Efficient estimation for functional accelerated failure time models

Abstract

We propose a functional accelerated failure time model to characterize the effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the bundled parameters cause immense numerical difficulties, but they also result in new challenges in theoretical development. By developing a general theoretical framework, we overcome the challenges arising from the bundled parameters and derive the convergence rate of the proposed estimator. Additionally, we prove that the finite-dimensional estimator is root- consistent, asymptotically normal and achieves the semiparametric information bound. Furthermore, we demonstrate the nonparametric optimality of the functional estimator and construct the asymptotic simultaneous confidence band. The proposed inference procedures are evaluated by extensive simulation studies and illustrated with an application to the National Health and Nutrition Examination Survey data.