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Inference in Cluster Randomized Trials with Matched Pairs

Author

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  • Yuehao Bai
  • Jizhou Liu
  • Azeem M. Shaikh
  • Max Tabord-Meehan

Abstract

This paper considers the problem of inference in cluster randomized trials where treatment status is determined according to a "matched pairs'' design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the cluster; by a "matched pairs'' design we mean that a sample of clusters is paired according to baseline, cluster-level covariates and, within each pair, one cluster is selected at random for treatment. We study the large-sample behavior of a weighted difference-in-means estimator and derive two distinct sets of results depending on if the matching procedure does or does not match on cluster size. We then propose a single variance estimator which is consistent in either regime. Combining these results establishes the asymptotic exactness of tests based on these estimators. Next, we consider the properties of two common testing procedures based on t-tests constructed from linear regressions, and argue that both are generally conservative in our framework. We additionally study the behavior of a randomization test which permutes the treatment status for clusters within pairs, and establish its finite-sample and asymptotic validity for testing specific null hypotheses. Finally, we propose a covariate-adjusted estimator which adjusts for additional baseline covariates not used for treatment assignment, and establish conditions under which such an estimator leads to improvements in precision. A simulation study confirms the practical relevance of our theoretical results.

Suggested Citation

  • Yuehao Bai & Jizhou Liu & Azeem M. Shaikh & Max Tabord-Meehan, 2022. "Inference in Cluster Randomized Trials with Matched Pairs," Papers 2211.14903, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2211.14903
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    References listed on IDEAS

    as
    1. Yuehao Bai, 2022. "Optimality of Matched-Pair Designs in Randomized Controlled Trials," Papers 2206.07845, arXiv.org.
    2. Jiang, Liang & Liu, Xiaobin & Zhang, Yichong, 2020. "Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs," Economics and Statistics Working Papers 15-2020, Singapore Management University, School of Economics.
    3. Yuehao Bai, 2022. "Optimality of Matched-Pair Designs in Randomized Controlled Trials," American Economic Review, American Economic Association, vol. 112(12), pages 3911-3940, December.
    4. Fangzhou Su & Peng Ding, 2021. "Model‐assisted analyses of cluster‐randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 994-1015, November.
    5. Liang Jiang & Xiaobin Liu & Peter C.B. Phillips & Yichong Zhang, 2020. "Bootstrap Inference for Quantile Treatment Effects in Randomized Experiments with Matched Pairs," Cowles Foundation Discussion Papers 2249, Cowles Foundation for Research in Economics, Yale University.
    6. Max Cytrynbaum, 2021. "Optimal Stratification of Survey Experiments," Papers 2111.08157, arXiv.org, revised Aug 2023.
    7. Yuehao Bai & Jizhou Liu & Max Tabord-Meehan, 2022. "Inference for Matched Tuples and Fully Blocked Factorial Designs," Papers 2206.04157, arXiv.org, revised Nov 2023.
    Full references (including those not matched with items on IDEAS)

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