Mark-specific hazard ratio model with missing multivariate marks

An objective of randomized placebo-controlled preventive HIV vaccine efficacy (VE) trials is to assess the relationship between vaccine effects to prevent HIV acquisition and continuous genetic distances of the exposing HIVs to multiple HIV strains represented in the vaccine. The set of genetic distances, only observed in failures, is collectively termed the 'mark.' The objective has motivated a recent study of a multivariate mark-specific hazard ratio model in the competing risks failure time analysis framework. Marks of interest, however, are commonly subject to substantial missingness, largely due to rapid post-acquisition viral evolution. In this article, we investigate the mark-specific hazard ratio model with missing multivariate marks and develop two inferential procedures based on (i) inverse probability weighting (IPW) of the complete cases, and (ii) augmentation of the IPW estimating functions by leveraging auxiliary data predictive of the mark. Asymptotic properties and finite-sample performance of the inferential procedures are presented. This research also provides general inferential methods for semiparametric density ratio/biased sampling models with missing data. We apply the developed procedures to data from the HVTN 502 'Step' HIV VE trial.