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Cited by 322Statistical Methods in Clinical TrialsOptimal Experimental Design MethodsAdvanced Causal Inference Techniques

Properties of permuted-block randomization in clinical trials

Matts, John P., Lachin, John M.·1988·Controlled Clinical Trials
DOI 10.1016/0197-2456(88)90047-5
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Abstract

This article describes some of the important statistical properties of the commonly used permuted-block design, also known simply as blocked-randomization. Under a permutation model for statistical tests, proper analyses should employ tests that incorporate the blocking used in the randomization. These include the block-stratified Mantel-Haenszel chi-square test for binary data, the blocked analysis of variance F test, and the blocked nonparametric linear rank test. It is common, however, to ignore the blocking in the analysis. For these tests, it is shown that the size of a test obtained from an analysis incorporating the blocking (say T), versus an analysis ignoring the blocking (say TI), is related to the intrablock correlation coefficient (R) as TI = T(1-R). For blocks of common length 2m, the range of R is from -1/(2m-1) to 1. Thus, if there is a positive intrablock correlation, which is more likely than not for m greater than 1, an analysis ignoring blocking will be unduly conservative. Permutation tests are also presented for the case of stratified analyses within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for the analysis when responses from some patients are assumed to be missing-at-random. An alternative strategy that requires no assumptions is to perform the analysis using only the subset of complete blocks in which no observations are missing. The Blackwell-Hodges model is used to assess the potential for selection bias induced by investigator attempts to guess which treatment is more likely to be assigned to each incoming patient. In an unmasked trial, the permuted-block design provides substantial potential for selection bias in the comparison of treatments due to the predictability of the assignments that is induced by the requirement of balance within blocks. Further, this bias is not eliminated by the use of random block sizes. We also modify the Blackwell-Hodges model to allow for selection bias only when the investigator is able to discern the next assignment with certainty. This type of bias is reduced by the use of random block sizes and is eliminated only if the possible block sizes are unknown to the investigators. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimation of treatment effects due to covariate imbalances. For the permuted-block design, the variance of this bias approaches that of complete randomization as the half-block length m----infinity.(ABSTRACT TRUNCATED AT 400 WORDS)

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Authors
Matts, J. P., & Lachin, J. M.
Affiliations
  • University of Minnesota (US)
  • George Washington University (US)
Corresponding author
Matts, John P.
ORCID
Lachin, John M.
Venue
Controlled Clinical Trials
Publisher
Elsevier BV
Published
1988-12
Volume
9
Issue
4
Pages
327-344
ISSN
0197-2456 (ISSN-L)
DOI
10.1016/0197-2456(88)90047-5
OpenAlex
W2005415125
Cited by
321
References
18
Citations by year
2026: 14 · 2025: 13 · 2024: 23 · 2023: 22 · 2022: 19 · 2021: 18 · 2020: 33 · 2019: 14 · 2018: 6 · 2017: 15 · 2016: 13 · 2015: 18 · 2014: 16 · 2013: 12 · 2012: 15
FWCI
4.39
Type
journal article
Language
en
Open access
closed
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Controlled Clinical Trials (publishedVersion)
  • PubMed (publishedVersion)
Funders
  • U.S. Public Health Service (R01-DI-39826)
  • National Heart, Lung, and Blood Institute (HL15265)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords
permuted block randomization, permutation tests, nonparametric rank tests, stratified analysis, selection bias, covariate imbalance, treatment effect estimation
MeSH terms
Analysis of Variance, Clinical Trials as Topic, Humans, Random Allocation, Research Design, Models, Statistical

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