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Survival analysis with temporal covariate effects

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  • Limin Peng
  • Yijian Huang

Abstract

We propose a natural generalization of the Cox regression model, in which the regression coefficients have direct interpretations as temporal covariate effects on the survival function. Under the conditionally independent censoring mechanism, we develop a smoothing-free estimation procedure with a set of martingale-based equations. Our estimator is shown to be uniformly consistent and to converge weakly to a Gaussian process. A simple resampling method is proposed for approximating the limiting distribution of the estimated coefficients. Second-stage inferences with time-varying coefficients are developed accordingly. Simulations and a real example illustrate the practical utility of the proposed method. Finally, we extend this proposal of temporal covariate effects to the general class of linear transformation models and also establish a connection with the additive hazards model. Copyright 2007, Oxford University Press.

Suggested Citation

  • Limin Peng & Yijian Huang, 2007. "Survival analysis with temporal covariate effects," Biometrika, Biometrika Trust, vol. 94(3), pages 719-733.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:719-733
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    File URL: http://hdl.handle.net/10.1093/biomet/asm058
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    Citations

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    Cited by:

    1. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear-Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 396-424, June.
    2. Naseri, Masoud & Baraldi, Piero & Compare, Michele & Zio, Enrico, 2016. "Availability assessment of oil and gas processing plants operating under dynamic Arctic weather conditions," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 66-82.
    3. Shuang Ji & Limin Peng & Yu Cheng & HuiChuan Lai, 2012. "Quantile Regression for Doubly Censored Data," Biometrics, The International Biometric Society, vol. 68(1), pages 101-112, March.
    4. Xiaomeng Qi & Zhangsheng Yu, 2023. "Kernel regression for cause-specific hazard models with time-dependent coefficients," Computational Statistics, Springer, vol. 38(1), pages 263-283, March.
    5. Tianyu Zhan & Douglas E. Schaubel, 2019. "Semiparametric temporal process regression of survival-out-of-hospital," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 322-340, April.
    6. J. E. Soh & Yijian Huang, 2021. "A varying-coefficient model for gap times between recurrent events," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 437-459, July.
    7. Yingye Zheng & Tianxi Cai & Janet L. Stanford & Ziding Feng, 2010. "Semiparametric Models of Time-Dependent Predictive Values of Prognostic Biomarkers," Biometrics, The International Biometric Society, vol. 66(1), pages 50-60, March.
    8. Yijian Huang, 2017. "Restoration of Monotonicity Respecting in Dynamic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 613-622, April.
    9. Jun Yan & Jian Huang, 2009. "Partly Functional Temporal Process Regression with Semiparametric Profile Estimating Functions," Biometrics, The International Biometric Society, vol. 65(2), pages 431-440, June.
    10. Guoqing Diao & Anand N. Vidyashankar & Sarah Zohar & Sandrine Katsahian, 2021. "Competing Risks Model with Short-Term and Long-Term Covariate Effects for Cancer Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 142-159, April.
    11. Glenn Heller, 2021. "The added value of new covariates to the brier score in cox survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 1-14, January.
    12. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    13. Teng Fei & John Hanfelt & Limin Peng, 2023. "Evaluating the association between latent classes and competing risks outcomes with multiphenotype data," Biometrics, The International Biometric Society, vol. 79(1), pages 488-501, March.
    14. Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
    15. Li, Ruosha & Peng, Limin, 2014. "Varying coefficient subdistribution regression for left-truncated semi-competing risks data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 65-78.

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