[Paper Review] Optimal design of experiments in the presence of network-correlated outcomes.

Guillaume Basse, Edoardo M. Airoldi|arXiv (Cornell University)|Jul 3, 2015

Advanced Causal Inference Techniques26 references11 citations

TL;DR

This paper proposes an optimal treatment allocation strategy in randomized experiments when outcomes are correlated through a pre-existing network. By modeling network-induced correlations within a potential outcomes framework, the method minimizes the integrated mean squared error of the average treatment effect estimate, significantly outperforming standard designs that ignore network structure, as shown through analytical decomposition and simulations.

ABSTRACT

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 pre-intervention. 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.

Motivation & Objective

• To address the challenge of correlated outcomes in randomized experiments when network structures are available before intervention.
• To develop a causal model that explicitly incorporates network-induced correlation in potential outcomes.
• To derive an optimal treatment allocation strategy that minimizes the integrated mean squared error of the average treatment effect estimator.
• To provide theoretical insights into design efficiency through analytical decomposition of the mean squared error.
• To demonstrate empirically that network-aware designs outperform conventional designs ignoring network structure.

Proposed method

• Formalizes a class of models that encode network correlation in potential outcomes using a network-structured covariance structure.
• Applies the potential outcomes framework to define the average treatment effect under network correlation.
• Derives an optimal treatment allocation rule by minimizing the integrated mean squared error of the ATE estimator.
• Employs an analytical decomposition of the mean squared error to reveal the impact of network structure on design efficiency.
• Uses simulation studies to compare the proposed design against standard randomization and other baseline allocations.
• Incorporates network topology (e.g., degree distribution, clustering) as inputs to the optimization process.

Experimental results

Research questions

• RQ1 How does network correlation among outcomes affect the precision of average treatment effect estimation in randomized experiments?
• RQ2 What is the optimal treatment allocation rule when outcome correlations are informed by a pre-intervention network?
• RQ3 How does the proposed method reduce estimation error compared to standard randomization that ignores network structure?
• RQ4 What role do network features—such as degree and clustering—play in determining optimal design efficiency?
• RQ5 Can analytical decomposition of the mean squared error reveal actionable insights for experimental design under network dependence?

Key findings

• The proposed optimal design significantly reduces the integrated mean squared error of the average treatment effect estimator compared to standard randomization.
• Analytical decomposition reveals that network structure affects variance and bias trade-offs, with high-degree nodes requiring careful allocation to minimize error.
• Simulations show consistent improvements in estimation precision when treatment allocation accounts for network correlation, especially in networks with strong clustering.
• The optimal allocation rule assigns treatment in a way that balances the influence of connected units, reducing dependence-induced estimation inefficiency.
• Design efficiency gains are most pronounced in networks with high clustering and heterogeneous node degrees.
• Ignoring network structure leads to suboptimal variance reduction and increased estimation error, even under standard randomization.