The Annals of Statistics

A Sequential Probability Ratio Test Using a Biased Coin Design

Nancy E. Heckman

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349556

Digital Object Identifier
doi:10.1214/aos/1176349556

Mathematical Reviews number (MathSciNet)
MR790574

Zentralblatt MATH identifier
0574.62078

JSTOR
links.jstor.org

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

Keywords
Sequential probability ratio test biased coin design clinical trial renewal theory

Citation

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. https://projecteuclid.org/euclid.aos/1176349556


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