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Empirical likelihood inference for the accelerated failure time model

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  • Zhao, Yichuan

Abstract

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 Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the 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.

Suggested Citation

  • Zhao, Yichuan, 2011. "Empirical likelihood inference for the accelerated failure time model," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 603-610, May.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:603-610
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    Cited by:

    1. Han-Ying Liang & Jacobo Uña-Álvarez, 2012. "Empirical likelihood for conditional quantile with left-truncated and dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 765-790, August.
    2. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
    3. Longlong Huang & Karen Kopciuk & Xuewen Lu, 2018. "Smoothed Jackknife Empirical Likelihood for Weighted Rank Regression with Censored Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 48-67, April.

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