Likelihood-Based Methods for Assessing Principal Surrogate Endpoints in Vaccine Trials

When evaluating principal surrogate biomarkers in vaccine trials, missingness in potential outcomes requires prediction using auxiliary variables and/or augmented study design with a close-out placebo vaccination (CPV) component. The estimated likelihood approach, which separates the estimation of biomarker distribution from the maximization of the estimated likelihood, has often been adopted. Here, we develop a likelihood-based approach that jointly estimates the two parts and describe the methods for selecting auxiliary variables as risk predictors and/or biomarker predictors. Through numerical studies, we observe that in a standard trial design without a CPV component, the two methods achieve similar performance in estimation of the risk model and the marker model. However, for trials augmented with a CPV component, using the likelihood-based method achieves better estimation performance compared to the estimated likelihood method. Moreover, in the presence of a large number of covariates from which to select, the ML method achieves comparable or better performance compared to the EL method in both designs. While the CPV component has not yet been implemented in existing vaccine trials, our results have applications in the planning of future vaccine trials. We illustrate the method using data from a dengue vaccine trial.