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Exact properties of Efron’s biased coin randomization procedure. (English) Zbl 1189.62130
Summary: B. Efron [Biometrika 58, 403–417 (1971; Zbl 0226.62086)] developed a restricted randomization procedure to promote balance between two treatment groups in a sequential clinical trial. He called this the biased coin design. He also introduced the concept of accidental bias, and investigated properties of the procedure with respect to both accidental and selection bias, balance, and randomization-based inference using the steady-state properties of the induced Markov chain. We revisit this procedure, and derive closed-form expressions for the exact properties of the measures derived asymptotically in Efron’s paper. In particular, we derive the exact distribution of the treatment imbalance and the variance-covariance matrix of the treatment assignments. These results have application in the design and analysis of clinical trials, by providing exact formulas to determine the role of the coin’s bias probability in the context of selection and accidental bias, balancing properties and randomization-based inference.

62L05 Sequential statistical design
62E15 Exact distribution theory in statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C60 Computational problems in statistics (MSC2010)
62K99 Design of statistical experiments
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