Generating Survival Times Using Cox Proportional Hazards Models with Cyclic and Piecewise Time-Varying Covariates
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Generating Survival Times Using Cox Proportional Hazards Models with Cyclic and Piecewise Time‑Varying Covariates Yunda Huang1,2 · Yuanyuan Zhang1 · Zong Zhang3 · Peter B. Gilbert1,4 Received: 12 March 2019 / Revised: 9 September 2019 / Accepted: 8 January 2020 © The Author(s) 2020
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. Keywords Correlates of risk · Joint modeling of longitudinal and survival data · Survival data simulations · Time-dependent covariate · Zero-protection threshold Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1256 1-020-09266-3) contains supplementary material, which is available to authorized users. * Yunda Huang [email protected] 1
Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave. North, Seattle, WA 98109, USA
2
Department of Global Health, University of Washington, Seattle, WA 98105, USA
3
Department of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA
4
Department of Biostatistics, University of Washington, Seattle, WA 98195, USA
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Statistics in Biosciences
1 Introduction Time-to-event outcomes with cyclic time-varying covariates are frequently encountered in biomedical studies that involve multiple or repeated administrations of an intervention. For example, the plasma concentration of a drug taken orally daily to prevent a certain infection would usually fluctuate on a daily cycle, and it is often of interest to identify whether and how the cyclic drug concentration associates with the hazard of infection. In the two harmonized Antibody Mediated Prevention (AMP) Phase 2b
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