Estimation of Stratified Mark-Specific Proportional Hazards Models Under Two-Phase Sampling with Application to HIV Vaccine Efficacy Trials

An objective of preventive HIV vaccine efficacy trials is to understand how vaccine-induced immune responses to specific protein sequences of HIV-1 associate with subsequent infection with specific sequences of HIV, where the immune response biomarkers are measured in vaccine recipients via a two-phase sampling design. Motivated by this objective, we investigate the stratified mark-specific proportional hazards model under two-phase biomarker sampling, where the mark is the genetic distance of an infecting HIV-1 sequence to an HIV-1 sequence represented inside the vaccine. Estimation and inference procedures based on inverse probability weighting of complete-cases and on augmented inverse probability weighting of complete-cases are developed. Asymptotic properties of the estimators are derived and their finite-sample performances are examined in simulation studies. The methods are shown to have satisfactory performance and are applied to the RV144 vaccine trial to assess whether immune response correlates of HIV-1 infection are stronger for HIV-1 infecting sequences similar to the vaccine than for sequences distant from the vaccine.