  In two harmonized efficacy studies to prevent HIV infection through multiple
infusions of the monoclonal antibody VRC01, a key objective is to evaluate
whether the serum concentration of VRC01, which changes cyclically over time
along with the infusion schedule, is associated with the rate of HIV infection.
Simulation studies are needed in the development of such survival models. In
this paper, we consider simulating event time data with a continuous
time-varying covariate whose values vary with time through multiple drug
administration cycles, and whose effect on survival changes differently before
and after a threshold within each cycle. The latter accommodates settings with
a zero-protection biomarker threshold above which the drug provides a varying
level of protection depending on the biomarker level, but below which the drug
provides no protection. We propose two simulation approaches: one based on
simulating survival data under a single-dose regimen first before data are
aggregated over multiple doses, and another based on simulating survival data
directly under a multiple-dose regimen. We generate time-to-event data
following a Cox proportional hazards model based on inverting the cumulative
hazard function and a log link function for relating the hazard function to the
covariates. The method's validity is assessed in two sets of simulation
experiments. The results indicate that the proposed procedures perform well in
producing data that conform to their cyclic nature and assumptions of the Cox
proportional hazards model.
