Causal Inference under Network Interference Using a Mixture of Randomized Experiments

In randomized experiments, the classic Stable Unit Treatment Value Assumption (SUTVA) posits that the outcome for one experimental unit is unaffected by the treatment assignments of other units. However, this assumption is frequently violated in settings such as online marketplaces and social networks, where interference between units is common. We address the estimation of the total treatment effect in a network interference model by employing a mixed randomization design that combines two widely used experimental methods: Bernoulli randomization, where treatment is assigned independently to each unit, and cluster-based randomization, where treatment is assigned at the aggregate level. The mixed randomization design simultaneously incorporates both methods, thereby mitigating the bias present in cluster-based designs. We propose an unbiased estimator for the total treatment effect under this mixed design and show that its variance is bounded by $O(d^2 n^{-1} p^{-1} (1-p)^{-1})$, where $d$ is the maximum degree of the network, $n$ is the network size, and $p$ is the treatment probability. Additionally, we establish a lower bound of $\Omega(d^{1.5} n^{-1} p^{-1} (1-p)^{-1})$ for the variance of any mixed design. Moreover, when the interference weights on the network's edges are unknown, we propose a weight-invariant design that achieves a variance bound of $O(d^3 n^{-1} p^{-1} (1-p)^{-1})$, which is aligned with the estimator introduced by Cortez-Rodriguez et al. (2023) under similar conditions.