Pseudo value method for ultra high-dimensional semiparametric models with life-time data

Abstract

We develop a new procedure called "pseudo value method" (PVM) that can handle ultra high-dimensional variable selection problems for semiparametric survival models. While there has only been the sure independence screening (SIS)-type strategy for ultra high-dimensional life-time data so far in literature, the new unified methodology covers a much broader class of survival models including general transformation models and the accelerated failure time (AFT) model. The proposed method is versatile because the conversion involved easily casts the current problem of interest into a regular linear regression framework.Through this translation, all the existing and powerful techniques developed for the linear regression problems can be leveraged to tackle the new challenge at almost no extra cost.Numerical performance of PVM has also demonstrated promising results: in addition to outperforming the (iterative) SIS for the Cox model, the new method can also accurately select the effective variables for probit, proportional odds and the AFT models, amongst which, to the best of our knowledge, has been studied under the ultra high-dimensional context on a case-by-case basis. Our unified Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) method was also applied to analyse Diffuse large-B-cell lymphoma data, which discovered genes that may be overlooked yet be influential. This finding itself can potentially be of scientific importance.