in the process of gathering informative variables. To carry out valid statistical analysis, it is imperative to screen out noisy variables that have no predictive value for explaining the outcome variable. In this paper, we develop a screening method for handling large-sized survival data, where the sample size n is large and the dimension p of covariates is of non-polynomial order of the sample size n, or the so-called NP-dimension. We rigorously establish theoretical results for the proposed method and conduct numerical studies to assess its performance. Our research offers multiple extensions of existing work and enlarges the scope of high-dimensional data analysis. The proposed method capitalizes on the connections among useful regression settings and offers a computationally efficient screening procedure. Our method can be applied to different situations with large-scale data including genomic data.