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On Estimation and Tests of Time‐Varying Effects in the Proportional Hazards Model

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  • Thomas H. Scheike
  • Torben Martinussen

Abstract

. Cox's proportional hazards model is routinely used in many applied fields, some times, however, with too little emphasis on the fit of the model. In this paper, we suggest some new tests for investigating whether or not covariate effects vary with time. These tests are a natural and integrated part of an extended version of the Cox model. An important new feature of the suggested test is that time constancy for a specific covariate is examined in a model, where some effects of other covariates are allowed to vary with time and some are constant; thus making successive testing of time‐dependency possible. The proposed techniques are illustrated with the well‐known Mayo liver disease data, and a small simulation study investigates the finite sample properties of the tests.

Suggested Citation

  • Thomas H. Scheike & Torben Martinussen, 2004. "On Estimation and Tests of Time‐Varying Effects in the Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 51-62, March.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:1:p:51-62
    DOI: 10.1111/j.1467-9469.2004.00372.x
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    Cited by:

    1. Tobias Bluhmki & Dennis Dobler & Jan Beyersmann & Markus Pauly, 2019. "The wild bootstrap for multivariate Nelson–Aalen estimators," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 97-127, January.
    2. Sun, Liuquan & Zhu, Liang & Sun, Jianguo, 2009. "Regression analysis of multivariate recurrent event data with time-varying covariate effects," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2214-2223, November.
    3. Korakot Wichitsa-nguan & Henning Läuter & Hannelore Liero, 2016. "Estimability in Cox models," Statistical Papers, Springer, vol. 57(4), pages 1121-1140, December.
    4. P. Saha & P. J. Heagerty, 2010. "Time-Dependent Predictive Accuracy in the Presence of Competing Risks," Biometrics, The International Biometric Society, vol. 66(4), pages 999-1011, December.
    5. Zhengnan Huang & Hongjiu Zhang & Jonathan Boss & Stephen A Goutman & Bhramar Mukherjee & Ivo D Dinov & Yuanfang Guan & for the Pooled Resource Open-Access ALS Clinical Trials Consortium, 2017. "Complete hazard ranking to analyze right-censored data: An ALS survival study," PLOS Computational Biology, Public Library of Science, vol. 13(12), pages 1-21, December.
    6. Marc Ditzhaus & Arnold Janssen, 2020. "Bootstrap and permutation rank tests for proportional hazards under right censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 493-517, July.
    7. Bhattacharjee, Arnab, 2009. "Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity," SIRE Discussion Papers 2009-22, Scottish Institute for Research in Economics (SIRE).
    8. Guanghui Wei & Douglas E. Schaubel, 2008. "Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards," Biometrics, The International Biometric Society, vol. 64(3), pages 724-732, September.
    9. Daniel A. Powers, 2010. "Assessing Group Differences in Estimated Baseline Survivor Functions From Cox Proportional Hazards Models," Sociological Methods & Research, , vol. 39(2), pages 157-187, November.
    10. Möst Lisa & Hothorn Torsten, 2015. "Conditional Transformation Models for Survivor Function Estimation," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 23-50, May.
    11. Wang, Qizhen & Zhu, Yingming & Wang, Yudong, 2017. "The effects of oil shocks on export duration of China," Energy, Elsevier, vol. 125(C), pages 55-61.
    12. Bieszk-Stolorz Beata, 2015. "Geometric Method of Determining Hazard for the Continuous Survival Function," Folia Oeconomica Stetinensia, Sciendo, vol. 15(1), pages 22-33, June.

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