*Stochastic models of vaccine trials using group randomization.

Abstract

To capture and assess all vaccine effects on transmission of infectious disease, the unit of study and analysis in vaccine trials should be groups where transmission occurs. Small groups (e.g., daycare centers) can be used as the unit of study for vaccine trials. Such group randomized trials (GRTs) can detect both direct and indirect vaccine effects, while individual randomized trials can only detect the direct effect of reduced susceptibility. In order to properly formulate the design of vaccine GRTs, there must be sufficient statistical power, i.e., to minimize the probability of failing to detect a vaccine effect. To examine transmission within small groups, two modeling approaches were applied with important contributions from each. A discrete stochastic compartmental (SC) model was used to describe each state of the group (in terms of the number of infected, susceptible or immune individuals). Exact numerical solution of this model resulted in the probability distribution for each state of the group at equilibrium; comparison of vaccinated vs. unvaccinated group probability distributions were used to calculate statistical power. Statistical power was greater when most transmission was internal. When natural immunity could be used to identify infected and susceptible subclasses, statistical power was often significantly improved by analysis that separated subclasses, rather than aggregating them. The second method, agent-based (AB) simulation, corroborated the SC analysis at equilibrium, but also allowed investigation of the dynamics in the number infected within the group. The AB simulations showed inherent oscillations in the number of infected within small groups, particularly when prevalence was low and most infections arose from inside the unit. If the number of infected was determined by interval sampling data from the group trials, then fluctuations around the mean value could result in estimates of endemic prevalence and statistical power that were both biased and had greater variance. The combined use of two modeling approaches that facilitated analyses at equilibrium and simulation of dynamics was productive. Corroboration of results at equilibrium validated the methods and evaluation of oscillations in the number of infected individuals around the mean value added another dimension to the analysis of statistical power.