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Empirical likelihood confidence intervals for regression parameters of the survival rate

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  • Yichuan Zhao
  • Song Yang

Abstract

The survival probability of patients plays an important role in biomedical settings. Based on the Jung [(1996), ‘Regression Analysis for Long-Term Survival Rate’, Biometrika, 83, 227–232] regression model for survival probability, Zhao [(2005), ‘Regression Analysis for Long-Term Survival Rate Via Empirical Likelihood’, Journal of Nonparametric Statistics, 17, 995–1007] developed an empirical likelihood (EL) confidence region for the vector of regression parameters. However, the proposed EL method does not work for a subset of regression parameters. In this paper, we develop EL confidence regions for any subset or a linear combination of the vectors of the regression parameters under the regression model. We propose two kinds of confidence intervals for the survival rate of a patient with the given covariates. A simulation study is carried out to compare the proposed method with the normal approximation-based method and nonparametric bootstrap method. Finally, we compare the proposed procedure with the existing method using a clinical trial data set.

Suggested Citation

  • Yichuan Zhao & Song Yang, 2012. "Empirical likelihood confidence intervals for regression parameters of the survival rate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 59-70.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:59-70
    DOI: 10.1080/10485252.2011.621024
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    Cited by:

    1. Faysal Satter & Yichuan Zhao & Ni Li, 2024. "Empirical likelihood inference for the panel count data with informative observation process," Statistical Papers, Springer, vol. 65(5), pages 3039-3061, July.
    2. Yu, Xue & Zhao, Yichuan, 2019. "Empirical likelihood inference for semi-parametric transformation models with length-biased sampling," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 115-125.
    3. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    4. Xue Yu & Yichuan Zhao, 2019. "Jackknife empirical likelihood inference for the accelerated failure time model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 269-288, March.

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