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Time-dependent cross ratio estimation for bivariate failure times

Author

Listed:
  • Tianle Hu
  • Bin Nan
  • Xihong Lin
  • James M. Robins

Abstract

In the analysis of bivariate correlated failure time data, it is important to measure the strength of association among the correlated failure times. One commonly used measure is the cross ratio. Motivated by Cox's partial likelihood idea, we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times. We show that the proposed estimator is consistent and asymptotically normal. Its finite sample performance is examined using simulation studies, and it is applied to the Australian twin data. Copyright 2011, Oxford University Press.

Suggested Citation

  • Tianle Hu & Bin Nan & Xihong Lin & James M. Robins, 2011. "Time-dependent cross ratio estimation for bivariate failure times," Biometrika, Biometrika Trust, vol. 98(2), pages 341-354.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:341-354
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    File URL: http://hdl.handle.net/10.1093/biomet/asr005
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    Citations

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    Cited by:

    1. Tianle Hu & Bin Nan & Xihong Lin, 2019. "Proportional cross-ratio model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 480-506, July.
    2. Tian Dai & Ying Guo & Limin Peng & Amita K. Manatunga, 2018. "A local agreement pattern measure based on hazard functions for survival outcomes," Biometrics, The International Biometric Society, vol. 74(1), pages 86-99, March.
    3. Steven Abrams & Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2020. "Nonparametric estimation of the cross ratio function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 771-801, June.
    4. Jose S. Romeo & Renate Meyer & Diego I. Gallardo, 2018. "Bayesian bivariate survival analysis using the power variance function copula," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 355-383, April.
    5. Ruosha Li & Xuelin Huang & Jorge Cortes, 2016. "Quantile residual life regression with longitudinal biomarker measurements for dynamic prediction," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 755-773, November.
    6. Jing Ning & Karen Bandeen-Roche, 2014. "Estimation of time-dependent association for bivariate failure times in the presence of a competing risk," Biometrics, The International Biometric Society, vol. 70(1), pages 10-20, March.
    7. 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.
    8. Lajmi Lakhal-Chaieb & Thierry Duchesne, 2017. "Association measures for bivariate failure times in the presence of a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 517-532, October.

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