The Dantzig variable selector has recently emerged as an powerful tool for fitting regularized regression models.A key advantage is that it does not pertain to a particular likelihood or objective function,as opposed to the existing penalized likelihood methods,and hence has the potential for wide applications.To our knowledge,all the Dantzig selector work has been performed with fully observed response variables.This paper proposes a new class of adaptive Dantzig variable selectors for linear regression models when the response variable is subject to right censoring.