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Rank regression for analysis of clustered data: A natural induced smoothing approach

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  • Fu, Liya
  • Wang, You-Gan
  • Bai, Zhidong

Abstract

We consider rank regression for clustered data analysis and investigate the induced smoothing method for obtaining the asymptotic covariance matrices of the parameter estimators. We prove that the induced estimating functions are asymptotically unbiased and the resulting estimators are strongly consistent and asymptotically normal. The induced smoothing approach provides an effective way for obtaining asymptotic covariance matrices for between- and within-cluster estimators and for a combined estimator to take account of within-cluster correlations. We also carry out extensive simulation studies to assess the performance of different estimators. The proposed methodology is substantially much faster in computation and more stable in numerical results than the existing methods. We apply the proposed methodology to a dataset from a randomized clinical trial.

Suggested Citation

  • Fu, Liya & Wang, You-Gan & Bai, Zhidong, 2010. "Rank regression for analysis of clustered data: A natural induced smoothing approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1036-1050, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1036-1050
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    References listed on IDEAS

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    1. You-Gan Wang & Yudong Zhao, 2008. "Weighted Rank Regression for Clustered Data Analysis," Biometrics, The International Biometric Society, vol. 64(1), pages 39-45, March.
    2. You-Gan Wang & Xu Lin, 2005. "Effects of Variance-Function Misspecification in Analysis of Longitudinal Data," Biometrics, The International Biometric Society, vol. 61(2), pages 413-421, June.
    3. You-Gan Wang, 2003. "Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance," Biometrika, Biometrika Trust, vol. 90(1), pages 29-41, March.
    4. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    5. B. M. Brown & You-Gan Wang, 2005. "Standard errors and covariance matrices for smoothed rank estimators," Biometrika, Biometrika Trust, vol. 92(1), pages 149-158, March.
    6. Lynn M. Johnson & Robert L. Strawderman, 2009. "Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data," Biometrika, Biometrika Trust, vol. 96(3), pages 577-590.
    7. Bernard Rosner & Robert J. Glynn & Mei-Ling Ting Lee, 2003. "Incorporation of Clustering Effects for the Wilcoxon Rank Sum Test: A Large-Sample Approach," Biometrics, The International Biometric Society, vol. 59(4), pages 1089-1098, December.
    8. Sin-Ho Jung, 2003. "Rank-based regression with repeated measurements data," Biometrika, Biometrika Trust, vol. 90(3), pages 732-740, September.
    9. Z. Jin & D. Y. Lin & Z. Ying, 2006. "Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 1-23, March.
    10. Bernard Rosner & Robert J. Glynn & Mei-Ling T. Lee, 2006. "Extension of the Rank Sum Test for Clustered Data: Two-Group Comparisons with Group Membership Defined at the Subunit Level," Biometrics, The International Biometric Society, vol. 62(4), pages 1251-1259, December.
    11. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
    12. You-Gan Wang & Min Zhu, 2006. "Rank-based regression for analysis of repeated measures," Biometrika, Biometrika Trust, vol. 93(2), pages 459-464, June.
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    Cited by:

    1. Riina Lemponen & Denis Larocque & Jaakko Nevalainen & Hannu Oja, 2012. "Weighted rank tests and Hodges-Lehmann estimates for the multivariate two-sample location problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 977-991, December.
    2. Li, Haifen & Zhang, Jiajia & Tang, Yincai, 2012. "Induced smoothing for the semiparametric accelerated hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4312-4319.
    3. Kyu Hyun Kim & Daniel J. Caplan & Sangwook Kang, 2023. "Smoothed quantile regression for censored residual life," Computational Statistics, Springer, vol. 38(2), pages 1001-1022, June.
    4. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    5. Liya Fu & Zhuoran Yang & Fengjing Cai & You-Gan Wang, 2021. "Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis," Computational Statistics, Springer, vol. 36(2), pages 781-804, June.
    6. Wang, You-Gan & Fu, Liya, 2011. "Rank regression for accelerated failure time model with clustered and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2334-2343, July.
    7. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.

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