Causal Inference under Network Interference Using a Mixture of Randomized Experiments

2023/08/31 by Yiming Jiang, He Wang, Jiang, Yiming +1 · 3 citations
Mathematics · #Advanced Causal Inference Techniques #Bernoulli's principle #Bounded function #Combinatorics #Discrete mathematics #Estimator #FOS: Computer and information sciences #Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #Statistics #Upper and lower bounds

paper · pdf · doi:10.48550/arxiv.2309.00141

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/08/31 · openalex created_date 2023/09/05 · openalex updated_date 2026/07/28

Abstract

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(d² 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 Ω(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(d³ n^-1 p^-1 (1-p)^-1), which is aligned with the estimator introduced by Cortez-Rodriguez et al. (2023) under similar conditions.

Cited by

• Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approach
• SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry

Related

• Limitations of design-based causal inference and A/B testing under arbitrary and network interference
• Staggered Rollout Designs Enable Causal Inference Under Interference Without Network Knowledge
• Elements of estimation theory for causal effects in the presence of network interference
• Design and analysis of experiments in networks: Reducing bias from interference
• Low-order outcomes and clustered designs: combining design and analysis for causal inference under network interference