Generating survival times using Cox proportional hazards models with cyclic time-varying covariates, with application to a multiple-dose monoclonal antibody clinical trial

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.