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Regression-assisted inference for the average treatment effect in paired experiments

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  • Colin B Fogarty

Abstract

SUMMARYIn paired randomized experiments, individuals in a given matched pair may differ on prognostically important covariates despite the best efforts of practitioners. We examine the use of regression adjustment to correct for persistent covariate imbalances after randomization, and present two regression-assisted estimators for the sample average treatment effect in paired experiments. Using the potential outcomes framework, we prove that these estimators are consistent for the sample average treatment effect under mild regularity conditions even if the regression model is improperly specified, and describe how asymptotically conservative confidence intervals can be constructed. We demonstrate that the variances of the regression-assisted estimators are no larger than that of the standard difference-in-means estimator asymptotically, and illustrate the proposed methods by simulation. The analysis does not require a superpopulation model, a constant treatment effect, or the truth of the regression model, and hence provides inference for the sample average treatment effect with the potential to increase power without unrealistic assumptions.

Suggested Citation

  • Colin B Fogarty, 2018. "Regression-assisted inference for the average treatment effect in paired experiments," Biometrika, Biometrika Trust, vol. 105(4), pages 994-1000.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:4:p:994-1000.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy034
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    Citations

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    Cited by:

    1. 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.
    2. Liang Jiang & Oliver B. Linton & Haihan Tang & Yichong Zhang, 2022. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Papers 2201.13004, arXiv.org, revised Jun 2023.
    3. Jiang, Liang & Phillips, Peter C.B. & Tao, Yubo & Zhang, Yichong, 2023. "Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations," Journal of Econometrics, Elsevier, vol. 234(2), pages 758-776.
    4. Liang Jiang & Liyao Li & Ke Miao & Yichong Zhang, 2023. "Adjustment with Many Regressors Under Covariate-Adaptive Randomizations," Papers 2304.08184, arXiv.org, revised Nov 2024.
    5. Zhao, Anqi & Ding, Peng, 2021. "Covariate-adjusted Fisher randomization tests for the average treatment effect," Journal of Econometrics, Elsevier, vol. 225(2), pages 278-294.
    6. Zhao, Anqi & Ding, Peng, 2024. "No star is good news: A unified look at rerandomization based on p-values from covariate balance tests," Journal of Econometrics, Elsevier, vol. 241(1).
    7. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    8. Edward Wu & Johann A. Gagnon-Bartsch, 2021. "Design-Based Covariate Adjustments in Paired Experiments," Journal of Educational and Behavioral Statistics, , vol. 46(1), pages 109-132, February.
    9. Max Cytrynbaum, 2023. "Covariate Adjustment in Stratified Experiments," Papers 2302.03687, arXiv.org, revised Jul 2024.
    10. Bai, Yuehao & Jiang, Liang & Romano, Joseph P. & Shaikh, Azeem M. & Zhang, Yichong, 2024. "Covariate adjustment in experiments with matched pairs," Journal of Econometrics, Elsevier, vol. 241(1).
    11. Yuehao Bai, 2022. "Optimality of Matched-Pair Designs in Randomized Controlled Trials," Papers 2206.07845, arXiv.org.
    12. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2023. "Regression adjustment in randomized controlled trials with many covariates," Papers 2302.00469, arXiv.org, revised Nov 2023.
    13. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2023. "Regression adjustment in randomized controlled trials with many covariates," STICERD - Econometrics Paper Series 627, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. 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.

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