Confidence intervals for the difference between two relative risks

We provide methods to estimate the confidence interval for the difference between two relative risks. Letting p₀, p₁, and p₂ be the probabilities of an event in three groups (i.e. control, treatment 1, treatment 2), our methods estimate a confidence interval for r = p₁/p₀ - p₂/p₀. We highlight that our methods can handle small sample sizes, covariates, and study populations from multiple strata. We specifically developed these methods for vaccine trials to estimate the difference between two vaccine efficacies, where VE₁ = 1 - p₁/p₀, VE₂ = 1 - p₂/p₀ and r = VE₂ - VE₁. We showcase our methods by using interim data from one of these trials to suggest that one dose of the human papillomavirus vaccine may be as efficacious as two doses of the vaccine.