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Multivariate failure times regression with a continuous auxiliary covariate

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  • Liu, Yanyan
  • Wu, Yuanshan
  • Zhou, Haibo

Abstract

How to take advantage of the available auxiliary covariate information when the primary covariate of interest is not measured is a frequently encountered question in biomedical study. In this paper, we consider the multivariate failure times regression analysis in which the primary covariate is assessed only in a validation set, but a continuous auxiliary covariate for it is available for all subjects in the study cohort. Under the frame of marginal hazard model, we propose to estimate the induced relative risk function in the non-validation set through kernel smoothing method and then obtain an estimated pseudo-partial likelihood function. The proposed estimator which maximizes the estimated pseudo-partial likelihood is shown to be consistent and asymptotically normal. We also give an estimator of the marginal cumulative baseline hazard function. Simulation studies are conducted to evaluate the finite sample performance of our proposed estimator. The proposed method is illustrated by analyzing a heart disease data from the Study of Left Ventricular Dysfunction (SOLVD).

Suggested Citation

  • Liu, Yanyan & Wu, Yuanshan & Zhou, Haibo, 2010. "Multivariate failure times regression with a continuous auxiliary covariate," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 679-691, March.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:3:p:679-691
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    References listed on IDEAS

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    1. Halbo Zhou & C.‐Y. Wang, 2000. "Failure time regression with continuous covariates measured with error," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 657-665.
    2. Yin, Guosheng & Li, Hui & Zeng, Donglin, 2008. "Partially Linear Additive Hazards Regression With Varying Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1200-1213.
    3. Jiancheng Jiang & Zhou Haibo, 2007. "Additive hazard regression with auxiliary covariates," Biometrika, Biometrika Trust, vol. 94(2), pages 359-369.
    4. Hu, Chengcheng & Lin, D.Y., 2004. "Semiparametric Failure Time Regression With Replicates of Mismeasured Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 105-118, January.
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    1. Chen, Yurong & Feng, Yanqin & Sun, Jianguo, 2015. "Regression analysis of multivariate current status data with auxiliary covariates under the additive hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 34-45.
    2. Xiaoping Shi & Yanyan Liu & Yuanshan Wu, 2014. "Auxiliary covariate in additive hazards regression for survival data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 101-113, March.
    3. Feifei Yan & Lin Zhu & Yanyan Liu & Jianwen Cai & Haibo Zhou, 2021. "Semiparametric regression based on quadratic inference function for multivariate failure time data with auxiliary information," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 269-299, April.
    4. Feifei Yan & Yanyan Liu & Jianwen Cai & Haibo Zhou, 2023. "Estimated quadratic inference function for correlated failure time data," Biometrics, The International Biometric Society, vol. 79(2), pages 1145-1158, June.
    5. Yanqin Feng & Yurong Chen, 2018. "Regression analysis of current status data with auxiliary covariates and informative observation times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 293-309, April.

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