  Randomized vaccine trials are used to assess vaccine efficacy and to
characterize the durability of vaccine induced protection. If efficacy is
demonstrated, the treatment of placebo volunteers becomes an issue. For
COVID-19 vaccine trials, there is broad consensus that placebo volunteers
should be offered a vaccine once efficacy has been established. This will
likely lead to most placebo volunteers crossing over to the vaccine arm, thus
complicating the assessment of long term durability. We show how to analyze
durability following placebo crossover and demonstrate that the vaccine
efficacy profile that would be observed in a placebo controlled trial is
recoverable in a trial with placebo crossover. This result holds no matter when
the crossover occurs and with no assumptions about the form of the efficacy
profile. We only require that the vaccine efficacy profile applies to the newly
vaccinated irrespective of the timing of vaccination. We develop different
methods to estimate efficacy within the context of a proportional hazards
regression model and explore via simulation the implications of placebo
crossover for estimation of vaccine efficacy under different efficacy dynamics
and study designs. We apply our methods to simulated COVID-19 vaccine trials
with durable and waning vaccine efficacy and a total follow-up of two years.
