The required size of cluster randomized trials of non-pharmaceutical interventions in epidemic settings

To control the SARS-CoV-2 pandemic and future pathogen outbreaks requires an understanding of which non-pharmaceutical interventions are effective at reducing transmission. Observational studies, however, are subject to biases, even when there is no true effect. Cluster randomized trials provide a means to conduct valid hypothesis tests of the effect of interventions on community transmission. While they may only require a short duration, they often require large sample sizes to achieve adequate power. However, the sample sizes required for such tests in an outbreak setting are largely undeveloped and the question of whether these designs are practical remains unanswered. We develop approximate sample size formulae and simulation-based sample size methods for cluster randomized trials in infectious disease outbreaks. We highlight key relationships between characteristics of transmission and the enrolled communities and the required sample sizes, describe settings where cluster randomized trials powered to detect a meaningful true effect size may be feasible, and provide recommendations for investigators in planning such trials. The approximate formulae and simulation banks may be used by investigators to quickly assess the feasibility of a trial, and then more detailed methods may be used to more precisely size the trial. For example, we show that community-scale trials requiring 220 clusters with 100 tested individuals per cluster are powered to identify interventions that reduce transmission by 40% in one generation interval, using parameters identified for SARS-CoV-2 transmission. For more modest treatment effects, or settings with extreme overdispersion of transmission, however, much larger sample sizes are required.