The Annals of Statistics

A Sequential Probability Ratio Test Using a Biased Coin Design

Nancy E. Heckman

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Consider a sequential probability ratio test comparing two treatments, where each subject receives only one of the treatments. Each subject's treatment assignment is determined by the flip of a biased coin, where the bias serves to balance the number of patients assigned to each treatment. The asymptotic properties of this test are studied, as the sample size approaches infinity. A renewal theorem is given for the joint distribution of the sample size, the imbalance in treatment assignment at the end of the experiment, and the excess over the stopping boundary. This theorem is used to calculate asymptotic expressions for the test's error probabilities.

Article information

Ann. Statist., Volume 13, Number 2 (1985), 789-794.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62L05: Sequential design
Secondary: 60K05: Renewal theory

Sequential probability ratio test biased coin design clinical trial renewal theory


Heckman, Nancy E. A Sequential Probability Ratio Test Using a Biased Coin Design. Ann. Statist. 13 (1985), no. 2, 789--794. doi:10.1214/aos/1176349556.

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