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Inference under Covariate-Adaptive Randomization

Author

Listed:
  • Federico A. Bugni

    (Institute for Fiscal Studies and Duke University)

  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Azeem M. Shaikh

    (Institute for Fiscal Studies and University of Chicago)

Abstract

This paper studies inference for the average treatment eff ect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum. Such schemes include, for example, Efron's biased-coin design and strati ed block randomization. When testing the null hypothesis that the average treatment eff ect equals a pre-speci fied value in such settings, we fi rst show that the usual two-sample t-test is conservative in the sense that it has limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level. In a simulation study, we fi nd that the rejection probability may in fact be dramatically less than the nominal level. We show further that these same conclusions remain true for a naïve permutation test, but that a modi fied version of the permutation test yields a test that is non-conservative in the sense that its limiting rejection probability under the null hypothesis equals the nominal level for a wide variety of randomization schemes. The modi fied version of the permutation test has the additional advantage that it has rejection probability exactly equal to the nominal level for some distributions satisfying the null hypothesis and some randomization schemes. Finally, we show that the usual t-test (on the coefficient on treatment assignment) in a linear regression of outcomes on treatment assignment and indicators for each of the strata yields a non-conservative test as well under even weaker assumptions on the randomization scheme. In a simulation study, we fi nd that the non-conservative tests have substantially greater power than the usual two-sample t-test.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2016. "Inference under Covariate-Adaptive Randomization," CeMMAP working papers CWP21/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:21/16
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    References listed on IDEAS

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    Cited by:

    1. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2018. "Inference Under Covariate-Adaptive Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1784-1796, October.
    2. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," Review of Economic Studies, Oxford University Press, vol. 85(3), pages 1577-1608.
    3. Ruoxuan Xiong & Susan Athey & Mohsen Bayati & Guido Imbens, 2019. "Optimal Experimental Design for Staggered Rollouts," Papers 1911.03764, arXiv.org, revised Aug 2020.
    4. Gonzalo Vazquez-Bare, 2017. "Identification and Estimation of Spillover Effects in Randomized Experiments," Papers 1711.02745, arXiv.org, revised Nov 2020.
    5. Young, Alwyn, 2019. "Channeling Fisher: randomization tests and the statistical insignificance of seemingly significant experimental results," LSE Research Online Documents on Economics 101401, London School of Economics and Political Science, LSE Library.
    6. John A. List & Azeem M. Shaikh & Yang Xu, 2019. "Multiple hypothesis testing in experimental economics," Experimental Economics, Springer;Economic Science Association, vol. 22(4), pages 773-793, December.
    7. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    8. Tymon Sloczynski, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," Working Papers 125, Brandeis University, Department of Economics and International Businesss School.
    9. Vishal Kamat, 2017. "Identification of Program Access Effects with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Oct 2020.
    10. Yichong Zhang & Xin Zheng, 2020. "Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization," Quantitative Economics, Econometric Society, vol. 11(3), pages 957-982, July.
    11. Simon Heß, 2017. "Randomization inference with Stata: A guide and software," Stata Journal, StataCorp LP, vol. 17(3), pages 630-651, September.
    12. Isaiah Andrews & Emily Oster, 2017. "A Simple Approximation for Evaluating External Validity Bias," NBER Working Papers 23826, National Bureau of Economic Research, Inc.
    13. Abhijit Banerjee & Sylvain Chassang & Sergio Montero & Erik Snowberg, 2017. "A Theory of Experimenters," CESifo Working Paper Series 6678, CESifo.
    14. Guiteras, Raymond P. & Levine, David I. & Polley, Thomas H., 2016. "The pursuit of balance in sequential randomized trials," Development Engineering, Elsevier, vol. 1(C), pages 12-25.

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    More about this item

    Keywords

    Covariate-adaptive randomization; strati ed block randomization; Efron's biased-coin design; treatment assignment; randomized controlled trial; permutation test; two-sample t-test; strata xed e ects;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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