In randomized placebo-controlled preventive HIV vaccine efficacy trials, an objective is to evaluate the relationship between vaccine efficacy to prevent infection and genetic distances of the exposing HIV strains to the multiple HIV sequences included in the vaccine construct, where the set of genetic distances is considered as the continuous multivariate “mark” observed in infected subjects only. This research develops a multivariate mark-specific hazard ratio model in the competing risks failure time analysis framework for the assessment of mark-specific vaccine efficacy. It allows improved efficiency of estimation by employing the semiparametric method of maximum profile likelihood estimation in the vaccine-to-placebo mark density ratio model. The model also enables the use of a more efficient estimation method for the overall log hazard ratio in the Cox model. In addition, we propose testing procedures to evaluate two relevant hypotheses concerning mark-specific vaccine efficacy. The asymptotic properties and finite-sample performance of the inferential procedures are investigated. Finally, we apply the proposed methods to data collected in the Thai RV144 HIV vaccine efficacy trial.