PCA Rerandomization

Zhang, Hengtao; Yin, Guosheng; Rubin, Donald B.

doi:10.1002/cjs.11765

Cited by 7 publications

(4 citation statements)

References 38 publications

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“…Schultzberg & Johansson (2019) developed an allocation scheme that stratifies on binary covariates followed by rerandomization on the continuous covariates. Zhang, Yin & Rubin (2021) presented a rerandomization strategy for high‐dimensional data, which first uses principal component analysis to identify proper strata and subsets of covariates for which rerandomization should be used. Wang, Wang & Liu (2023) extended the finite population asymptotic results to stratified experiments.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Rerandomization and optimal matching

Kalbfleisch

2023

Can J Statistics

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On average, randomization achieves balance in covariate distributions between treatment groups; yet in practice, chance imbalance exists post randomization, which increases the error in estimating treatment effects. This is an important issue, especially in cluster randomized trials, where the experimental units (the clusters) are highly heterogeneous and relatively few in number. To address this, several restricted randomization designs have been proposed to balance on a few covariates of particular interest. More recently, approaches involving rerandomization have been proposed that aim to achieve simultaneous balance on several important prognostic factors. In this article, we comment on some properties of rerandomized designs and propose a new design for comparing two or more treatments. This design combines optimal nonbipartite matching of the subjects together with rerandomization, both aimed at minimizing a measure of distance between elements in blocks to achieve reductions in the mean squared error of estimated treatment effects. Compared with the existing alternatives, the proposed design can substantially reduce the mean squared error of the estimated treatment effect. This enhanced efficiency is evaluated both theoretically and empirically, and robustness properties are also noted. The design is generalized to three or more treatment arms.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Rerandomization and optimal matching

Kalbfleisch

2023

Can J Statistics

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“…Again, power analyses will be notationally complex in order to incorporate the criterion for each tier. Other examples include criteria modified by ridge penalties (Branson & Shao, 2021) or principal component analysis (Zhang et al, 2023), which have been shown to increase precision in high-dimensional settings. We suspect that testing power may increase as well.…”

Section: Discussionmentioning

confidence: 99%

“…Since , many works have established 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;Li et al, 2020), stratified experiments (Wang et al, 2021), experiments with clusters (Lu et al, 2023) and experiments with high-dimensional covariates (Branson & Shao, 2021;Wang & Li, 2022;Zhang et al, 2023). A common theme is that causal effect estimators are more precise under rerandomization than complete randomization as long as covariates are associated with outcomes.…”

Section: Introductionmentioning

confidence: 99%

Power and sample size calculations for rerandomization

Branson

Ding

2023

Biometrika

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Summary Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that power. Such calculations are well-known for completely randomized experiments, but there can be many benefits to using other experimental designs. For example, it has 15 recently been established that rerandomization, where subjects are randomized until covariate balance is obtained, increases the precision of causal effect estimators. This work establishes the power of rerandomized treatment-control experiments, thereby allowing for sample size calculators. We find the surprising result that, while power is often greater under rerandomization than complete randomization, the opposite can occur for very small treatment effects. The reason is that inference under rerandomization can be 20 relatively more conservative, in the sense that it can have a lower type-I error at the same nominal significance level, and this additional conservativeness adversely affects power. This surprising result is due to treatment effect heterogeneity, a quantity often ignored in power analyses. We find that heterogeneity increases power for large effect sizes but decreases power for small effect sizes.

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“…We use the Mahalanobis distance as a balance measure. It is straightforward to extend our methods to RR using other balance measures, such as the Mahalanobis distance within tiers of covariate importance (Morgan and Rubin, 2015), rank‐based balance measure with estimated weights of the covariates (Johansson and Schultzberg, 2020), ridge RR (Branson and Shao, 2021), and PCA RR (Zhang et al., 2021).…”

Section: Discussionmentioning

confidence: 99%

Pair-Switching Rerandomization

Zhu

Liu

2022

Biometrics

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Rerandomization discards assignments with covariates unbalanced in the treatment and control groups to improve estimation and inference efficiency. However, the acceptance‐rejection sampling method used in rerandomization is computationally inefficient. As a result, it is time‐consuming for rerandomization to draw numerous independent assignments, which are necessary for performing Fisher randomization tests and constructing randomization‐based confidence intervals. To address this problem, we propose a pair‐switching rerandomization (PSRR) method to draw balanced assignments efficiently. We obtain the unbiasedness and variance reduction of the difference‐in‐means estimator and show that the Fisher randomization tests are valid under PSRR. Moreover, we propose an exact approach to invert Fisher randomization tests to confidence intervals, which is faster than the existing methods. In addition, our method is applicable to both nonsequentially and sequentially randomized experiments. We conduct comprehensive simulation studies to compare the finite‐sample performance of the proposed method with that of classical rerandomization. Simulation results indicate that PSRR leads to comparable power of Fisher randomization tests and is 3–23 times faster than classical rerandomization. Finally, we apply the PSRR method to analyze two clinical trial datasets, both of which demonstrate the advantages of our method.

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PCA Rerandomization

Cited by 7 publications

References 38 publications

Rerandomization and optimal matching

Rerandomization and optimal matching

Power and sample size calculations for rerandomization

Pair-Switching Rerandomization

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