We evaluate the effects of herd immunity on the power of vaccine trials. We consider large-scale trials in which persons are individually randomized to either placebo or vaccine. We evaluate the adequacy of naive power calculations that ignore the effects of herd immunity such as those based on the comparison of two independent binomials. We developed a simulation design to evaluate the quantitative effects of herd immunity on power. The simulation design accounted for nonhomogeneous mixing. We found that naive power calculations that ignore the effects of herd immunity can seriously overestimate power. In fact, we found that as sample size increases it is possible for the power to actually decrease. The reason is that herd immunity reduces the overall number of infections. In the situations we considered, power may eventually begin to decrease once the proportion of the population enrolled in the trial exceeds about 25%. We discuss the findings in the context of a pneumococcal vaccine trial for children. Our results serve as a cautionary note that naive sample size calculations for larger scale vaccine trials that ignore the impact of herd immunity can yield underpowered studies. Simulations such as that suggested here can help alert investigators to situations where significant dilution of power could result from ignoring the effects of herd immunity.

The article is dedicated to the memory of Blake Charvat