Covariate adjustment in randomization-based causal inference for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:msup></mml:math>factorial designs

Lu, Jiannan

doi:10.1016/j.spl.2016.07.010

Cited by 36 publications

(16 citation statements)

References 22 publications

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“…It imputes the missing potential outcomes under a compatible sharp null hypothesis, and then uses the studen- Our theory ignores covariates. The analysis of covariance is a classical topic (Fisher 1935) and still attracts attention (Lin 2013;Lu 2016a;Fogarty 2018b,a;Middleton 2018). Tukey (1993) and Rosenbaum (2002b) discussed strategies for testing sharp null hypotheses.…”

Section: Discussionmentioning

confidence: 99%

Randomization Tests for Weak Null Hypotheses in Randomized Experiments

Ding

2020

Journal of the American Statistical Association

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The Fisher randomization test (FRT) is appropriate for any test statistic, under a sharp null hypothesis that can recover all missing potential outcomes. However, it is often of interest to test a weak null hypothesis that the treatment does not affect the units on average. To use the FRT for a weak null hypothesis, we must address two issues. First, we need to impute the missing potential outcomes although the weak null hypothesis cannot determine all of them. Second, we need to choose a suitable test statistic. For a general weak null hypothesis, we propose an approach to imputing missing potential outcomes under a compatible sharp null hypothesis. With this imputation scheme, we advocate using a studentized statistic. The resulting FRT has multiple desirable features. First, it is model-free. Second, it is finite-sample exact under the sharp null hypothesis that we use to impute the potential outcomes. Third, it preserves correct large-sample type I errors under the weak null hypothesis of interest. Therefore, our FRT is agnostic to treatment effect heterogeneity. We establish a unified theory for general factorial experiments. We also extend it to stratified and clustered experiments.

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Section: Discussionmentioning

confidence: 99%

Randomization Tests for Weak Null Hypotheses in Randomized Experiments

Ding

2020

Journal of the American Statistical Association

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“…It is interesting to extend the discussion to covariate adjustment in more complicated settings, such as high dimensional covariates (Bloniarz et al ., ; Wager et al ., ; Lei and Ding, ), logistic regression for binary outcomes (Zhang et al ., ; Freedman, 2008d; Moore and van der Laan, ; Moore et al ., ) and adjustment using machine learning methods (Bloniarz et al ., ; Wager et al ., ; Wu and Gagnon‐Bartsch, ). It is also important to consider covariate adjustment for general non‐linear estimands (Zhang et al ., ; Jiang et al ., ; Tian et al ., ) and general designs (Middleton, ), such as blocking (Miratrix et al ., ; Bugni et al ., ), matched pairs (Fogarty, ), and factorial designs (Lu, ).…”

Section: Discussionmentioning

confidence: 99%

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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“…Practical limitations hinder the actualization of theoretical benefits: an issue which we now seek to mitigate. Recent work by Aronow and Middleton (2013), Lin (2013), Bloniarz et al (2016), Lu (2016) and Fogarty (2018) among others has shown how regression adjustment can be utilized to provide improved estimators for the average treatment effect in various experimental designs. In this work, we illustrate how regression adjustment can be utilized to yield improved variance estimators in finely stratified experiments while using the classical difference-in-means estimator for the average treatment effect, hence reducing estimator variance through fine stratification while preserving the so-called 'hands above the table' analysis (Freedman, 2008;Lin, 2013); see also Cox (2007) and Rosenbaum (2010), section 6, for more on the importance of transparency for facilitating critical discussion.…”

Section: An Insight From Classical Least Squares Theorymentioning

confidence: 99%

On Mitigating the Analytical Limitations of Finely Stratified Experiments

Fogarty

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Although attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations that are not present in block‐randomized experiments with multiple treated and control individuals in each block. In short, when using a weighted difference in means to estimate the sample average treatment effect, the traditional variance estimator in a paired experiment is conservative unless the pairwise average treatment effects are constant across pairs; however, in more coarsely stratified experiments, the corresponding variance estimator is unbiased if treatment effects are constant within blocks, even if they vary across blocks. Using insights from classical least squares theory, we present an improved variance estimator that is appropriate in finely stratified experiments. The variance estimator remains conservative in expectation but is asymptotically no more conservative than the classical estimator and can be considerably less conservative. The magnitude of the improvement depends on the extent to which effect heterogeneity can be explained by observed covariates. Aided by this estimator, a new test for the null hypothesis of a constant treatment effect is proposed. These findings extend to some, but not all, superpopulation models, depending on whether the covariates are viewed as fixed across samples.

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Covariate adjustment in randomization-based causal inference for2Kfactorial designs

Cited by 36 publications

References 22 publications

Randomization Tests for Weak Null Hypotheses in Randomized Experiments

Randomization Tests for Weak Null Hypotheses in Randomized Experiments

Rerandomization and Regression Adjustment

On Mitigating the Analytical Limitations of Finely Stratified Experiments

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