  Whenever possible, the efficacy of a new treatment, such as a drug or
behavioral intervention, is investigated by randomly assigning some individuals
to a treatment condition and others to a control condition, and comparing the
outcomes between the two groups. Often, when the treatment aims to slow an
infectious disease, groups or clusters of individuals are assigned en masse to
each treatment arm. The structure of interactions within and between clusters
can reduce the power of the trial, i.e. the probability of correctly detecting
a real treatment effect. We investigate the relationships among power,
within-cluster structure, between-cluster mixing, and infectivity by simulating
an infectious process on a collection of clusters. We demonstrate that current
power calculations may be conservative for low levels of between-cluster
mixing, but failing to account for moderate or high amounts can result in
severely underpowered studies. Power also depends on within-cluster network
structure for certain kinds of infectious spreading. Infections that spread
opportunistically through very highly connected individuals have unpredictable
infectious breakouts, which makes it harder to distinguish between random
variation and real treatment effects. Our approach can be used before
conducting a trial to assess power using network information if it is
available, and we demonstrate how empirical data can inform the extent of
between-cluster mixing.
