Similarity/equivalence trials for combination vaccines.

In a similarity or "equivalence" trial of a combination vaccine, we wish to show that the combination is sufficiently similar to the separately administered components in some measure of safety, immunogenicity, or efficacy to justify use of the combination. In this setting it is usually required to show similarity in one direction only; specifically, we design the trial to rule out superiority of the separate components by as much as a prespecified quantity theta 0 in an appropriate outcome measure (e.g., a difference or ratio). It is crucial that theta 0 be chosen to be clinically meaningful, so that any difference or ratio less than theta 0 is truly acceptable to clinicians. Estimation is generally more relevant than hypothesis testing in such a trial, and consequently it is natural to consider design and analysis in terms of confidence intervals. The same sample sizes can be obtained, however, from a hypothesis testing approach. The appropriate null hypothesis is that the separate components are superior to the combination by at least theta 0, with rejection of the hypothesis supporting a conclusion of similarity. It is not appropriate to design the trial to test the null hypothesis of no difference, as we would do if we wished to demonstrate superiority of the combination vaccine; failure to reject that hypothesis does not prove similarity, and we might reject the hypothesis when the true difference is unimportant clinically. Further, this inappropriate approach may result in a sample size either larger or smaller than necessary. Sample size formulations are available for various types of comparative measures, e.g., a difference of normally distributed means, a difference or ratio of proportions, and a ratio of hazards.