Cited by 308Statistical Methods in Clinical TrialsOptimal Experimental Design MethodsAdvanced Causal Inference Techniques

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Properties of the urn randomization in clinical trials

Wei, L.J., Lachin, John M.·1988·Controlled Clinical Trials

DOI 10.1016/0197-2456(88)90048-7

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Abstract

In this article we review the important statistical properties of the urn randomization (design) for assigning patients to treatment groups in a clinical trial. The urn design is the most widely studied member of the family of adaptive biased-coin designs. Such designs are a compromise between designs that yield perfect balance in treatment assignments and complete randomization which eliminates experimental bias. The urn design forces a small-sized trial to be balanced but approaches complete randomization as the size of the trial (n) increases. Thus, the urn design is not as vulnerable to experimental bias as are other restricted randomization procedures. In a clinical trial it may be difficult to postulate that the study subjects constitute a random sample from a well-defined homogeneous population. In this case, a randomization model provides a preferred basis for statistical inference. We describe the large-sample permutational null distributions of linear rank statistics for testing the equality of treatment groups based on the urn design. In general, these permutation tests may be different from those based on the population model, which is equivalent to assuming complete randomization. Poststratified subgroup analyses can also be performed on the basis of the urn design permutational distribution. This provides a basis for analyzing the subset of patients with observed responses when some patients' responses can be assumed to be missing-at-random. For multiple mutually exclusive strata, these tests are correlated. For this case, a combined covariate-adjusted test of treatment effect is described. Finally, we show how to generalize the urn design to a prospectively stratified trial with a fairly large number of strata.

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Authors: Wei, L. J., & Lachin, J. M.
Affiliations: University of Michigan (US)
George Washington University (US)
Corresponding author: Lachin, John M.
ORCID: Wei, L.J.
Lachin, John M.
Venue: Controlled Clinical Trials
Publisher: Elsevier BV
Published: 1988-12
Volume: 9
Issue: 4
Pages: 345-364
ISSN: 0197-2456 (ISSN-L)
DOI: 10.1016/0197-2456(88)90048-7
OpenAlex: W2080083219
Cited by: 308
References: 24
Citations by year: 2026: 4 · 2025: 8 · 2024: 13 · 2023: 14 · 2022: 6 · 2021: 21 · 2020: 14 · 2019: 14 · 2018: 6 · 2017: 11 · 2016: 13 · 2015: 9 · 2014: 23 · 2013: 10 · 2012: 17
FWCI: 3.39
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Controlled Clinical Trials (publishedVersion)
PubMed (publishedVersion)
Deep Blue (University of Michigan) (acceptedVersion)
Funders: National Institutes of Health (1r01am035952-01, 7r01ca045122-01)
National Cancer Institute (R01-CA-45122)
National Institute of Diabetes and Digestive and Kidney Diseases (N01-DK-2-2206)
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: restricted randomization, experimental bias, permutation tests, linear rank statistics
MeSH terms: Clinical Trials as Topic, Humans, Prospective Studies, Random Allocation, Research Design, Statistics as Topic, Models, Statistical

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