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 emergent after placebo vaccination. The key requirements are that surveillance strain distribution accurately reflect 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 modeling to better reflect the complexities of field trials with staggered entry, crossover, and smoothly varying strain specific vaccine efficacy We evaluate these 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 mis-specfication of the strain distribution. We also provide an approach for use when genotyping of the infecting strains of the trial participants has not been done.
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