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Tutorial: Survival Estimation for Cox Regression Models with Time-Varying Coe?cients Using SAS and R

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  • Thomas, Laine
  • Reyes, Eric M.

Abstract

Survival estimates are an essential compliment to multivariable regression models for time-to-event data, both for prediction and illustration of covariate effects. They are easily obtained under the Cox proportional-hazards model. In populations defined by an initial, acute event, like myocardial infarction, or in studies with long-term followup, the proportional-hazards assumption of constant hazard ratios is frequently violated. One alternative is to fit an interaction between covariates and a prespecified function of time, implemented as a time-dependent covariate. This effectively creates a time-varying coefficient that is easily estimated in software such as SAS and R. However, the usual programming statements for survival estimation are not directly applicable. Unique data manipulation and syntax is required, but is not well documented for either software. This paper offers a tutorial in survival estimation for the time-varying coefficient model, implemented in SAS and R. We provide a macro coxtvc to facilitate estimation in SAS where the current functionality is more limited. The macro is validated in simulated data and illustrated in an application.

Suggested Citation

  • Thomas, Laine & Reyes, Eric M., 2014. "Tutorial: Survival Estimation for Cox Regression Models with Time-Varying Coe?cients Using SAS and R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(c01).
    • Handle: RePEc:jss:jstsof:v:061:c01
    DOI: http://hdl.handle.net/10.18637/jss.v061.c01
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    References listed on IDEAS

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    1. Scheike, Thomas H. & Zhang, Mei-Jie, 2011. "Analyzing Competing Risk Data Using the R timereg Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i02).
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    Cited by:

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    2. Zijing Yang & Chengfeng Zhang & Yawen Hou & Zheng Chen, 2023. "Analysis of dynamic restricted mean survival time based on pseudo‐observations," Biometrics, The International Biometric Society, vol. 79(4), pages 3690-3700, December.
    3. Mark Pagell & Mary Parkinson & Anthony Veltri & John Gray & Frank Wiengarten & Michalis Louis & Brian Fynes, 2020. "The Tension Between Worker Safety and Organization Survival," Management Science, INFORMS, vol. 66(10), pages 4863-4878, October.
    4. Irfan Kanat & Yili Hong & T. S. Raghu, 2018. "Surviving in Global Online Labor Markets for IT Services: A Geo-Economic Analysis," Information Systems Research, INFORMS, vol. 29(4), pages 893-909, December.
    5. Amy Y. Li, 2017. "Dramatic Declines in Higher Education Appropriations: State Conditions for Budget Punctuations," Research in Higher Education, Springer;Association for Institutional Research, vol. 58(4), pages 395-429, June.
    6. Chen, Songnian, 2019. "Quantile regression for duration models with time-varying regressors," Journal of Econometrics, Elsevier, vol. 209(1), pages 1-17.
    7. Jörg Stolz & Anaïd Lindemann & Jean-Philippe Antonietti, 2019. "Sociological explanation and mixed methods: the example of the Titanic," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(3), pages 1623-1643, May.
    8. Arora, Gaurav & Feng, Hongli & Hennessy, David A. & Loesch, Charles R. & Kvas, Susan, 2021. "The impact of production network economies on spatially-contiguous conservation– Theoretical model with evidence from the U.S. Prairie Pothole Region," Journal of Environmental Economics and Management, Elsevier, vol. 107(C).

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