Ridge rerandomization: An experimental design strategy in the presence of covariate collinearity

Branson, Zach; Shao, Stephane

doi:10.1016/j.jspi.2020.07.002

Cited by 14 publications

(26 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, very few study has focused on the large number of covariates in the design stage of an experiment; two related ones are Branson and Shao [2021] and Zhang et al [2021] where the authors proposed ridge and PCA rerandomizations to deal with collinearity among covariates, an issue that becomes increasingly serious as the number of covariates increases with the sample size. There is even fewer study on the theoretical property of rerandomization when the amount of covariate information increases as the sample size grows.…”

Section: Recent Results and Challengesmentioning

confidence: 99%

Rerandomization with Diminishing Covariate Imbalance and Diverging Number of Covariates

Wang¹,

Li²

2021

Preprint

View full text Add to dashboard Cite

Completely randomized experiments have been the gold standard for drawing causal inference because they can balance all potential confounding on average. However, they can often suffer from unbalanced covariates for realized treatment assignments. Rerandomization, a design that rerandomizes the treatment assignment until a prespecified covariate balance criterion is met, has recently got attention due to its easy implementation, improved covariate balance and more efficient inference. Researchers have then suggested to use the treatment assignments that minimize the covariate imbalance, namely the optimally balanced design. This has caused again the long-time controversy between two philosophies for designing experiments: randomization versus optimal and thus almost deterministic designs. Existing literature argued that rerandomization with overly balanced observed covariates can lead to highly imbalanced unobserved covariates, making it vulnerable to model misspecification. On the contrary, rerandomization with properly balanced covariates can provide robust inference for treatment effects while sacrificing some efficiency compared to the ideally optimal design. In this paper, we show it is possible that, by making the covariate imbalance diminishing at a proper rate as the sample size increases, rerandomization can achieve its ideally optimal precision that one can expect with perfectly balanced covariates while still maintaining its robustness. In particular, we provide the sufficient and necessary condition on the number of covariates for achieving the desired optimality. Our results rely on a more dedicated asymptotic analysis for rerandomization, allowing both diminishing covariate imbalance threshold (or equivalently the acceptance probability) and diverging number of covariates. The derived theory for rerandomization provides a deeper understanding of its large-sample property and can better guide its practical implementation. Furthermore, it also helps reconcile the controversy between randomized and optimal designs.

show abstract

Section: Recent Results and Challengesmentioning

confidence: 99%

Rerandomization with Diminishing Covariate Imbalance and Diverging Number of Covariates

Wang¹,

Li²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Futhermore, an interesting direction for future work is exploring the power of rerandomized experiments that do not use the Mahalanobis distance. For example, Branson & Shao (2021) proposed using a modified Mahalanobis distance that incorporates a ridge penalty, such that precision is increased in high-dimensional or high-collinearity settings. Thus, we suspect that testing power may increase as well, compared to standard rerandomization.…”

Section: Discussionmentioning

confidence: 99%

“…Since Morgan & Rubin (2012), there has been a surge in works that establish the benefits of rerandomization; this includes experiments with tiers of covariates (Morgan & Rubin, 2015), sequential experiments (Zhou et al, 2018), factorial experiments (Branson et al, 2016;, stratified experiments (Wang et al, 2021), and experiments with highdimensional covariates (Branson & Shao, 2021;Zhang et al, 2021). A common theme of these works is that causal effect estimators are more precise under rerandomization than under complete randomization, especially if covariates are highly associated with the outcomes of the experiment.…”

Section: Introductionmentioning

confidence: 99%

Power and Sample Size Calculations for Rerandomized Experiments

Branson¹,

Li²,

Ding³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Power is an important aspect of experimental design, because it allows researchers to understand the chance of detecting causal effects if they exist. It is common to specify a desired level of power, and then compute the sample size necessary to obtain that level of power; thus, power calculations help determine how experiments are conducted in practice. Power and sample size calculations are readily available for completely randomized experiments; however, there can be many benefits to using other experimental designs. For example, in recent years it has been established that rerandomized designs, where subjects are randomized until a prespecified level of covariate balance is obtained, increase the precision of causal effect estimators. This work establishes the statistical power of rerandomized treatment-control experiments, thereby allowing for sample size calculators. Our theoretical results also clarify how power and sample size are affected by treatment effect heterogeneity, a quantity that is often ignored in power analyses. Via simulation, we confirm our theoretical results and find that rerandomization can lead to substantial sample size reductions; e.g., in many realistic scenarios, rerandomization can lead to a 25% or even 50% reduction in sample size for a fixed level of power, compared to complete randomization. Power and sample size calculators based on our results are in the R package rerandPower on CRAN.

show abstract

“…We use Mahalanobis distance as the balance measure. It is straightforward to extend our meth-ods to rerandomization using other balance measures, such as Mahalanobis distance within tiers of covariate importance (Morgan and Rubin, 2015), rank-based balance measure with estimated weights of covariates , ridge rerandomization (Branson and Shao, 2021), and PCA rerandomization (Zhang et al, 2021).…”

Section: Discussionmentioning

confidence: 99%

Pair-switching rerandomization

Zhu¹,

Liu²

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Ridge rerandomization: An experimental design strategy in the presence of covariate collinearity

Cited by 14 publications

References 37 publications

Rerandomization with Diminishing Covariate Imbalance and Diverging Number of Covariates

Rerandomization with Diminishing Covariate Imbalance and Diverging Number of Covariates

Power and Sample Size Calculations for Rerandomized Experiments

Pair-switching rerandomization

Contact Info

Product

Resources

About