Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates

Based on Stute’s weighted least squares method, we consider the estimate procedures for the accelerated failure time (AFT) model with high dimensional covariates. We use Kaplan–Meier weights and Stute’s estimator to account for censoring in least squares estimation. We consider two regularization approaches, the least absolute shrinkage and selection operator (LASSO) and minimax concave penalty (MCP) for estimation and variable selection in the AFT model. Our work includes the following contributions: (1) we adjust the penalty term in the objective function and show that this adjustment is crucial for the AFT model when the scales of covariates are heterogeneous; (2) with this adjustment, we also get a desired property for LASSO estimator in the AFT model, just like the uncensored case; (3) we replace a key assumption required in the high dimensional AFT model with a set of conditions which essentially require the fraction of censored data to be small; (4) we get selection consistency of MCP in the AFT model.