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February 2012 Sequential monitoring with conditional randomization tests
Victoria Plamadeala, William F. Rosenberger
Ann. Statist. 40(1): 30-44 (February 2012). DOI: 10.1214/11-AOS941

Abstract

Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a population model. We describe a computational method to implement sequential monitoring in a randomization-based context. In particular, we discuss a new technique for the computation of approximate conditional tests following restricted randomization procedures and then apply this technique to approximate the joint distribution of sequentially computed conditional randomization tests. We also describe the computation of a randomization-based analog of the information fraction. We apply these techniques to a restricted randomization procedure, Efron’s [Biometrika 58 (1971) 403–417] biased coin design. These techniques require derivation of certain conditional probabilities and conditional covariances of the randomization procedure. We employ combinatoric techniques to derive these for the biased coin design.

Citation

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Victoria Plamadeala. William F. Rosenberger. "Sequential monitoring with conditional randomization tests." Ann. Statist. 40 (1) 30 - 44, February 2012. https://doi.org/10.1214/11-AOS941

Information

Published: February 2012
First available in Project Euclid: 15 March 2012

zbMATH: 1246.62177
MathSciNet: MR3013178
Digital Object Identifier: 10.1214/11-AOS941

Subjects:
Primary: 62E15 , 62K99
Secondary: 62J10 , 62L05

Keywords: biased coin design , conditional reference set , Random walk , restricted randomization , sequential analysis

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 1 • February 2012
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