Empirical Likelihood for Censored Linear Regression and Variable Selection.

Abstract

The linear regression model for right censored data, also known as the accelerated failure time model using the logarithm of survival time as the response variable, is a useful alternative to the Cox proportional hazards model. Empirical likelihood as a nonparametric approach has been demonstrated to have many desirable merits thanks to its robustness against model misspecification. However, the linear regression model with right censored data cannot directly benefit from the empirical likelihood for inferences mainly due to dependent elements in estimating equations of the conventional approach. In this paper, we propose an empirical likelihood approach with a new estimating equation for linear regression with right censored data. A nested coordinate algorithm with majorization is used for solving the optimization problems with nondifferentiable objective function. We show that the Wilks theorem holds for the new empirical likelihood. We also consider the variable selection problem with empirical likelihood when the number of predictors can be large. Since the new estimating equation is nondifferentiable, a quadratic approximation is applied to study the asymptotic properties of penalized empirical likelihood. We prove the oracle properties and evaluate the properties with simulated data. We apply our method to a SEER small intestine cancer dataset.