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Weighted Empirical Likelihood for Accelerated Life Model with Various Types of Censored Data

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  • Jian-Jian Ren

    (Statistics Program, Department of Mathematics, University of Maryland, College Park, MD 20742, USA)

  • Yiming Lyu

    (The Janssen Pharmaceutical Company of Johnson & Johnson, New Brunswick, NJ 08933, USA)

Abstract

In analysis of survival data, the Accelerated Life Model (ALM) is one of the widely used semiparametric models, and we often encounter various types of censored survival data, such as right censored data, doubly censored data, interval censored data, partly interval-censored data, etc. For complicated types of censored data, the studies of statistical inferences on the ALM are very technical and challenging mathematically, thus up to now little work has been done. In this article, we extend the concept of weighted empirical likelihood (WEL) from univariate case to multivariate case, and we apply it to the ALM, which leads to an estimation approach, called weighted maximum likelihood estimator , as well as the WEL based confidence interval for the regression parameter. Our proposed procedures are applicable to various types of censored data under a unified framework, and some simulation results are presented.

Suggested Citation

  • Jian-Jian Ren & Yiming Lyu, 2024. "Weighted Empirical Likelihood for Accelerated Life Model with Various Types of Censored Data," Stats, MDPI, vol. 7(3), pages 1-11, September.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:3:p:57-954:d:1470527
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    References listed on IDEAS

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    1. Jian‐Jian Ren, 2003. "Goodness of fit tests with interval censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 211-226, March.
    2. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    3. Mai Zhou, 2005. "Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model," Biometrika, Biometrika Trust, vol. 92(2), pages 492-498, June.
    4. Jian-Jian Ren & Tonya Riddlesworth, 2014. "Empirical likelihood bivariate nonparametric maximum likelihood estimator with right censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 913-930, October.
    5. Zhou, Mai & Li, Gang, 2008. "Empirical likelihood analysis of the Buckley-James estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 649-664, April.
    6. Jian-Jian Ren, 2001. "Weighted Empirical Likelihood Ratio Confidence Intervals for the Mean with Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 498-516, September.
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