Gaussian Prepivoting for Finite Population Causal Inference

Cohen, Peter; Fogarty, Colin B.

doi:10.1111/rssb.12439

Cited by 8 publications

(3 citation statements)

References 34 publications

(71 reference statements)

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“…Compare Corollary 5 with Corollary 1 to see that the unadjusted τn / se n , whereas proper under complete randomization, is no longer proper under ReM due to the non-normal limiting distribution of τ π n . Cohen and Fogarty (2020) also noticed this phenomenon and gave a numeric example. They proposed a prepivoting approach to improve studentization.…”

Section: Frt With Rerandomizationmentioning

confidence: 83%

Covariate-adjusted Fisher randomization tests for the average treatment effect

Zhao

Ding

2020

Preprint

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Fisher's randomization test (frt) delivers exact p-values under the strong null hypothesis of no treatment effect on any units whatsoever and allows for flexible covariate adjustment to improve the power. Of interest is whether the procedure could also be valid for testing the weak null hypothesis of zero average treatment effect. Towards this end, we evaluate two general strategies for frt with covariate-adjusted test statistics: that based on the residuals from an outcome model with only the covariates, and that based on the output from an outcome model with both the treatment and the covariates. Based on theory and simulation, we recommend using the ordinary least squares (ols) fit of the observed outcome on the treatment, centered covariates, and their interactions for covariate adjustment, and conducting frt with the robust tvalue of the treatment as the test statistic. The resulting frt is finite-sample exact for the strong null hypothesis, asymptotically valid for the weak null hypothesis, and more powerful than the unadjusted analog under alternatives, all irrespective of whether the linear model is correctly specified or not. We develop the theory for complete randomization, cluster randomization, stratified randomization, and rerandomization, respectively, and give a recommendation for the test procedure and test statistic under each design. We first focus on the finite-population perspective and then extend the result to the super-population perspective, highlighting the difference in standard errors. Motivated by the similarity in procedure, we also evaluate the design-based properties of five existing permutation tests originally for linear models and show the superiority of the proposed frt for testing the treatment effects.

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Section: Frt With Rerandomizationmentioning

confidence: 83%

Covariate-adjusted Fisher randomization tests for the average treatment effect

Zhao

Ding

2020

Preprint

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“…The observed treated-minus-control difference in means centered by the sample average treatment effect has an expectation equal to zero under both constant and heterogeneous effects in a completely randomized design; however, the variance for the difference in means computed under the assumption of constant effects may be too large or too small if instead effects are heterogeneous (Cohen & Fogarty, 2022;Ding, 2017;Loh et al, 2017). A single mode of inference that is both exact under constant effects and asymptotically correct for the weak null is attained by instead employing a studentized randomization distribution, where one simply permutes the centered difference in means divided by a suitable standard error estimator; see Bai et al (2021) for developments in adaptively paired experiments, and see Janssen (1997) and Chung and Romano (2013) for related developments in robust permutation tests.…”

Section: Introductionmentioning

confidence: 99%

Testing Weak Nulls in Matched Observational Studies

Fogarty

2022

Biometrics

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We develop sensitivity analyses for the sample average treatment effect in matched observational studies while allowing unit‐level treatment effects to vary. The methods may be applied to studies using any optimal without‐replacement matching algorithm. In contrast to randomized experiments and to paired observational studies, we show for general matched designs that over a large class of test statistics, any procedure bounding the worst‐case expectation while allowing for arbitrary effect heterogeneity must be unnecessarily conservative if treatment effects are actually constant across individuals. We present a sensitivity analysis which bounds the worst‐case expectation while allowing for effect heterogeneity, and illustrate why it is generally conservative if effects are constant. An alternative procedure is presented that is asymptotically sharp if treatment effects are constant, and that is valid for testing the sample average effect under additional restrictions which may be deemed benign by practitioners. Simulations demonstrate that this alternative procedure results in a valid sensitivity analysis for the weak null hypothesis under a host of reasonable data‐generating processes. The procedures allow practitioners to assess robustness of estimated sample average treatment effects to hidden bias while allowing for effect heterogeneity in matched observational studies.

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“…In contrast, the Fisher randomization tests performed well. In general, many scholars advocate Fisher randomization tests as a credible and flexible inference approach over asymptotic inference based on extensive empirical studies (Bind and Rubin, 2020; Keele, 2015; Proschan and Dodd, 2019; Young, 2019) and theoretical analyses (Branson, 2021; Cohen and Fogarty, 2022; Caughey et al., 2021; Luo et al., 2021; Wu and Ding, 2021; Zhao and Ding, 2021).…”

Section: Introductionmentioning

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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Gaussian Prepivoting for Finite Population Causal Inference

Cited by 8 publications

References 34 publications

Covariate-adjusted Fisher randomization tests for the average treatment effect

Covariate-adjusted Fisher randomization tests for the average treatment effect

Testing Weak Nulls in Matched Observational Studies

Pair-Switching Rerandomization

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