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Generating Survival Times Using Cox Proportional Hazards Models with Cyclic and Piecewise Time-Varying Covariates

Author

Listed:
  • Yunda Huang

    (Fred Hutchinson Cancer Research Center
    University of Washington)

  • Yuanyuan Zhang

    (Fred Hutchinson Cancer Research Center)

  • Zong Zhang

    (Carnegie Mellon University)

  • Peter B. Gilbert

    (Fred Hutchinson Cancer Research Center
    University of Washington)

Abstract

Time-to-event outcomes with cyclic time-varying covariates are frequently encountered in biomedical studies that involve multiple or repeated administrations of an intervention. In this paper, we propose approaches to generating event times for Cox proportional hazards models with both time-invariant covariates and a continuous cyclic and piecewise time-varying covariate. Values of the latter covariate change over time through cycles of interventions and its relationship with hazard differs before and after a threshold within each cycle. The simulations of data are based on inverting the cumulative hazard function and a log link function for relating the hazard function to the covariates. We consider closed-form derivations with the baseline hazard following the exponential, Weibull, or Gompertz distribution. We propose two simulation approaches: one based on simulating survival data under a single-dose regimen first before data are aggregated over multiple-dosing cycles and another based on simulating survival data directly under a multiple-dose regimen. We consider both fixed intervals and varying intervals of the drug administration schedule. The method’s validity is assessed in simulation experiments. The results indicate that the proposed procedures perform well in generating data that conform to their cyclic nature and assumptions of the Cox proportional hazards model.

Suggested Citation

  • Yunda Huang & Yuanyuan Zhang & Zong Zhang & Peter B. Gilbert, 2020. "Generating Survival Times Using Cox Proportional Hazards Models with Cyclic and Piecewise Time-Varying Covariates," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 324-339, December.
    • Handle: RePEc:spr:stabio:v:12:y:2020:i:3:d:10.1007_s12561-020-09266-3
    DOI: 10.1007/s12561-020-09266-3
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    References listed on IDEAS

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    1. Leemis, Lawrence M. & Shih, Li-Hsing & Reynertson, Kurt, 1990. "Variate generation for accelerated life and proportional hazards models with time dependent covariates," Statistics & Probability Letters, Elsevier, vol. 10(4), pages 335-339, September.
    2. Marlena Maziarz & Patrick Heagerty & Tianxi Cai & Yingye Zheng, 2017. "On longitudinal prediction with time-to-event outcome: Comparison of modeling options," Biometrics, The International Biometric Society, vol. 73(1), pages 83-93, March.
    3. Lawrence M. Leemis, 1987. "Technical Note—Variate Generation for Accelerated Life and Proportional Hazards Models," Operations Research, INFORMS, vol. 35(6), pages 892-894, December.
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