  Assessing immune responses to study vaccines as surrogates of protection
plays a central role in vaccine clinical trials. Motivated by three ongoing or
pending HIV vaccine efficacy trials, we consider such surrogate endpoint
assessment in a randomized placebo-controlled trial with case-cohort sampling
of immune responses and a time to event endpoint. Based on the principal
surrogate definition under the principal stratification framework proposed by
Frangakis and Rubin [Biometrics 58 (2002) 21--29] and adapted by Gilbert and
Hudgens (2006), we introduce estimands that measure the value of an immune
response as a surrogate of protection in the context of the Cox proportional
hazards model. The estimands are not identified because the immune response to
vaccine is not measured in placebo recipients. We formulate the problem as a
Cox model with missing covariates, and employ novel trial designs for
predicting the missing immune responses and thereby identifying the estimands.
The first design utilizes information from baseline predictors of the immune
response, and bridges their relationship in the vaccine recipients to the
placebo recipients. The second design provides a validation set for the
unmeasured immune responses of uninfected placebo recipients by immunizing them
with the study vaccine after trial closeout. A maximum estimated likelihood
approach is proposed for estimation of the parameters. Simulated data examples
are given to evaluate the proposed designs and study their properties.
