  In order to meet regulatory approval, pharmaceutical companies often must
demonstrate that new vaccines reduce the total risk of a post-infection outcome
like transmission, symptomatic disease, severe illness, or death in randomized,
placebo-controlled trials. Given that infection is a necessary precondition for
a post-infection outcome, one can use principal stratification to partition the
total causal effect of vaccination into two causal effects: vaccine efficacy
against infection, and the principal effect of vaccine efficacy against a
post-infection outcome in the patients that would be infected under both
placebo and vaccination. Despite the importance of such principal effects to
policymakers, these estimands are generally unidentifiable, even under strong
assumptions that are rarely satisfied in real-world trials. We develop a novel
method to nonparametrically point identify these principal effects while
eliminating the monotonicity assumption and allowing for measurement error.
Furthermore, our results allow for multiple treatments, and are general enough
to be applicable outside of vaccine efficacy. Our method relies on the fact
that many vaccine trials are run at geographically disparate health centers,
and measure biologically-relevant categorical pretreatment covariates. We show
that our method can be applied to a variety of clinical trial settings where
vaccine efficacy against infection and a post-infection outcome can be jointly
inferred. This can yield new insights from existing vaccine efficacy trial data
and will aid researchers in designing new multi-arm clinical trials.
