Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments

Middleton, Joel A.; Aronow, Peter M.

doi:10.1515/spp-2013-0002

Cited by 56 publications

(74 citation statements)

References 21 publications

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“…Future research could entail extensions to cluster randomized trials wherein clusters of individuals are independently randomized to treatment or control, with all individuals in the same cluster receiving the same randomization assignment. Causal inference methods for individually randomized studies are not necessarily valid for cluster randomized trials (Middleton and Aronow, 2015), such that the methods that are considered in this paper may not be directly applicable to cluster randomized trials.…”

Section: Discussionmentioning

confidence: 99%

Generalizing Evidence from Randomized Trials Using Inverse Probability of Sampling Weights

Buchanan

Hudgens

Cole

et al. 2018

Journal of the Royal Statistical Society Series A: Statistics in Society

102

124

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Summary Results obtained in randomized trials may not easily generalize to target populations. Whereas in randomized trials the treatment assignment mechanism is known, the sampling mechanism by which individuals are selected to participate in the trial is typically not known and assuming random sampling from the target population is often dubious. We consider an inverse probability of sampling weighted (IPSW) estimator for generalizing trial results to a target population. The IPSW estimator is shown to be consistent and asymptotically normal. A consistent sandwich-type variance estimator is derived and simulation results are presented comparing the IPSW estimator to a previously proposed stratified estimator. The methods are then utilized to generalize results from two randomized trials of HIV treatment to all people living with HIV in the United States.

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Section: Discussionmentioning

confidence: 99%

Generalizing Evidence from Randomized Trials Using Inverse Probability of Sampling Weights

Buchanan

Hudgens

Cole

et al. 2018

Journal of the Royal Statistical Society Series A: Statistics in Society

102

124

View full text Add to dashboard Cite

show abstract

“…For more technical discussion, see Ding (2014), Aronow et al (2014, and Middleton and Aronow (2015); for regularity conditions of the finite population central limit theorems, see Hájek (1960) and Lehmann (1998).…”

Section: Randomization-based Estimatormentioning

confidence: 99%

Decomposing Treatment Effect Variation

Ding

Feller

Miratrix³

2018

Journal of the American Statistical Association

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Understanding and characterizing treatment effect variation in randomized experiments has become essential for going beyond the "black box" of the average treatment effect. Nonetheless, traditional statistical approaches often ignore or assume away such variation. In the context of a randomized experiment, this paper proposes a framework for decomposing overall treatment effect variation into a systematic component that is explained by observed covariates, and a remaining idiosyncratic component. Our framework is fully randomization-based, with estimates of treatment effect variation that are fully justified by the randomization itself. Our framework can also account for noncompliance, which is an important practical complication. We make several key contributions. First, we show that randomization-based estimates of systematic variation are very similar in form to estimates from fully-interacted linear regression and two stage least squares. Second, we use these estimators to develop an omnibus test for systematic treatment effect variation, both with and without noncompliance. Third, we propose an R 2 -like measure of treatment effect variation explained by covariates and, when applicable, noncompliance. Finally, we assess these methods via simulation studies and apply them to the Head Start Impact Study, a large-scale randomized experiment.

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“…other randomization-based causal inferences invoked CLTs implicitly without a formal proof, e.g., rerandomization in Morgan and Rubin (2012), factorial experiments in Dasgupta et al (2015) and Ding (2016), and clustered randomized experiments in Middleton and Aronow (2015).…”

mentioning

confidence: 99%

“…This feature did not appear in any CLTs for sample surveys and rank statistics, but did appear in the variance formula of the difference-in-means estimator in Neyman (1923). Because of the generality of the new CLTs, they are readily applicable to many existing causal inference problems, including instrumental variable estimation, randomization tests with more than two treatment levels, multiple randomization tests, rerandomization to ensure covariate balance Rubin 2012, 2015;Li, Ding, and Rubin 2016), regression adjustment for completely randomized experiments (Freedman 2008a,b;Lin 2013), clustered randomized experiments (Middleton and Aronow 2015), and unbalanced factorial experiments (Dasgupta et al 2015), etc. The new CLTs not only justify the asymptotic properties of some existing procedures, but also help to establish new results that did not appear in the previous literature.…”

mentioning

confidence: 99%

General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference

Ding

2017

Journal of the American Statistical Association

163

184

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Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators, which, in many but not all cases, are related to asymptotic Normal distributions ensured by central limit theorems. Although previous literature has established various forms of central limit theorems for statistical inference in super population models, we still need general and convenient forms of central limit theorems for some randomization-based causal analysis of experimental data, where the parameters of interests are functions of a finite population and randomness comes solely from the treatment assignment. We use central limit theorems for sample surveys and rank statistics to establish general forms of the finite population central limit theorems that are particularly useful for proving asymptotic distributions of randomization tests under the sharp null hypothesis of zero individual causal effects, and for obtaining the asymptotic repeated sampling distributions of the causal effect estimators. The new central limit theorems hold for general experimental designs with multiple treatment levels and multiple treatment factors, and are immediately applicable for studying the asymptotic properties of many methods in causal inference, including instrumental variable, regression adjustment, rerandomization, clustered randomized experiments, and so on. Previously, the asymptotic properties of these problems are often based on heuristic arguments, which in fact rely on general forms of finite population central limit theorems that have not been established before. Our new theorems fill in this gap by providing more solid theoretical foundation for asymptotic randomization-based causal inference.

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Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments

Cited by 56 publications

References 21 publications

Generalizing Evidence from Randomized Trials Using Inverse Probability of Sampling Weights

Generalizing Evidence from Randomized Trials Using Inverse Probability of Sampling Weights

Decomposing Treatment Effect Variation

General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference

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