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Quantile regression analysis of case-cohort data


  • Zheng, Ming
  • Zhao, Ziqiang
  • Yu, Wen


Case-cohort designs provide a cost effective way to conduct epidemiological follow-up studies in which event times are the outcome variables. This paper develops a quantile regression approach to the analysis of case-cohort data. Quantile regression is a highly useful tool to delineate relationships between the outcome variable and covariates. Unbiased functional estimating equations are constructed, resulting in asymptotically unbiased estimators. Efficient algorithms based on minimizing L1-type convex functions are given. Uniform consistency and weak convergence of the resulting estimators are established. Error estimation and confidence intervals are obtained by applying a specially designed resampling procedure for case-cohort data. Simulation studies are conducted to assess the performance of the proposed method. An example is also provided for illustration.

Suggested Citation

  • Zheng, Ming & Zhao, Ziqiang & Yu, Wen, 2013. "Quantile regression analysis of case-cohort data," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 20-34.
  • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:20-34
    DOI: 10.1016/j.jmva.2013.07.004

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    References listed on IDEAS

    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Wenbin Lu & Anastasios A. Tsiatis, 2006. "Semiparametric transformation models for the case-cohort study," Biometrika, Biometrika Trust, vol. 93(1), pages 207-214, March.
    3. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    4. Michal Kulich & D.Y. Lin, 2004. "Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 832-844, January.
    5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    6. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    7. Peng, Limin & Huang, Yijian, 2008. "Survival Analysis With Quantile Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 637-649, June.
    8. Kani Chen, 2001. "Generalized case-cohort sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 791-809.
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