Efficient Estimation for the Accelerated Failure Time Model

The accelerated failure time model provides a natural formulation of the effects of covariates on potentially censored response variable. The existing semiparametric estimators are computationally intractable and statistically inefficient. In this article we propose an approximate nonparametric maximum likelihood method for the accelerated failure time model with possibly time-dependent covariates. We estimate the regression parameters by maximizing a kernel-smoothed profile likelihood function. The maximization can be achieved through conventional gradient-based search algorithms. The resulting estimators are consistent and asymptotically normal. The limiting covariance matrix attains the semiparametric efficiency bound and can be consistently estimated. We also provide a consistent estimator for the error distribution. Extensive simulation studies demonstrate that the asymptotic approximations are accurate in practical situations and the new estimators are considerably more efficient than the existing ones. Illustrations with clinical and epidemiologic studies are provided.