Change Point Inference in the Presence of Missing Covariates for Principal Surrogate Evaluation in Vaccine Trials

We consider the use of threshold-based regression models for evaluating immune response biomarkers as principal surrogate markers of a vaccine's protective effect. Threshold-based regression models, which allow the relationship between a clinical outcome and a covariate to change dramatically across a threshold value in the covariate, have been studied by various authors under fully observed data. Limited research, however, has examined these models in the presence of missing covariates, such as the counterfactual potential immune responses of a participant in the placebo arm of a standard vaccine trial had s/he been assigned to the vaccine arm instead. Based on a hinge model for a threshold effect of the principal surrogate on vaccine efficacy, we develop a regression methodology that consists of two components: (1) The estimated likelihood method is employed to handle missing potential outcomes, and (2) a penalty is imposed on the estimated likelihood to ensure satisfactory finite sample performance. We develop a method that allows joint estimation of all model parameters as well as a two-step method that separates the estimation of the threshold parameter from the rest of the parameters. Stable iterative algorithms are developed to implement the two methods and the asymptotic properties of the proposed estimators are established. In simulation studies, the proposed estimators are shown to have satisfactory finite sample performance. The proposed methods are applied to analyze a real dataset collected from dengue vaccine efficacy trials to predict how vaccine efficacy varies with an individual's potential immune response if receiving vaccine.