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Which design is better? Ehrenfest urn versus biased coin

Part of: Sequential methods Markov processes

Published online by Cambridge University Press:  19 February 2016

Yung-Pin Chen
Yung-Pin Chen*
Affiliation:
Smith College
*
∗ Postal address: Department of Mathematics, Smith College, Northampton, Massachusetts, 01063, USA. Email address: ypchen@neal.smith.edu
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Abstract

Two features are desired in designing a sequential clinical trial: randomness and balance. The former makes the ground for valid statistical inferences and the latter strengthens efficiency in inference procedures. Unfortunately randomness and balance can be in conflict with one another, and clinicians may be caught between the need for both of them. This paper raises an interesting question: can one design consistently achieve more balance than another when both designs own the same randomness? The Ehrenfest urn design is presented to allocate two treatments under a sequential clinical trial, and its balance and randomness properties are investigated. The design is compared with the biased coin design with imbalance tolerance.

Keywords

Sequential clinical trialEhrenfest urn designbiased coin designbig stick designimbalance toleranceselection biasMarkov chainhigh-order transition probability

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 62L05: Sequential design
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 738 - 749
Copyright
Copyright © Applied Probability Trust 2000 

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