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Quantile regression analysis of case-cohort data

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

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 122 (2013)
    Issue (Month): C ()
    Pages: 20-34

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    Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:20-34

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    Related research

    Keywords: Case-cohort design; Counting process; Estimating equation; Random weighting; Simple random sampling; Uniform consistency; Weak convergence;

    References

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    1. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    2. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    3. Wenbin Lu & Anastasios A. Tsiatis, 2006. "Semiparametric transformation models for the case-cohort study," Biometrika, Biometrika Trust, vol. 93(1), pages 207-214, March.
    4. 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.
    5. Kani Chen, 2001. "Generalized case-cohort sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 791-809.
    6. 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.
    7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    8. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
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