Estimation of trajectory of protective efficacy in infectious disease prevention trials using recurrent event times

In studies of infectious disease prevention, the level of protective efficacy of medicinal products such as vaccines and prophylactic drugs tends to vary over time. Many products require administration of multiple doses at scheduled times, as opposed to one-off or continual intervention. Accurate information on the trajectory of the level of protective efficacy over time facilitates informed clinical recommendations and implementation strategies, for example, with respect to the timing of administration of the doses. Based on concepts from pharmacokinetic and pharmacodynamic modeling, we propose a non-linear function for modeling the trajectory after each dose. The cumulative effect of multiple doses of the products is captured by an additive series of the function. The model has the advantages of parsimony and interpretability, while remaining flexible in capturing features of the trajectories. We incorporate this series into the Andersen-Gill model for analysis of recurrent event time data and compare it with alternative parametric and non-parametric functions. We use data on clinical malaria disease episodes from a trial of four doses of an anti-malarial drug combination for chemoprevention to illustrate, and evaluate the performance of the methods using simulation. The proposed method out-performed the alternatives in the analysis of real data in terms of Akaike and Bayesian Information Criterion. It also accurately captured the features of the protective efficacy trajectory such as the area under curve in simulations. The proposed method has strong potential to enhance the evaluation of disease prevention measures and improve their implementation strategies.