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 transmission 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. We focus on settings where interference can be considered to be constrained by a network – specifically, the underlying contact network between treated and untreated clusters in a cluster-randomized trial. When there is contact between clusters that could lead to disease transmission, the randomized treatment effect will be attenuated relative to what would occur if all clusters were to receive treatment. This source of interference, however, is potentially measurable.
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. The resulting estimator is applied to data used for sample size estimation in the design of a cluster-randomized trial of combination HIV prevention.