Rerandomization in $2^{K}$ factorial experiments

Li, Xinran; Ding, Peng; Rubin, Donald B.

doi:10.1214/18-aos1790

Cited by 22 publications

(18 citation statements)

References 28 publications

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“…It is conceptually straightforward to extend the results to rerandomization with tiers of covariates (Morgan and Rubin 2015;Li et al 2018). Recently, Zhou et al (2018 discussed sequential rerandomization, and Li et al (2019) discussed rerandomization in 2 K factorial experiments with tiers of both covariates and factorial effects. It is important to discuss regression adjustment after these rerandomizations.…”

Section: Discussionmentioning

confidence: 99%

“…We consider only symmetric quantile ranges because they have the shortest lengths (Casella and Berger (2002), theorem 9.3.2). The S-optimal adjusted estimator also has the smallest asymptotic variance among all estimators in equation (1) (Li et al (2019), proposition 4). Conversely, if all adjusted estimators in equation (1) are asymptotically Gaussian, then the estimator with the smallest asymptotic variance is an S-optimal estimator.…”

Section: S-optimal Regression Adjustmentmentioning

confidence: 91%

“…In this paper, we consider only symmetric quantile range because all the asymptotic distributions are symmetric around τ . The S-optimal regressionadjusted estimator also has the smallest asymptotic variance among all estimators in (1) (Li et al 2019). Moreover, if all regression-adjusted estimators in (1) are asymptotically Gaussian, then the one with the smallest asymptotic variance is S-optimal.…”

Section: S-optimal Regression Adjustmentmentioning

confidence: 96%

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Rerandomization and Regression Adjustment

Ding

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome‐generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance in the analysis stage. We can embed blocking in a wider class of experimental design called rerandomization, and extend the classical analysis of covariance to more general regression adjustment. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference‐in‐means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization inference framework, we establish a unified theory allowing the designer and analyser to have access to different sets of covariates. We find that asymptotically, for any given estimator with or without regression adjustment, rerandomization never hurts either the sampling precision or the estimated precision, and, for any given design with or without rerandomization, our regression‐adjusted estimator never hurts the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference. To quantify these statements theoretically, we discuss optimal regression‐adjusted estimators in terms of the sampling precision and the estimated precision, and then measure the additional gains of the designer and the analyser. We finally suggest the use of rerandomization in the design and regression adjustment in the analysis followed by the Huber–White robust standard error.

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Section: Discussionmentioning

confidence: 99%

Section: S-optimal Regression Adjustmentmentioning

confidence: 91%

Section: S-optimal Regression Adjustmentmentioning

confidence: 96%

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Rerandomization and Regression Adjustment

Ding

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…In this paper, we focus on randomized experiments with two treatment arms. Rerandomization has been extended to multiple arms experiments (Branson et al, 2016;Li et al, 2020). In the multiple arms experiments, we need to balance multiple contrasts of covariate means simultaneously.…”

Section: Discussionmentioning

confidence: 99%

Pair-switching rerandomization

Zhu¹,

Liu²

2021

Preprint

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Rerandomization discards assignments with covariates unbalanced in the treatment and control groups to improve the estimation and inference efficiency. However, the acceptance-rejection sampling method used by rerandomization is computationally inefficient. As a result, it is timeconsuming for classical rerandomization to draw numerous independent assignments, which are necessary for constructing Fisher randomization tests. To address this problem, we propose a pair-switching rerandomization method to draw balanced assignments much efficiently. We show that the difference-in-means estimator is unbiased for the average treatment effect and the Fisher randomization tests are valid under pair-switching rerandomization. In addition, our method is applicable in both non-sequentially and sequentially randomized experiments. We conduct comprehensive simulation studies to compare the finite-sample performances of the proposed method and classical rerandomization. Simulation results indicate that pair-switching rerandomization leads to comparable power of Fisher randomization tests and is 4-18 times faster than classical rerandomization. Finally, we apply the pair-switching rerandomization method to analyze two clinical trial data sets, both demonstrating the advantages of our method.

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“…(2018) and Li et al. (2020) for the vanilla treatment‐versus‐control experiment and 2 K factorial experiment respectively. Zhou et al.…”

Section: Introductionmentioning

confidence: 99%

Response-Adaptive Rerandomization

Zhang

Yin

2021

Journal of the Royal Statistical Society Series C: Applied Statistics

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Randomized experiments are the gold standard for estimating treatment effects, as randomization potentially removes the differences of covariates across treatment groups. However, covariateimbalanced allocation often occurs in a single-shot assignment and thus dampens the estimation precision. To remedy this issue, Morgan and Rubin (2012) proposed rerandomization (RR) for twoarm experiments, which repeatedly randomizes enrolled units and terminates the process when the Mahalanobis distance of covariates across groups meets a predefined threshold. This scheme is shown to well control the covariate balance and thus improve the statistical efficiency.Since the publication of the seminal paper by Morgan and Rubin (2012), many works have been conducted to generalize RR practically or theoretically. For example, Morgan and Rubin (2015)

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Rerandomization in $2^{K}$ factorial experiments

Cited by 22 publications

References 28 publications

Rerandomization and Regression Adjustment

Rerandomization and Regression Adjustment

Pair-switching rerandomization

Response-Adaptive Rerandomization

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