Empirical likelihood inference for the accelerated failure time model

Accelerated failure time (AFT) models are useful regression tools to study the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among them, Fygenson and Ritov (1994) proposed an estimating equation which is monotone in the regression parameter and has some excellent properties. However, there exists a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of empirical log-likelihood ratio for the regression parameter based on the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method.