Empirical likelihood inference for the accelerated failure time model. (English) Zbl 1209.62091
Summary: Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by M. Fygenson and Y. Ritov [Ann. Stat. 22, No. 2, 732–746 (1994; Zbl 0807.62032)]. However, there is a serious under-coverage problem for small sample sizes. We derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order 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.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G15 | Nonparametric tolerance and confidence regions |
| 65C60 | Computational problems in statistics (MSC2010) |
Keywords:
average length; confidence interval/region; coverage probability; monotone estimating equation; right censoringCitations:
Zbl 0807.62032Software:
emplikReferences:
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