Sampling‐based Randomised Designs for Causal Inference under the Potential Outcomes Framework

Branson, Zach; Dasgupta, Tirthankar

doi:10.1111/insr.12339

Cited by 6 publications

(5 citation statements)

References 37 publications

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“…However, the results in the previous paragraph only hold when the variances S 2 1 and S 2 0 are fixed, and it's difficult to imagine a scenario where an increase in S 2 ⌧ does not also increase S 2 1 , which adversely affects power. For example, previous works studying treatment effect heterogeneity have considered datagenerating models like Y i (1) = Y i (0) + ⌧ + ⌧ Y i (0) for some heterogeneity parameter ⌧ (Ding et al, 2016;Branson & Dasgupta, 2020). In this case, S 2 1 = (1 + ⌧ ) 2 S 2 0 and S 2 ⌧ = 2 ⌧ S 2 0 , and thus more heterogeneity increases both S 2 1 and S 2 ⌧ .…”

Section: H3 With Treatment Effect Heterogeneitymentioning

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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Section: H3 With Treatment Effect Heterogeneitymentioning

confidence: 99%

Power and sample size calculations for rerandomization

Branson

Ding

2023

Biometrika

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“…However, the results in the previous paragraph only hold when the variances S 2 1 and S 2 0 are fixed, and it's difficult to imagine a scenario where an increase in S 2 τ does not also increase S 2 1 , which adversely affects power. For example, previous works studying treatment effect heterogeneity have considered data-generating models like Y i (1) = Y i (0) + τ + σ τ Y i (0) for some heterogeneity parameter σ τ (Ding et al, 2016;Branson & Dasgupta, 2020). In this case, S 2 1 = (1 + σ τ ) 2 S 2 0 and S 2 τ = σ 2 τ S 2 0 , and thus more heterogeneity increases both S 2 1 and S 2 τ .…”

Section: Treatment Effect Heterogeneitymentioning

confidence: 99%

Power and Sample Size Calculations for Rerandomized Experiments

Branson¹,

Li²,

Ding³

2022

Preprint

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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.

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“…which is actually the variance of √ n(τ − τ ) under the CRSE (Imbens and Rubin 2015;Branson and Dasgupta 2019). Throughout the paper, we will also use the explicit conditioning on ReSEM to emphasize that we are studying the repeated sampling properties under ReSEM.…”

Section: Asymptotic Distribution Under Rerandomizationmentioning

confidence: 99%

“…In a standard randomized survey experiment, the first step is a simple random sampling (SRS) and the second step is a completely randomized experiment (CRE); see, e.g., Imbens and Rubin (2015, Chapter 6) and Branson and Dasgupta (2019). For descriptive convenience, we call it a completely randomized survey experiment (CRSE).…”

Section: Introductionmentioning

confidence: 99%

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Rejective Sampling, Rerandomization and Regression Adjustment in Survey Experiments

Yang¹,

Qu²,

Li³

2021

Preprint

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Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morgan and Rubin (2012), chance imbalances often exist in covariate distributions between different treatment groups even under completely randomized experiments. Not surprisingly, such covariate imbalances also occur in randomized survey experiments. Furthermore, the covariate imbalances happen not only between different treatment groups, but also between the sampled experimental units and the overall population of interest. In this paper, we propose a two-stage rerandomization design that can actively avoid undesirable covariate imbalances at both the sampling and treatment assignment stages. We further develop asymptotic theory for rerandomized survey experiments, demonstrating that rerandomization provides better covariate balance, more precise treatment effect estimators, and shorter large-sample confidence intervals. We also propose covariate adjustment to deal with remaining covariate imbalances after rerandomization, showing that it can further improve both the sampling and estimated precision. Our work allows general relationship among covariates at the sampling, treatment assignment and analysis stages, and generalizes both rerandomization in classical randomized experiments (Morgan and Rubin 2012) and rejective sampling in survey sampling (Fuller 2009).

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Sampling‐based Randomised Designs for Causal Inference under the Potential Outcomes Framework

Cited by 6 publications

References 37 publications

Power and sample size calculations for rerandomization

Power and sample size calculations for rerandomization

Power and Sample Size Calculations for Rerandomized Experiments

Rejective Sampling, Rerandomization and Regression Adjustment in Survey Experiments

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