Electronic Journal of Statistics

A new design strategy for hypothesis testing under response adaptive randomization

Alessandro Baldi Antognini, Alessandro Vagheggini, Maroussa Zagoraiou, and Marco Novelli

Full-text: Open access


The aim of this paper is to provide a new design strategy for response adaptive randomization in the case of normal response trials aimed at testing the superiority of one of two available treatments. In particular, we introduce a new test statistic based on the treatment allocation proportion ensuing the adoption of a suitable response adaptive randomization rule that could be more efficient and uniformly more powerful with respect to the classical Wald test. We analyze the conditions under which the suggested strategy, derived by matching an asymptotically best response adaptive procedure and a suitably chosen target allocation, could induce a monotonically increasing power that discriminates with high precision the chosen alternatives. Moreover, we introduce and analyze new classes of targets aimed at maximizing the power of the new statistical test, showing both analytically and via simulations i) how the power function of the suggested test increases as the ethical skew of the chosen target grows, namely overcoming the usual trade-off between ethics and inference, and ii) the substantial gain of inferential precision ensured by the proposed approach.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 2454-2481.

Received: April 2018
First available in Project Euclid: 25 July 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62L05: Sequential design 62K05: Optimal designs
Secondary: 62G20: Asymptotic properties

Asymptotic inference efficient randomized adaptive design ethics power sequential allocations

Creative Commons Attribution 4.0 International License.


Baldi Antognini, Alessandro; Vagheggini, Alessandro; Zagoraiou, Maroussa; Novelli, Marco. A new design strategy for hypothesis testing under response adaptive randomization. Electron. J. Statist. 12 (2018), no. 2, 2454--2481. doi:10.1214/18-EJS1458. https://projecteuclid.org/euclid.ejs/1532484336

Export citation


  • [1] Atkinson, A. C. and A. Biswas (2005). Bayesian adaptive biased-coin designs for clinical trials with normal responses., Biometrics 61, 118–125.
  • [2] Atkinson, A. C. and A. Biswas (2014)., Randomised Response-Adaptive Designs in Clinical Trials. Boca Raton: Chapman & Hall/CRC Press.
  • [3] Azriel, D., M. Mandel, and Y. Rinott (2012). Optimal allocation to maximize power of two-sample tests for binary response., Biometrika 99, 101–113.
  • [4] Baldi Antognini, A. and A. Giovagnoli (2010). Compound optimal allocation for individual and collective ethics in binary clinical trials., Biometrika 97, 935–946.
  • [5] Baldi Antognini, A. and A. Giovagnoli (2015)., Adaptive Designs for Sequential Treatment Allocation. Chapman & Hall/CRC Biostatistics.
  • [6] Baldi Antognini, A., A. Vagheggini, and M. Zagoraiou (2016). Is the classical wald test always suitable under response-adaptive randomization?, Statistical Methods in Medical Research, available online, DOI: 10.1177/ 0962280216680241.
  • [7] Baldi Antognini, A. and M. Zagoraiou (2015). On the almost sure convergence of adaptive allocation procedures., Bernoulli 21, 881–908.
  • [8] Bandyopadhyay, U. and A. Biswas (2001). Adaptive designs for normal responses with prognostic factors., Biometrika 88, 409–419.
  • [9] CHMP (2007). Reflection paper on methodological issues in confirmatory clinical trials planned with an adaptive design. Available on, line.
  • [10] FDA (2010). Guidance for industry. Adaptive design clinical trials for drugs and biologics (draft document). Available on, line.
  • [11] Hu, F. and W. F. Rosenberger (2003). Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons., Journal of the American Statistical Association 98, 671–678.
  • [12] Hu, F. and W. F. Rosenberger (2006)., The Theory of Response-Adaptive Randomization in Clinical Trials. New York: John Wiley & Sons.
  • [13] Hu, F. and L.-X. Zhang (2004). Asymptotic properties of doubly adaptive biased coin designs for multi-treatment clinical trials., The Annals of Statistics 32, 268–301.
  • [14] Hu, F., L.-X. Zhang, and X. He (2009). Efficient randomized adaptive designs., The Annals of Statistics 37, 2543–2560.
  • [15] Ivanova, A., A. Biswas, and A. Lurie (2006). Response-adaptive designs for continuous outcomes., Journal of Statistical Planning and Inference 136, 1845–1852.
  • [16] Lehmann, E. L. (1999)., Elements of large-sample theory. Springer Verlag, New York.
  • [17] Melfi, V. and C. Page (2000). Estimation after adaptive allocation., Journal of Statistical Planning and Inference 29, 353–363.
  • [18] Rosenberger, W. F. and J. L. Lachin (2002)., Randomization in Clinical Trials: Theory and Practice. John Wiley & Sons, New York.
  • [19] Rosenberger, W. F., N. Stallard, A. Ivanova, C. N. Harper, and M. L. Ricks (2001). Optimal adaptive designs for binary response trials., Biometrics 57, 909–913.
  • [20] Thall, P. F., P. Fox, and J. Wathen (2015). Some caveats for outcome adaptive randomization in clinical trials. In O. Sverdlov (Ed.), Modern adaptive randomized clinical trials: statistical and practical aspects, pp. 287–305. Oxford: Chapman & Hall/CRC Biostatistics.
  • [21] Thall, P. F., P. Fox, and J. Wathen (2015). Statistical controversies in clinical research: scientific and ethical problems with adaptive randomization in comparative clinical trials., Annals of Oncology 26, 1621–1628.
  • [22] Tymofyeyev, Y., W. F. Rosenberger, and F. Hu (2007). Implementing optimal allocation in sequential binary response experiments., Journal of the American Statistical Association 102, 224–234.
  • [23] Yi, Y. and X. Wang (2011). Comparison of Wald, score, and likelihood ratio tests for response adaptive designs., Journal of Statistical Theory and Applications 10, 553–569.
  • [24] Zhang, L.-X. and W. F. Rosenberger (2006). Response-adaptive randomization for clinical trials with continuous outcomes., Biometrics 62, 562–569.