Skip to main content
SpringerLink
Log in

Empirical likelihood inference for censored median regression with weighted empirical hazard functions

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In recent years, median regression models have been shown to be useful for analyzing a variety of censored survival data in clinical trials. For inference on the regression parameter, there have been a variety of semiparametric procedures. However, the accuracy of such procedures in terms of coverage probability can be quite low when the censoring rate is heavy. In this paper, based on weighted empirical hazard functions, we apply an empirical likelihood (EL) ratio method to the median regression model with censoring data and derive the limiting distribution of EL ratio. Confidence region for the regression parameter can then be obtained accordingly. Furthermore, we compared the proposed method with the standard method through extensive simulation studies. The proposed method almost always outperformed the existing method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bassett G., Koenker R. (1978). Asymptotic theory of least absolute regression. Journal of the American Statistical Association 73, 618–622

    Article  MATH  MathSciNet  Google Scholar 

  • Buckley J., James I. (1979). Linear regression with censored data. Biometrika 66, 429–436

    Article  MATH  Google Scholar 

  • DiCiccio T.J., Hall P., Romano J. (1991). Empirical likelihood is Bartlett-correctable. The Annnals of Statistics 19, 1053–1061

    Article  MATH  MathSciNet  Google Scholar 

  • Einmahl J.H., McKeague I.W. (1999). Confidence tubes for multiple quantile plots via empirical likelihood. The Annals of Statistics 27, 1348–1367

    Article  MATH  MathSciNet  Google Scholar 

  • Glenn, N. L., Zhao, Y. (2006). Weighted empirical likelihood estimates and their robustness properties. Computational Statistics and Data Analysis, in press.

  • Hall P., La Scala B. (1990). Methodology and algorithms of empirical likelihood. International Statistical Review 58, 109–127

    Article  MATH  Google Scholar 

  • Hollander M., McKeague I.W., Yang J. (1997). Likelihood ratio-based confidence bands for survival functions. Journal of the American Statistical Association 92, 215–226

    Article  MATH  MathSciNet  Google Scholar 

  • Jung S. (1996). Quasi-likelihood for median regression models. Journal of the American Statistical Association 91, 251–257

    Article  MATH  MathSciNet  Google Scholar 

  • Koenker R., Bassett G. (1978). Regression quantiles. Econometrica 46, 33–50

    Article  MATH  MathSciNet  Google Scholar 

  • Koul H., Susarla V., Van Ryzin J. (1981). Regression analysis with randomly right-censored data. The Annals of Statistics 9, 1276–1288

    Article  MATH  MathSciNet  Google Scholar 

  • Lai T.L., Ying Z. (1988). Stochastic integrals of empirical-type processes with applications to censored regression. Journal of Multivariate Analysis 27, 334–358

    Article  MATH  MathSciNet  Google Scholar 

  • Lai T.L., Ying Z. (1992). Linear rank statistics in regression analysis with censored or truncated data. Journal of Multivariate Analysis 40, 13–45

    Article  MATH  MathSciNet  Google Scholar 

  • Li G., Van Keilegom I. (2002). Likelihood ratio confidence bands in nonparametric regression with censored data. Scandinavian Journal of Statistics 29, 547–562

    Article  MATH  MathSciNet  Google Scholar 

  • Li G., Wang Q.H. (2003). Empirical likelihood regression analysis for right censored data. Statistica Sinica 13, 51–68

    MATH  MathSciNet  Google Scholar 

  • McKeague I.W., Subramanian S., Sun Y. (2001). Median regression and the missing information principle. Journal of Nonparametric Statistics 13, 709–727

    Article  MATH  MathSciNet  Google Scholar 

  • McKeague I.W., Zhao Y. (2002). Simultaneous confidence bands for ratios of survival functions via empirical likelihood. Statistics and Probability Letters 60, 405–415

    Article  MATH  MathSciNet  Google Scholar 

  • McKeague I.W., Zhao Y. (2005). Comparing distribution function vial empirical likelihood. The International Journal of Biostatistics 5, 1–20

    MathSciNet  Google Scholar 

  • McKeague I.W., Zhao Y. (2006). Width-scaled confidence bands for survival functions. Statistics and Probability Letters 76, 327–339

    Article  MATH  MathSciNet  Google Scholar 

  • Owen A. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237–249

    Article  MATH  MathSciNet  Google Scholar 

  • Owen A. (1990). Empirical likelihood and confidence regions. The Annals of Statistics 18, 90–120

