An improved variable selection procedure for adaptive Lasso in high-dimensional survival analysis.

Motivated by high-dimensional genomic studies, we develop an improved procedure for adaptive Lasso in high-dimensional survival analysis. The proposed procedure effectively reduces the false discoveries while successfully maintaining the false negative proportions, which improves the existing adaptive Lasso procedures. The implementation of the proposed procedure is straightforward and it is sufficiently flexible to accommodate large-scale problems where traditional procedures are impractical. To quantify the uncertainty of variable selection and control the family-wise error rate, a multiple sample-splitting based testing algorithm is developed. The practical utility of the proposed procedure are examined through simulation studies. The methods developed are then applied to a multiple myeloma data set.