Variable selection is fundamental to high-dimensional survival modeling. The regularized least squares method with appropriate penalty is a widely used method for simultaneous variable selection and coefficient estimation in linear regression, including accelerated failure time (AFT) model in survival analysis. I will discuss a variable selection technique which is based on a regularized weighted least squares method. Quadratic programming is used to solve this regularized weighted least squares objective function with  constraints and constraints that come due to the censored observations from the right censored data. This technique can be applied to survival data with  e.g. microarray data set. Simulation studies and real data example will be provided for illustration. In the beginning of this talk I will discuss the censoring effect on the Kaplan-Meier estimates when
data are generated from different skewed failure time distributions.