Covariate-Adaptive Randomization in Network Data
Open AccessUsers linked together through a network often tend to have similar behaviors. This phenomenon is usually known as network interactions, which can be demonstrated by the network effect and the spill-over effect. Users' characteristics, the covariates, are often correlated with their outcomes. Therefore, one should incorporate both the covariates and the network information in a carefully designed randomization to improve the estimation of the average treatment effect (ATE) for network A/B testing. In this dissertation, we propose three new adaptive procedures to balance both the network and the covariate and show that the resulting imbalance measures are Op(1). We also demonstrate the relationships between the improved balance and the increased efficiency for estimating the ATE in terms of the reduction of the mean square error (MSE). Specifically, we combine the imbalance measures from Covariate Adaptive Randomization and Network Adaptive Randomization and prove their Op(1). We then introduce a linear model that includes both network interactions and covariates. We derive the MSE of the difference-in-mean estimator, proving the consistency under bounded cases. Furthermore, we propose a new pairwise randomization under the network-only model and prove the consistency for the corresponding estimator. We extend the new network imbalance measure to the more general model with covariates. We prove the covariate imbalance measures remain Op(1) and demonstrate the MSE is o(1). Our proof generalizes the drift in Markov chain to moment conditions, overcoming the challenge of the complex correlation between connected users. These provide a theoretical guarantee of our proposed procedures. Numerical studies are conducted to evaluate the performance of our proposed procedures using both hypothetical and real data. The studies involve the Erdös-Rényi random graph and the clustering graph. We start with multivariate regression and develop it into the generalized linear model. We also consider network transitivity to mimic practical scenarios. The results demonstrate the advanced performance of our proposed randomization in terms of controlled imbalance measures and the reduction of MSE. The effectiveness and robustness are illustrated by the greater comparability of the treatment groups as well as the consistency in estimating the ATE.
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