Rank Inferences for The Accelerated Failure Time Models

Abstract

By linearly relating the logarithm of survival time to the covariates, the semi-parametric accelerated failure time model is often used to examine the covariate effect, providing easy and direct interpretation. In some applications, the assumption that the covariate effect is linear and constant may be too restrictive. Hence it is desirable to develop more flexible models incorporating nonlinear or varying covariate effects. We consider the partially linear and varying coefficients accelerated failure time models for the analysis of right censored data. Rank-based inferential procedures along with the kernel smoothing are proposed. Asymptotic normality of proposed estimators is established. In computation, the procedures can be implemented by linear programming and a cross validation method is also proposed to choose the smoothing parameter. Furthermore, a resampling scheme, which perturbs the objective function repeatedly, is developed to estimate the asymptotic covariance matrix. In addition, variable selection for the partially linear model is involved.