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

Peter B. Gilbert,Zong Zhang,Yuanyuan Zhang,Yunda Huang

doi:10.1007/s12561-020-09266-3

Peter B. Gilbert, Zong Zhang + Show 2 more

Open Access

https://doi.org/10.1007/s12561-020-09266-3

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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.

Highlights

Time-to-event outcomes with cyclic time-varying covariates are frequently encountered in biomedical studies that involve multiple or repeated administrations of an intervention
VRC01 is a monoclonal antibody that has been shown to neutralize most strains of the HIV virus in laboratory studies, and the Antibody Mediated Prevention (AMP) trials will test whether VRC01 reduces the rate of HIV infection compared to placebo
We considered simulating event time data with a continuous timevarying and piecewise covariate

Summary

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. 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 efficacy trials (ClinicalTrials.gov #NCT02716675 & #NCT02568215), more than 4500 HIV-uninfected participants at high risk for acquiring HIV infection are randomized to receive 10 infusions every 8 weeks of either VRC01 or placebo and followed for 80 weeks for the study endpoint of HIV infection [1]. VRC01 is a monoclonal antibody that has been shown to neutralize most strains of the HIV virus in laboratory studies, and the AMP trials will test whether VRC01 reduces the rate of HIV infection compared to placebo.

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