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Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood

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  • YANQING SUN
  • RAJESHWARI SUNDARAM
  • YICHUAN ZHAO

Abstract

. The Cox model with time‐dependent coefficients has been studied by a number of authors recently. In this paper, we develop empirical likelihood (EL) pointwise confidence regions for the time‐dependent regression coefficients via local partial likelihood smoothing. The EL simultaneous confidence bands for a linear combination of the coefficients are also derived based on the strong approximation methods. The EL ratio is formulated through the local partial log‐likelihood for the regression coefficient functions. Our numerical studies indicate that the EL pointwise/simultaneous confidence regions/bands have satisfactory finite sample performances. Compared with the confidence regions derived directly based on the asymptotic normal distribution of the local constant estimator, the EL confidence regions are overall tighter and can better capture the curvature of the underlying regression coefficient functions. Two data sets, the gastric cancer data and the Mayo Clinic primary biliary cirrhosis data, are analysed using the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:444-462
    DOI: 10.1111/j.1467-9469.2008.00634.x
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    References listed on IDEAS

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    1. Rong Liu & Yichuan Zhao, 2021. "Empirical likelihood inference for generalized additive partially linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 569-585, September.
    2. Fei Heng & Yanqing Sun & Seunggeun Hyun & Peter B. Gilbert, 2020. "Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 731-760, October.
    3. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    4. Tang, Xingyu & Li, Jianbo & Lian, Heng, 2013. "Empirical likelihood for partially linear proportional hazards models with growing dimensions," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 22-32.
    5. 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.
    6. 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.

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