Threshold regression is plausible to model the relationship between the risk of infectious disease to the vaccine-induced surrogate biomarker response. Despite its appealing interpretation, limited research has been conducted to study the model when covariates are missing, which is due to two phase sampling design. We focus on studying the hinge threshold regression model with interaction term to better understand the association between the vaccine-induced response with the risk of disease, and adopt estimated likelihood method to tackle missing covariate issue. A reweighted iterative algorithm is proposed for parameter estimation and the asymptotic properties of the proposed estimator are derived. The finite sample properties of the estimator including both estimation and inference are shown in simulation studies and the practical application of the proposed is illustrated through the dengue data collected from dengue vaccine efficacy trial.