  In this paper, we propose two variable selection methods for adjusting the
censoring information for survival times, such as the restricted mean survival
time. To adjust for the influence of censoring, we consider an inverse survival
probability weighting (ISPW) for subjects with events. We derive a least
absolute shrinkage and selection operator (lasso)-type variable selection
method, which considers an inverse weighting for of the squared losses, and an
information criterion-type variable selection method, which applies an inverse
weighting of the survival probability to the power of each density function in
the likelihood function. We prove the consistency of the ISPW lasso estimator
and the maximum ISPW likelihood estimator. The performance of the ISPW lasso
and ISPW information criterion are evaluated via a simulation study with six
scenarios, and then their variable selection ability is demonstrated using data
from two clinical studies. The results confirm that ISPW lasso and the ISPW
likelihood function produce good estimation accuracy and consistent variable
selection. We conclude that our two proposed methods are useful variable
selection tools for adjusting the censoring information for survival time
analyses.
