Adaptive Randomization in Network Data
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Network data have appeared frequently in recent research. For example, in comparing the effects of different types of treatment, network models have been proposed to improve the quality of estimation and hypothesis testing. In this paper, we focus on efficiently estimating the average treatment effect using an adaptive randomization procedure in networks. We work on models of causal frameworks, for which the treatment outcome of a subject is affected by its own covariate as well as those of its neighbors. Moreover, we consider the case in which, when we assign treatments to the current subject, only the subnetwork of existing subjects is revealed. New randomized procedures are proposed to minimize the mean squared error of the estimated differences between treatment effects. In network data, it is usually difficult to obtain theoretical properties because the numbers of nodes and connections increase simultaneously. Under mild assumptions, our proposed procedure is closely related to a time-varying inhomogeneous Markov chain. We then use Lyapunov functions to derive the theoretical properties of the proposed procedures. The advantages of the proposed procedures are also demonstrated by extensive simulations and experiments on real network data.
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