A promising new approach for preventing HIV infection is passive administration of a broadly neutralizing antibody (bNab). The first efficacy study, AMP, is ongoing in 4200 volunteers assigned to receive 10 infusions of the VRC01 bNab or placebo over 72 weeks. A secondary objective assesses whether and how the serum concentration of VRC01 over time associates with the rate of HIV infection in VRC01 recipients, using a nested case-control sampling design, a pharmacokinetic model for the time-concentration curve, and a model for predicting the timing of HIV infection based on HIV diagnostic, sequence, and viral load data. We develop two inferential methods for addressing this objective, one based on checking whether HIV infections tend to occur at times when serum concentrations are known to be low based on infusion dates and the pharmacokinetic model, and another based on comparing concentrations at times of HIV infection to average concentrations over the follow-up period of HIV uninfected controls. The methods are studied in simulations of the AMP study and compared to a Cox model with a time-dependent covariate, and extend to account for features of the HIV infection outcome.