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Stratification Trees for Adaptive Randomization in Randomized Controlled Trials


  • Max Tabord-Meehan


This paper proposes an adaptive randomization procedure for two-stage randomized controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimize the variance of an estimator for the average treatment effect (ATE). We consider selection from a class of stratified randomization procedures which we call stratification trees: these are procedures whose strata can be represented as decision trees, with differing treatment assignment probabilities across strata. By using the first wave to estimate a stratification tree, we simultaneously select which covariates to use for stratification, how to stratify over these covariates, as well as the assignment probabilities within these strata. Our main result shows that using this randomization procedure with an appropriate estimator results in an asymptotic variance which is minimal in the class of stratification trees. Moreover, the results we present are able to accommodate a large class of assignment mechanisms within strata, including stratified block randomization. In a simulation study, we find that our method, paired with an appropriate cross-validation procedure ,can improve on ad-hoc choices of stratification. We conclude by applying our method to the study in Karlan and Wood (2017), where we estimate stratification trees using the first wave of their experiment.

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  • Max Tabord-Meehan, 2018. "Stratification Trees for Adaptive Randomization in Randomized Controlled Trials," Papers 1806.05127,, revised Jan 2020.
  • Handle: RePEc:arx:papers:1806.05127

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    References listed on IDEAS

    1. Jinyong Hahn & Keisuke Hirano & Dean Karlan, 2011. "Adaptive Experimental Design Using the Propensity Score," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 96-108, January.
    2. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2017. "Using Instrumental Variables for Inference about Policy Relevant Treatment Effects," NBER Working Papers 23568, National Bureau of Economic Research, Inc.
    3. Nathan Kallus, 2018. "Optimal a priori balance in the design of controlled experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 85-112, January.
    4. Carneiro, Pedro & Lee, Sokbae & Wilhelm, Daniel, 2016. "Optimal Data Collection for Randomized Control Trials," IZA Discussion Papers 9908, Institute of Labor Economics (IZA).
    5. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    6. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
    7. Rachel Glennerster & Kudzai Takavarasha, 2013. "Running Randomized Evaluations: A Practical Guide," Economics Books, Princeton University Press, edition 1, number 10085, December.
    8. Eric Mbakop & Max Tabord-Meehan, 2016. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Papers 1609.03167,, revised Dec 2019.
    9. Kasy, Maximilian, 2016. "Why Experimenters Might Not Always Want to Randomize, and What They Could Do Instead," Political Analysis, Cambridge University Press, vol. 24(3), pages 324-338, July.
    10. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
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    Cited by:

    1. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2019. "Inference under covariateā€adaptive randomization with multiple treatments," Quantitative Economics, Econometric Society, vol. 10(4), pages 1747-1785, November.

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