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IPCW Estimator for Kendall's Tau under Bivariate Censoring

Author

Listed:
  • Lakhal Lajmi

    (Université Laval)

  • Rivest Louis-Paul

    (Université Laval)

  • Beaudoin David

    (Université Laval)

Abstract

We investigate the nonparametric estimation of Kendall's coefficient of concordance, ?, for measuring the association between two variables under bivariate censoring. The proposed estimator is a modification of the estimator introduced by Oakes (1982), using a Horvitz-Thompson-type correction for the pairs that are not orderable. With censored data, a pair is orderable if one can establish whether the uncensored pair is discordant or concordant using the data available for that pair. Our estimator is shown to be consistent and asymptotically normally distributed. A simulation study shows that the proposed estimator performs well when compared with competing alternatives. The various methods are illustrated with a real data set.

Suggested Citation

  • Lakhal Lajmi & Rivest Louis-Paul & Beaudoin David, 2009. "IPCW Estimator for Kendall's Tau under Bivariate Censoring," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-22, February.
    • Handle: RePEc:bpj:ijbist:v:5:y:2009:i:1:n:8
    DOI: 10.2202/1557-4679.1121
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    References listed on IDEAS

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    1. Nan, Bin & Lin, Xihong & Lisabeth, Lynda D. & Harlow, Sioban D., 2006. "Piecewise Constant Cross-Ratio Estimation for Association of Age at a Marker Event and Age at Menopause," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 65-77, March.
    2. Manatunga, Amita K. & Oakes, David, 1996. "A Measure of Association for Bivariate Frailty Distributions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 60-74, January.
    3. Adin-Cristian Andrei & Susan Murray, 2006. "Estimating the quality-of-life-adjusted gap time distribution of successive events subject to censoring," Biometrika, Biometrika Trust, vol. 93(2), pages 343-355, June.
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    Cited by:

    1. Lajmi Lakhal-Chaieb & Richard J. Cook & Xihong Lin, 2010. "Inverse Probability of Censoring Weighted Estimates of Kendall's τ for Gap Time Analyses," Biometrics, The International Biometric Society, vol. 66(4), pages 1145-1152, December.
    2. Austin, Matthew D. & Betensky, Rebecca A., 2014. "Eliminating bias due to censoring in Kendall’s tau estimators for quasi-independence of truncation and failure," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 16-26.
    3. Hsieh, Jin-Jian, 2010. "Estimation of Kendall's tau from censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1613-1621, June.
    4. Ruosha Li & Yu Cheng & Qingxia Chen & Jason Fine, 2017. "Quantile association for bivariate survival data," Biometrics, The International Biometric Society, vol. 73(2), pages 506-516, June.

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