Estimation of the overall treatment effect in the presence of interference in cluster-randomized trials of infectious disease prevention.

An issue that remains challenging in the field of causal inference is how to relax the assumption of no interference between units. Interference occurs when the treatment of one unit can affect the outcome of another, a situation which is likely to arise with outcomes that may depend on social interactions, such as occurrence of infectious disease. Existing methods to accommodate interference largely depend upon an assumption of "partial interference" - interference only within identifiable groups but not among them. There remains a considerable need for development of methods that allow further relaxation of the no-interference assumption. This paper focuses on an estimand that is the difference in the outcome that one would observe if the treatment were provided to all clusters compared to that outcome if treatment were provided to none - referred as the overall treatment effect. In trials of infectious disease prevention, the randomized treatment effect estimate will be attenuated relative to this overall treatment effect if a fraction of the exposures in the treatment clusters come from individuals who are outside these clusters. This source of interference - contacts sufficient for transmission that are with treated clusters - is potentially measurable. In this manuscript, we leverage epidemic models to infer the way in which a given level of interference affects the incidence of infection in clusters. This leads naturally to an estimator of the overall treatment effect that is easily implemented using existing software.