Some New Advances in Covariate-Adaptive Randomization
Open AccessIn randomized controlled experiments, covariate-adaptive randomization (CAR) balances treatment allocation over important covariates. In the literature, most of the well-developed CAR designs are limited to balancing over categorical variables. However, continuous covariates are as essential as discrete covariates in the estimation of average treatment effect (ATE) and other statistical inference. Moreover, under relatively complex CAR designs, it is hard to derive the theoretical properties of imbalance measures between treatment groups and the asymptotic properties of ATE estimators. Thus, a small amount of work has been done in related topics, which results in limited use of CAR in practice. In this dissertation, we first propose a new CAR design to balance the treatment allocation over both continuous and discrete covariates, meanwhile establish the theoretical properties of the proposed design to show its advantages and practical value in clinical trials studies. Our new CAR procedure is introduced in Chapter 2, which is based on minimization using a weighted sum of Mahalanobis distance and squared within-stratum differences as the imbalance measure. It is shown that under the proposed CAR design, the joint process of the within-stratum differences and the squared term of Mahalanobis distance is a positive recurrent Markov chain. When n subjects have been assigned to treatment groups, the Mahalanobis distance is of order Op(1/n) and the within-stratum differences are of order Op(1). The theoretical properties of the estimation of ATE are obtained, including the asymptotic variance of the estimators under the proposed CAR design, complete randomization and rerandomization. The advantages of the new procedure are demonstrated by numerical studies and a real clinical trial data analysis. In the field of data science and online experiments, A/B testing has become a popular topic as a form of randomized controlled experiment. One of the most difficult challenges in the large-scale A/B testing is that the subjects in the experiment can communicate and interact with each other. These interactions may affect other subjects’ behavior and thus have effects on the outcome, resulting in violation of the stable unit treatment value assumption (SUTVA). When subjects form a network through communication and interaction, additional network effects start to influence their outcomes. This phenomenon is called spillover effects or social interference. Spillover effects often exit in online experiments and complicate the evaluation of ATE and hypothesis testing. Ignoring users’ interference and using regular CAR design and statistical analysis based on SUTVA may cause inaccurate inference such as estimation bias and invalid conclusion of the hypothesis testing. To eliminate the estimation bias caused by spillover effects, several recent advances suggest to perform complete randomization at the cluster level of subjects. However, important cluster covariates are not considered in these randomization designs, thus there may be imbalanced treatment allocation over the distributions of cluster’s covariates and the statistical inference may be harmed. To address these concerns, in Chapter 4, we propose a cluster-adaptive network A/B testing scheme consisting of a cluster-adaptive randomization to balance the cluster’s covariates and a cluster-adjusted estimator to obtain a valid estimation. We establish the theoretical properties of the Mahalanobis distance measuring covariates imbalance as well as the asymptotic normality for the proposed estimator of ATE. These results not only suggest that our network A/B testing scheme achieves an unbiased estimation with higher efficiency, but also demonstrate the benefit of improving the balancing condition of clusters’ covariates between treatment groups. Numerical studies are conducted on randomly generated network graphs and real-world network graphs.
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