A class of semi parametric regressions for the accelerated failure time model

In this paper a general class of nonparametric test statistics, which includes both linear and nonlinear rank tests for the accelerated failure time model, is inverted into estimating equations for multiple regression. For right-censored data this general class of semiparametric regression procedures includes the linear rank estimators of Tsiatis (1990), extends the Theil-Sen estimator based on Kendall's τ to multiple regression, and introduces several new families of regression methods based on inverting nonlinear rank tests. These new families include the weighted generalised logrank estimators and the weighted logit-rank estimators. Several estimators of the standard errors of the regression coefficients are given. The regression coefficient estimators are consistent and asymptotically normal with variances that can be consistently estimated. Several linear and nonlinear rank-based estimators of the regression parameters and several methods of estimating their standard errors and the corresponding confidence intervals are compared in a small sample simulation in settings with and without outliers among the covariates. In these simulations the generalised logrank estimators performed well as compared to the logrank estimators when there was no outlier among the covariates and had less bias than the logrank estimators when covariate outliers existed.