Properties of the Random Block Design for Clinical Trials

  • Hui ShaoEmail author
  • William F. Rosenberger
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


To avoid deterministic treatment allocations in the permuted block design (PBD), many clinical trialists prefer randomizing the block sizes as well. While such a procedure is rarely formalized, it is generally assumed that the design will be less predictable. In this paper, we formalize the random block design by assuming a discrete uniform distribution for block size. The aim of this study is to provide a statistical understanding of the RBD, by investigating its distributional properties, including the degree of predictability and variability of treatment imbalance.


Block Size Random Block Design Discrete Uniform Distribution Correct Guess Prior Allocation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Professor Rosenberger was supported by a scholarship from the German-American Fulbright Kommission, and also by the Department of Medical Statistics, RWTH Aachen University.


  1. 1.
    Berger, V.W.: Selection Bias and Covariate Imbalance in Randomized Clinical Trials. Wiley, Chichester (2005)CrossRefGoogle Scholar
  2. 2.
    Blackwell, D., Hodges, J.L.: Design for the control of selection bias. Ann. Math. Stat. 28, 449–460 (1957)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Chen, Y.P.: Which design is better? Ehrenfest urn versus biased coin. Adv. Appl. Probab. 32, 738–749 (2000)zbMATHGoogle Scholar
  4. 4.
    Heussen, N.: Der Einfluss der Randomisierung in Blöcken zufälliger Länge auf die Auswertung klinischer Studien mittels Randomisationstest. RWTH Aachen University, Aachen (2004)Google Scholar
  5. 5.
    Macian, N., Pereira, B., Shinjo, C., Dubray, C., Pickering, G.: Fibromyalgia, milnacipran and experimental pain modulation: study protocol for a double blind randomized controlled trial. Trials 16, 134 (2015)CrossRefGoogle Scholar
  6. 6.
    Matts, J.P., Lachin, J.M.: Properties of permuted-block randomization in clinical trials. Control. Clin. Trials 9, 327–344 (1988)CrossRefGoogle Scholar
  7. 7.
    Shah, B., Berger, J.S., Amoroso, N.S., Mai, X., Lorin, J.D., Danoff, A., Schwartzbard, A.Z., Lobach, I., Guo, Y., Feit, F., Slater, J., Attubato, M.J., Sedlis, S.P.: Periprocedural glycemic control in patients with diabetes mellitus undergoing coronary angiography with possible percutaneous coronary intervention. Am. J. Cardiol. 113, 1474–1480 (2014)CrossRefGoogle Scholar
  8. 8.
    Shao, H.: Exact properties of restricted randomization procedures. George Mason University, Fairfax (2015)Google Scholar
  9. 9.
    Zhao, W., Weng, Y., Wu, Q., Palesch, Y.: Quantitative comparison of randomization designs in sequential clinical trials based on treatment balance and allocation randomness. Pharm. Stat. 11, 39–48 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of StatisticsGeorge Mason UniversityFairfaxUSA

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