  We review standard mediation assumptions as they apply to identifying
antibody effects in a randomized vaccine trial and propose new study designs to
allow identification of an estimand that was previously unidentifiable. For
these mediation analyses, we partition the total ratio effect (one minus the
vaccine effect) from a randomized vaccine trial into indirect (effects through
antibodies) and direct effects (other effects). Identifying $\lambda$, the
proportion of the total effect due to an indirect effect, depends on a
cross-world quantity, the potential outcome among vaccinated individuals with
antibody levels as if given placebo, or vice versa. We review assumptions for
identifying $\lambda$ and show that there are two versions of $\lambda$, unless
the effect of adding antibodies to the placebo arm is equal in magnitude to the
effect of subtracting antibodies from the vaccine arm. We focus on the case
when individuals in the placebo arm are unlikely to have the needed antibodies.
In that case, if a standard assumption (given confounders, potential mediators
and potential outcomes are independent) is true, only one version of $\lambda$
is identifiable, and if not neither is identifiable. We propose alternatives
for identifying the other version of $\lambda$, using experimental design to
identify a formerly cross-world quantity. Two alternative experimental designs
use a three arm trial with the extra arm being passive immunization
(administering monoclonal antibodies), with or without closeout vaccination.
Another alternative is to combine information from a placebo-controlled vaccine
trial with a placebo-controlled passive immunization trial.
