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Empirical likelihood for linear transformation models with interval-censored failure time data

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  • Zhang, Zhigang
  • Zhao, Yichuan

Abstract

For regression analysis of interval-censored failure time data, Zhang et al. (2005) [40] proposed an estimating equation approach to fit linear transformation models. In this paper, we develop two empirical likelihood (EL) inference approaches for the regression parameters based on the generalized estimating equations. The limiting distributions of log-empirical likelihood ratios are derived and empirical likelihood confidence intervals for any specified component of regression parameters are obtained. We carry out extensive simulation studies to compare the proposed methods with the method discussed by Zhang et al. (2005) [40]. The simulation results demonstrate that the EL and jackknife EL methods for linear transformation models have better performance than the existing normal approximation method based on coverage probability of confidence intervals in most cases, and they enable us to overcome an under-coverage problem for the confidence intervals of the regression parameters using a normal approximation when sample sizes are small and right censoring is heavy. Two real data examples are provided to illustrate our procedures.

Suggested Citation

  • Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:398-409
    DOI: 10.1016/j.jmva.2013.01.003
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    References listed on IDEAS

    as
    1. Chenlei Leng & Cheng Yong Tang, 2012. "Penalized empirical likelihood and growing dimensional general estimating equations," Biometrika, Biometrika Trust, vol. 99(3), pages 703-716.
    2. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    3. Cheng, Guang & Zhao, Yichuan & Li, Bo, 2012. "Empirical likelihood inferences for the semiparametric additive isotonic regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 172-182.
    4. Liang Peng & Yongcheng Qi & Ingrid Van Keilegom, 2012. "Jackknife empirical likelihood method for copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 74-92, March.
    5. Peter Bacchetti & Christopher Quale, 2002. "Generalized Additive Models with Interval-Censored Data and Time-Varying Covariates: Application to Human Immunodeficiency Virus Infection in Hemophiliacs," Biometrics, The International Biometric Society, vol. 58(2), pages 443-447, June.
    6. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    7. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    8. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    9. Yang, Hanfang & Zhao, Yichuan, 2012. "Smoothed empirical likelihood for ROC curves with censored data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 254-263.
    10. Peng, Liang & Qi, Yongcheng & Van Keilegom, Ingrid, 2012. "Jackknife empirical likelihood method for copulas," LIDAM Reprints ISBA 2012013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Feng, Huijun & Peng, Liang, 2012. "Jackknife empirical likelihood tests for error distributions in regression models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 63-75.
    12. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    13. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    14. Wen Yu & Yunting Sun & Ming Zheng, 2011. "Empirical likelihood method for linear transformation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 331-346, April.
    15. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2008. "Empirical likelihood for non-degenerate U-statistics," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 599-607, April.
    16. Yang, Hanfang & Zhao, Yichuan, 2013. "Smoothed jackknife empirical likelihood inference for the difference of ROC curves," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 270-284.
    17. Cheng Yong Tang & Chenlei Leng, 2010. "Penalized high-dimensional empirical likelihood," Biometrika, Biometrika Trust, vol. 97(4), pages 905-920.
    18. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 137-151, January.
    19. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
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    3. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Aug 2024.
    4. Xiaohui Yuan & Huixian Li & Tianqing Liu, 2021. "Empirical likelihood inference for rank regression with doubly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 25-73, March.
    5. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Zhouping Li & Jinfeng Xu & Wang Zhou, 2016. "On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 49-69, March.
    7. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. 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.
    9. Hui-Ling Lin & Zhouping Li & Dongliang Wang & Yichuan Zhao, 2017. "Jackknife empirical likelihood for the error variance in linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 151-166, April.
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    12. Du, Mingyue & Li, Huiqiong & Sun, Jianguo, 2021. "Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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