  The COVID-19 pandemic due to the novel coronavirus SARS CoV-2 has inspired
remarkable breakthroughs in development of vaccines against the virus and the
launch of several phase 3 vaccine trials in Summer 2020 to evaluate vaccine
efficacy (VE). Trials of vaccine candidates using mRNA delivery systems
developed by Pfizer-BioNTech and Moderna have shown substantial VEs of 94-95%,
leading the US Food and Drug Administration to issue Emergency Use
Authorizations and subsequent widespread administration of the vaccines. As the
trials continue, a key issue is the possibility that VE may wane over time.
Ethical considerations dictate that all trial participants be unblinded and
those randomized to placebo be offered vaccine, leading to trial protocol
amendments specifying unblinding strategies. Crossover of placebo subjects to
vaccine complicates inference on waning of VE. We focus on the particular
features of the Moderna trial and propose a statistical framework based on a
potential outcomes formulation within which we develop methods for inference on
whether or not VE wanes over time and estimation of VE at any post-vaccination
time. The framework clarifies assumptions made regarding individual- and
population-level phenomena and acknowledges the possibility that subjects who
are more or less likely to become infected may be crossed over to vaccine
differentially over time. The principles of the framework can be adapted
straightforwardly to other trials.