    Article  MATH  MathSciNet  Google Scholar 

  • Parzen M.I., Wei L.J., Ying Z. (1994). A resampling method based on pivotal functions. Biometrika 81, 341–350

    Article  MATH  MathSciNet  Google Scholar 

  • Powell J.L. (1984). Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25, 303–325

    Article  MATH  MathSciNet  Google Scholar 

  • Powell J.L. (1986). Censored regression quantiles. Journal of Econometrics 32, 143–155

    Article  MATH  MathSciNet  Google Scholar 

  • Qin G., Jing B.Y. (2001). Empirical likelihood for censored linear regression. Scandinavian Journal of Statistics 28, 661–673

    Article  MATH  MathSciNet  Google Scholar 

  • Qin G., Tsao M. (2003). Empirical likelihood inference for median regression models for censored survival data. Journal of Multivariate Analysis 85, 416–430

    Article  MATH  MathSciNet  Google Scholar 

  • Rao J.N.K., Scott A.J. (1981). The analysis of categorical data from complex sample surveys: chi-squared tests for goodness of fit and independence in two-way tables. Journal of the American Statistical Association 76, 221–230

    Article  MATH  MathSciNet  Google Scholar 

  • Ritov Y. (1990). Estimation in a linear regression model with censored data. The Annals of Statistics 18, 303–328

    Article  MATH  MathSciNet  Google Scholar 

  • Tsiatis A.A. (1990). Estimating regression parameters using linear rank tests for censored data. The Annals of Statistics 18, 354–372

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Q.H., Jing B.Y. (1999). Empirical likelihood for partial linear models with fixed designs. Statistics and Probability Letters 41, 425–433

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Q.H., Rao J.N.K. (2001). Empirical likelihood for linear regression models under imputation for missing responses. The Canadian Journal of Statistics 29, 597–608

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Q.H., Rao J.N.K. (2002). Empirical likelihood-based inference in linear errors-in-covariables models with validation data. Biometrika 89, 345-358

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Q.H., Wang J.L. (2001). Inference for the mean difference in the two-sample random censorship model. Journal of Multivariate Analysis 79, 295–315

    Article  MATH  MathSciNet  Google Scholar 

  • Wei L.J., Ying Z., Lin D.Y. (1990). Linear regression analysis of censored survival data based on rank tests. Biometrika 19, 845–851

    Article  MathSciNet  Google Scholar 

  • Yang S. (1997a). A generalization of the product-limit estimator with an application to censored regression. The Annals of Statistics 25, 1088-1108

    Article  MATH  Google Scholar 

  • Yang S. (1997b). Extended weighted log-rank estimating functions in censored regression. Journal of the American Statistical Association 92, 977–984

    Article  MATH  Google Scholar 

  • Yang S. (1999). Censored median regression using weighted empirical survival and hazard functions. Journal of the American Statistical Association 94, 137–145

    Article  MATH  MathSciNet  Google Scholar 

  • Yang S., Prentice R.L. (2005). Semiparametric analysis of short term and long term relative risks with two sample survival data. Biometrika 92, 1–17

    Article  MATH  MathSciNet  Google Scholar 

  • Ying Z. (1993). A large sample study of rank estimation for censored regression data. The Annals of Statistics 21, 76–99

    Article  MATH  MathSciNet  Google Scholar 

  • Ying Z., Jung S.H., Wei L.J. (1995). Survival analysis with median regression models. Journal of the American Statistical Association 90, 178–184

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao Y. (2005). Regression analysis for long-term survival rate via empirical likelihood. Journal of Nonparametric Statistics 17, 995–1007

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao Y., Hsu Y.S. (2005). Semiparametric analysis for additive risk model via empirical likelihood. Communications in Statistics–Simulation and Computation 34, 135–143

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao Y., Qin G. (2006). Inference for the mean residual life function via empirical likelihood. Communications in Statistics—Theory and Methods 35, 1025–1036

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Yichuan Zhao

  2. Office of Biostatistics Research, National Heart, Lung, and Blood Institute, 6701 Rockledge Drive, MSC 7938, Bethesda, MD, 20892, USA

    Song Yang

Authors
  1. Yichuan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Song Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yichuan Zhao.

About this article

Cite this article

Zhao, Y., Yang, S. Empirical likelihood inference for censored median regression with weighted empirical hazard functions. AISM 60, 441–457 (2008). https://doi.org/10.1007/s10463-006-0110-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10463-006-0110-4

Keywords

Search

Navigation