Assessing pharmacokinetic marker correlates of outcome, with application to antibody prevention efficacy trials

The Antibody Mediated Prevention efficacy trials are the first studies to evaluate whether passive administration of a broadly neutralizing monoclonal antibody can prevent human immunodeficiency virus (HIV) acquisition. The trials randomize 4600 HIV-negative volunteers to receive 10 infusions of the monoclonal antibody VRC01 or placebo. The primary objective compares the incidence of HIV infection between the study groups. The secondary objective assesses whether and how a marker defined as the serum concentration of VRC01 over time associates with the instantaneous rate of HIV infection, using a two-phase sampling design, a pharmacokinetic model for the time-concentration curve, and an estimator of HIV infection times. While a Cox model with a time-dependent covariate constitutes an important approach to this problem, the low interindividual versus intraindividual marker variability limits its power, motivating us to develop two alternative methods that condition on outcome status: (1) an indirect method that checks whether HIV-infected cases have unexpectedly long times from the most recent infusion to the estimated infection date and (2) a direct method that checks whether the marker itself is unexpectedly low at estimated infection dates. In simulations and a pseudo Antibody Mediated Prevention application, we find that method (2) (but not (1)) has greater power than the Cox model. We also find that the quality of the infection time estimator majorly impacts method performance, and thus, incorporating details of an optimized estimator is critical. The methods apply more generally for assessing a time-dependent longitudinal marker as a correlate of risk when the marker trajectory is modeled pharmacokinetically.