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Sequential monitoring with conditional randomization tests. (English) Zbl 1246.62177

Summary: 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, B. Efron’s [Biometrika 58, 403–417 (1971; Zbl 0226.62086)] 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.

MSC:

62L05 Sequential statistical design
62P10 Applications of statistics to biology and medical sciences; meta analysis
62L10 Sequential statistical analysis
62L15 Optimal stopping in statistics
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 0226.62086
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Full Text: DOI arXiv Euclid

References:

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