Deployment of the recently licensed CYD-TDV dengue vaccine requires understanding of how the risk of dengue disease in vaccine recipients depends jointly on a host biomarker measured after vaccination (neutralization titer - NAb) and on a "mark" feature of the dengue disease failure event (the amino acid sequence distance of the dengue virus to the dengue sequence represented in the vaccine). The CYD14 phase 3 trial of CYD-TDV measured NAb via case-cohort sampling and the mark in dengue disease failure events, with about a third missing marks. We addressed the question of interest by developing inferential procedures for the stratified mark-specific proportional hazards model with missing covariates and missing marks. Two hybrid approaches are investigated that leverage both augmented inverse probability weighting and nearest neighborhood hot deck multiple imputation. The two approaches differ in how the imputed marks are pooled in estimation. Our investigation shows that NNHD imputation can lead to biased estimation without properly selected neighborhood. Simulations show that the developed hybrid methods perform well with unbiased NNHD imputations from proper neighborhood selection. The new methods applied to CYD14 show that NAb is strongly inversely associated with risk of dengue disease in vaccine recipients, more strongly against dengue viruses with shorter distances.