  Combating the SARS-CoV2 pandemic will require the fast development of
effective preventive vaccines. Regulatory agencies may open accelerated
approval pathways for vaccines if an immunological marker can be established as
a mediator of a vaccine's protection. A rich source of information for
identifying such correlates are large-scale efficacy trials of COVID-19
vaccines, where immune responses are measured subject to a case-cohort sampling
design. We propose two approaches to estimation of mediation parameters in the
context of case-cohort sampling designs. We establish the theoretical
large-sample efficiency of our proposed estimators and evaluate them in a
realistic simulation to understand whether they can be employed in the analysis
of COVID-19 vaccine efficacy trials.
