Statistical approaches to establishing vaccine safety

In a vaccine safety trial, the primary interest is to demonstrate that the vaccine is sufficiently safe, rejecting the null hypothesis that the relative risk of an adverse event attributable to the new vaccine is above a prespecified value, greater than one. We evaluate the exact probability of type I error of the likelihood score test, with sample size determined by normal approximation, by enumeration of the binomial outcomes in the rejection region and show that it exceeds the nominal level. In the case of rare adverse events, we recommend the Poisson approximation as an alternative and develop the corresponding conditional and unconditional tests. We give sample size and power calculations for these tests. We also propose optimal randomization strategies which either (i) minimize the total number of adverse cases or (ii) minimize the expected number of subjects when the vaccine is unsafe. We illustrate the proposed methods using a hypothetical vaccine safety study.