Optimal design of experiments in the presence of network-correlated outcomes

We consider the problem of how to assign treatment in a randomized experiment, when the correlation among the outcomes is informed by a network available preintervention. Working within the potential outcome causal framework, we develop a class of models that posit such a correlation structure among the outcomes, and a strategy for allocating treatment optimally, for the goal of minimizing the integrated mean squared error of the estimated average treatment effect. We provide insights into features of the optimal designs via an analytical decomposition of the mean squared error used for optimization. We illustrate how the proposed treatment allocation strategy improves on allocations that ignore the network structure, with extensive simulations.