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Joint Inferences on Vaccine Efficacy Against Infection and Disease with Application to the First HIV Vaccine Efficacy Trial

In many clinical trials, subjects are followed for two stages of outcomes, and it is of interest to compare the incidence of each outcome between two randomized groups. The outcome of the first stage may influence the outcome of the second stage. Moreover, the relative risks of the two outcomes may be linked, with the time-dependent profile of relative risk for the second outcome functionally dependent on that of the first. For example, during exposure to HIV, virologic and host factors simultaneously impact the probability of infection and the subsequent viral trajectories, and the efficacy of a tested vaccine to prevent infection and to prevent viral failure may work in concert. We address this problem by modeling the relationship between the stage two hazard function and covariates via Cox's proportional hazards model (Cox, 1972), with the stage one log-hazard ratio θ (·) at the first event time T l included as a covariate. With θ(·) estimated using three methods, 1) nonparametric kernel smoothing; 2) locally parametric penalized splines; and 3) fully parametric cubic linear splines, we subsequently develop inference procedures for the regression parameter in the stage two Cox model based on each of the estimator of θ(·). The inferential procedures are studied in simulations and are illustrated with application to data from the world's first preventive HIV vaccine efficacy trial.