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Inference under covariate-adaptive randomization with multiple treatments

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 in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More speci cally, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni et al. (2018), covariate-adaptive randomization refers to randomization schemes that fi rst stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum. Importantly, in contrast to Bugni et al. (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a "fully saturated" linear regression, i.e., a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity consistent estimator of the asymptotic variance are invalid in the sense that they may have limiting rejection probability under the null hypothesis strictly greater than the nominal level; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact in the sense that they have limiting rejection probability under the null hypothesis equal to the nominal level. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with "strata fi xed effects," i.e., a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are conservative in the sense that they have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact, thereby generalizing results in Bugni et al. (2018) for the case of a single treatment to multiple treatments. A simulation study and an empirical application illustrate the practical relevance of our theoretical results.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2019. "Inference under covariate-adaptive randomization with multiple treatments," CeMMAP working papers CWP04/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:04/19
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    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/CWP041919.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Covariate-adaptive randomization; multiple treatments; stratifi ed block randomization; Efron's biased-coin design; treatment assignment; randomized controlled trial; strata fixed effects; saturated regression;

    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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