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Qini Curves for Multi-armed Treatment Rules

Author

Listed:
  • Sverdrup, Erik

    (Monash U)

  • Wu, Han

    (Two Sigma)

  • Athey, Susan

    (Stanford U)

  • Wager, Stefan

    (Stanford U)

Abstract

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout.

Suggested Citation

  • Sverdrup, Erik & Wu, Han & Athey, Susan & Wager, Stefan, 2024. "Qini Curves for Multi-armed Treatment Rules," Research Papers 4216, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:4216
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    References listed on IDEAS

    as
    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Eitan Zemel, 1980. "The Linear Multiple Choice Knapsack Problem," Operations Research, INFORMS, vol. 28(6), pages 1412-1423, December.
    3. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.
    4. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    5. Luedtke Alexander R. & van der Laan Mark J., 2016. "Optimal Individualized Treatments in Resource-Limited Settings," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 283-303, May.
    6. Kosuke Imai & Michael Lingzhi Li, 2023. "Experimental Evaluation of Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 242-256, January.
    7. Gerber, Alan S. & Green, Donald P. & Larimer, Christopher W., 2008. "Social Pressure and Voter Turnout: Evidence from a Large-Scale Field Experiment," American Political Science Review, Cambridge University Press, vol. 102(1), pages 33-48, February.
    8. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    9. Hans Kellerer & Ulrich Pferschy & David Pisinger, 2004. "Knapsack Problems," Springer Books, Springer, number 978-3-540-24777-7, March.
    10. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, November.
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