Pretest and shrinkage estimation strategies in accelerated failure time model

Abstract

This paper focuses on the accelerated failure time model which is often suggested as an alternative to the Cox proportional hazards model. We propose pretest and shrinkage estimation methods for estimating the regression parameters in the accelerated failure time model for right-censored data when some of the parameters shrink to a restricted subspace. Shrinkage estimators take information from the unrestricted model and provide an efficient estimate of the regression parameters by shrinking the unrestricted estimate toward the restricted model estimate. This technique increases the bias in the estimation process but reduces the overall mean-squared error, which offsets the bias. We show that if the shrinkage dimension exceeds two, the risk of the shrinkage estimator is strictly less than that of the maximum-likelihood estimator. Extensive numerical studies are conducted to evaluate the performance of the pretest and shrinkage estimators. An empirical application is provided to illustrate the practical usefulness of the proposed estimators.