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Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data

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  • Douglas E. Schaubel

Abstract

Sequentially ordered multivariate failure time data are often observed in biomedical studies and inter-event, or gap, times are often of interest. Generally, standard hazard regression methods cannot be applied to the gap times because of identifiability issues and induced dependent censoring. We propose estimating equations for fitting proportional hazards regression models to the gap times. Model parameters are shown to be consistent and asymptotically normal. Simulation studies reveal the appropriateness of the asymptotic approximations in finite samples. The proposed methods are applied to renal failure data to assess the association between demographic covariates and both time until wait-listing and time from wait-listing to kidney transplantation. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Douglas E. Schaubel, 2004. "Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data," Biometrika, Biometrika Trust, vol. 91(2), pages 291-303, June.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:291-303
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    Citations

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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. Jieli Ding & Liuquan Sun, 2017. "Additive mixed effect model for recurrent gap time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 223-253, April.
    3. Jin-Jian Hsieh & A. Adam Ding & Weijing Wang, 2011. "Regression Analysis for Recurrent Events Data under Dependent Censoring," Biometrics, The International Biometric Society, vol. 67(3), pages 719-729, September.
    4. Chia-Hui Huang & Bowen Li & Chyong-Mei Chen & Weijing Wang & Yi-Hau Chen, 2017. "Subdistribution Regression for Recurrent Events Under Competing Risks: with Application to Shunt Thrombosis Study in Dialysis Patients," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 339-356, December.
    5. Kang, Fangyuan & Sun, Liuquan & Zhao, Xingqiu, 2015. "A class of transformed hazards models for recurrent gap times," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 151-167.
    6. Jean‐Yves Dauxois & Sophie Sencey, 2009. "Non‐parametric Tests for Recurrent Events under Competing Risks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 649-670, December.
    7. Kevin He & Yun Li & Panduranga S. Rao & Randall S. Sung & Douglas E. Schaubel, 2020. "Prognostic score matching methods for estimating the average effect of a non-reversible binary time-dependent treatment on the survival function," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 451-470, July.
    8. Xiaoyan Sun & Limin Peng & Yijian Huang & HuiChuan J. Lai, 2016. "Generalizing Quantile Regression for Counting Processes With Applications to Recurrent Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 145-156, March.
    9. Hong Zhu, 2014. "Non-parametric Analysis of Gap Times for Multiple Event Data: An Overview," International Statistical Review, International Statistical Institute, vol. 82(1), pages 106-122, April.
    10. Zhao, Xiaobing & Zhou, Xian, 2014. "Sufficient dimension reduction on marginal regression for gaps of recurrent events," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 56-71.
    11. Chia-Hui Huang & Yi-Hau Chen, 2017. "Regression analysis for bivariate gap time with missing first gap time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 83-101, January.
    12. Chia-Hui Huang, 2019. "Mixture regression models for the gap time distributions and illness–death processes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 168-188, January.
    13. Jie Fan & Somnath Datta, 2013. "On Mann–Whitney tests for comparing sojourn time distributions when the transition times are right censored," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 149-166, February.
    14. Poulami Maitra & Leila D. A. F. Amorim & Jianwen Cai, 2020. "Multiplicative rates model for recurrent events in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 134-157, January.
    15. Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.
    16. Sankaran, P.G. & Anisha, P., 2012. "Additive hazards models for gap time data with multiple causes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1454-1462.

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