Abstract
SARS-CoV-2 continues to evolve and the vaccine efficacy against variants is challenging to estimate. It is now common in phase III vaccine trials to provide vaccine to those randomized to placebo once efficacy has been demonstrated, precluding a direct assessment of placebo controlled vaccine efficacy after placebo vaccination. In this work, we extend methods developed for estimating vaccine efficacy post placebo vaccination to allow variant specific time varying vaccine efficacy, where time is measured since vaccination. The key idea is to infer counterfactual strain specific placebo case counts by using surveillance data that provide the proportions of the different strains. This blending of clinical trial and observational data allows estimation of strain-specific time varying vaccine efficacy, or sieve effects, including for strains that emerge after placebo vaccination. The key requirements are that the surveillance strain distribution accurately reflects the strain distribution for a placebo group throughout follow-up after placebo group vaccination, and that at least one strain is present before and after placebo vaccination. For illustration, we develop a Poisson approach for an idealized design under a rare disease assumption and then use a proportional hazards model to address staggered entry, staggered crossover, and smoothly varying strain specific vaccine efficacy. We evaluate these methods by theoretical work and simulations, and demonstrate that useful estimation of the efficacy profile is possible for strains that emerge after vaccination of the placebo group. An important principle is to incorporate sensitivity analyses to guard against misspecification of the strain distribution.