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Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models

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  • Z. JIN
  • D. Y. LIN
  • Z. YING

Abstract

. Multivariate failure time data arises when each study subject can potentially ex‐perience several types of failures or recurrences of a certain phenomenon, or when failure times are sampled in clusters. We formulate the marginal distributions of such multivariate data with semiparametric accelerated failure time models (i.e. linear regression models for log‐transformed failure times with arbitrary error distributions) while leaving the dependence structures for related failure times completely unspecified. We develop rank‐based monotone estimating functions for the regression parameters of these marginal models based on right‐censored observations. The estimating equations can be easily solved via linear programming. The resultant estimators are consistent and asymptotically normal. The limiting covariance matrices can be readily estimated by a novel resampling approach, which does not involve non‐parametric density estimation or evaluation of numerical derivatives. The proposed estimators represent consistent roots to the potentially non‐monotone estimating equations based on weighted log‐rank statistics. Simulation studies show that the new inference procedures perform well in small samples. Illustrations with real medical data are provided.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:scjsta:v:33:y:2006:i:1:p:1-23
    DOI: 10.1111/j.1467-9469.2005.00487.x
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    Cited by:

    1. 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.
    2. Bo Liu & Wenbin Lu & Jiajia Zhang, 2014. "Accelerated intensity frailty model for recurrent events data," Biometrics, The International Biometric Society, vol. 70(3), pages 579-587, September.
    3. Wenjing Yin & Sihai Dave Zhao & Feng Liang, 2022. "Bayesian penalized Buckley-James method for high dimensional bivariate censored regression models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 282-318, April.
    4. Liya Fu & Zhuoran Yang & Yan Zhou & You-Gan Wang, 2021. "An efficient Gehan-type estimation for the accelerated failure time model with clustered and censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 679-709, October.
    5. Peng Liu & Yijian Huang & Kwun Chuen Gary Chan & Ying Qing Chen, 2023. "Semiparametric Trend Analysis for Stratified Recurrent Gap Times Under Weak Comparability Constraint," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 455-474, July.
    6. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    7. Chen, Pengcheng & Zhang, Jiajia & Zhang, Riquan, 2013. "Estimation of the accelerated failure time frailty model under generalized gamma frailty," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 171-180.
    8. 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.
    9. Jin, Zhezhen & He, Wenqing, 2016. "Local linear regression on correlated survival data," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 285-294.

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