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Identification and Inference on Treatment Effects under Covariate-Adaptive Randomization and Imperfect Compliance

Author

Listed:
  • Federico A. Bugni
  • Mengsi Gao
  • Filip Obradovic
  • Amilcar Velez

Abstract

Randomized controlled trials (RCTs) frequently utilize covariate-adaptive randomization (CAR) (e.g., stratified block randomization) and commonly suffer from imperfect compliance. This paper studies the identification and inference for the average treatment effect (ATE) and the average treatment effect on the treated (ATT) in such RCTs with a binary treatment. We first develop characterizations of the identified sets for both estimands. Since data are generally not i.i.d. under CAR, these characterizations do not follow from existing results. We then provide consistent estimators of the identified sets and asymptotically valid confidence intervals for the parameters. Our asymptotic analysis leads to concrete practical recommendations regarding how to estimate the treatment assignment probabilities that enter in estimated bounds. In the case of the ATE, using sample analog assignment frequencies is more efficient than using the true assignment probabilities. On the contrary, using the true assignment probabilities is preferable for the ATT.

Suggested Citation

  • Federico A. Bugni & Mengsi Gao & Filip Obradovic & Amilcar Velez, 2024. "Identification and Inference on Treatment Effects under Covariate-Adaptive Randomization and Imperfect Compliance," Papers 2406.08419, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2406.08419
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    References listed on IDEAS

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    1. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    3. Martin Huber & Lukas Laffers & Giovanni Mellace, 2017. "Sharp IV Bounds on Average Treatment Effects on the Treated and Other Populations Under Endogeneity and Noncompliance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 56-79, January.
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