IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v41y2026i4d10.1007_s00180-026-01748-0.html

Balanced random assignments for multiple treatment groups using the Cube method

Author

Listed:
  • Ejub Talovic

    (University of Neuchâtel, Institute of Statistics)

  • Yves Tillé

    (University of Neuchâtel, Institute of Statistics)

Abstract

In this article, we introduce a novel approach for achieving covariate balance across multiple treatment groups using a modified version of the Cube method, traditionally employed in survey sampling for generating balanced samples. This enhanced Cube method facilitates the assignment of participants to multiple treatment groups in a balanced manner, while accounting for multiple covariates. Importantly, our method accommodates scenarios where treatment groups may have unequal sizes and where inclusion probabilities may differ across units and groups. We also propose a randomization test to assess the treatment effects. Additionally, we provide a variance approximation and corresponding estimator that enable the construction of confidence intervals for the treatment effects.

Suggested Citation

  • Ejub Talovic & Yves Tillé, 2026. "Balanced random assignments for multiple treatment groups using the Cube method," Computational Statistics, Springer, vol. 41(4), pages 1-20, June.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:4:d:10.1007_s00180-026-01748-0
    DOI: 10.1007/s00180-026-01748-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-026-01748-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-026-01748-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhenzhen Xu & John D. Kalbfleisch, 2010. "Propensity Score Matching in Randomized Clinical Trials," Biometrics, The International Biometric Society, vol. 66(3), pages 813-823, September.
    2. Christopher Harshaw & Fredrik Sävje & Daniel A. Spielman & Peng Zhang, 2024. "Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(548), pages 2934-2946, October.
    3. Yang, Haoyu & Qin, Yichen & Wang, Fan & Li, Yang & Hu, Feifang, 2023. "Balancing covariates in multi-arm trials via adaptive randomization," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    4. Raphaël Jauslin & Bardia Panahbehagh & Yves Tillé, 2022. "Sequential spatially balanced sampling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(8), December.
    5. D. R. Cox, 2009. "Randomization in the Design of Experiments," International Statistical Review, International Statistical Institute, vol. 77(3), pages 415-429, December.
    6. Anton Grafström & Yves Tillé, 2013. "Doubly balanced spatial sampling with spreading and restitution of auxiliary totals," Environmetrics, John Wiley & Sons, Ltd., vol. 24(2), pages 120-131, March.
    7. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
    8. Ho, Daniel E. & Imai, Kosuke & King, Gary & Stuart, Elizabeth A., 2007. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis, Cambridge University Press, vol. 15(3), pages 199-236, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yves Tillé, 2022. "Some Solutions Inspired by Survey Sampling Theory to Build Effective Clinical Trials," International Statistical Review, International Statistical Institute, vol. 90(3), pages 481-498, December.
    2. Wilmer Prentius, 2024. "Locally correlated Poisson sampling," Environmetrics, John Wiley & Sons, Ltd., vol. 35(2), March.
    3. Tomasz Bąk, 2021. "Spatial sampling methods modified by model use," Statistics in Transition New Series, Polish Statistical Association, vol. 22(2), pages 143-154, June.
    4. Matei Alina, 2021. "Book Review," Journal of Official Statistics, Sciendo, vol. 37(4), pages 1079-1081, December.
    5. Zhenzhen Xu & John D. Kalbfleisch, 2013. "Repeated Randomization and Matching in Multi-Arm Trials," Biometrics, The International Biometric Society, vol. 69(4), pages 949-959, December.
    6. G. Alleva & G. Arbia & P. D. Falorsi & V. Nardelli & A. Zuliani, 2023. "Optimal two-stage spatial sampling design for estimating critical parameters of SARS-CoV-2 epidemic: Efficiency versus feasibility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 983-999, September.
    7. Robertson, Blair & Price, Chris & Reale, Marco, 2026. "Double dipping with balanced sampling," Statistics & Probability Letters, Elsevier, vol. 228(C).
    8. Maria Michela Dickson & Yves Tillé, 2016. "Ordered spatial sampling by means of the traveling salesman problem," Computational Statistics, Springer, vol. 31(4), pages 1359-1372, December.
    9. Pashley Nicole E. & Basse Guillaume W. & Miratrix Luke W., 2021. "Conditional as-if analyses in randomized experiments," Journal of Causal Inference, De Gruyter, vol. 9(1), pages 264-284, January.
    10. Juha Heikkinen & Helena M. Henttonen & Matti Katila & Sakari Tuominen, 2025. "Stratified, Spatially Balanced Cluster Sampling for Cost‐Efficient Environmental Surveys," Environmetrics, John Wiley & Sons, Ltd., vol. 36(5), July.
    11. Rosa M. Di Biase & Marzia Marcheselli & Caterina Pisani, 2025. "Achieving spatial balance in environmental surveys under constant inclusion probabilities or inclusion density functions," Environmetrics, John Wiley & Sons, Ltd., vol. 36(1), January.
    12. ak Tomasz B, 2021. "Spatial sampling methods modified by model use," Statistics in Transition New Series, Statistics Poland, vol. 22(2), pages 143-154, June.
    13. Liu, Yan & Chen, Xi & Yan, Zhijun, 2019. "Depression in the House: The Effects of Household Air Pollution from Solid Fuel Use in China," IZA Discussion Papers 12654, IZA Network @ LISER.
    14. Noemi Kreif & Richard Grieve & Rosalba Radice & Zia Sadique & Roland Ramsahai & Jasjeet S. Sekhon, 2012. "Methods for Estimating Subgroup Effects in Cost-Effectiveness Analyses That Use Observational Data," Medical Decision Making, , vol. 32(6), pages 750-763, November.
    15. Do, Manh Hung & Nguyen, Trung Thanh & Grote, Ulrike, 2023. "Land consolidation, rice production, and agricultural transformation: Evidence from household panel data for Vietnam," Economic Analysis and Policy, Elsevier, vol. 77(C), pages 157-173.
    16. Taylor, David & Roberts, Jessica & Rose, Vanessa & Gyani, Alex & Shlonsky, Aron, 2025. "Examining the impact of an accommodation and support intervention in reducing homelessness amongst care leavers in Australia: A hybrid type-1 implementation-effectiveness study using propensity score methods," Children and Youth Services Review, Elsevier, vol. 179(C).
    17. Federico Biagi & Daniele Bondonio & Alberto Martini, 2015. "Counterfactual Impact Evaluation of Enterprise Support Programmes. Evidence from a Decade of Subsidies to Italian Firm," ERSA conference papers ersa15p1619, European Regional Science Association.
    18. Zichen Deng & Maarten Lindeboom, 2021. "Early-life Famine Exposure, Hunger Recall and Later-life Health," Tinbergen Institute Discussion Papers 21-054/V, Tinbergen Institute.
    19. Leah Warfield Smith & Randall Lee Rose & Alex R. Zablah & Heath McCullough & Mohammad “Mike” Saljoughian, 2023. "Examining post-purchase consumer responses to product automation," Journal of the Academy of Marketing Science, Springer, vol. 51(3), pages 530-550, May.
    20. Baron, Opher & Callen, Jeffrey L. & Segal, Dan, 2023. "Does the bullwhip matter economically? A cross-sectional firm-level analysis," International Journal of Production Economics, Elsevier, vol. 259(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:41:y:2026:i:4:d:10.1007_s00180-026-01748-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.