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Biometrika 1992 79(1):13-24; doi:10.1093/biomet/79.1.13
© 1992 by Biometrika Trust
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An improved method for deriving optimal one-sided group sequential tests

JOHN D. EALES and CHRISTOPHER JENNISON

1Department of Mathematics and Statistics, Polytechnic South West Drake Circus, Plymouth PL4 8AA, U. K.
2School of Mathematical Sciences, University of Bath Bath BA2 7AY, U. K.

SUMMARY

We derive one-sided group sequential tests for normal responses which minimize expected sample size; minimization is at a single value of the normal mean or integrated with respect to a normal density. The methods employed are much faster and also numerically more stable than those of Jennison (1987). They provide solutions for cases with as many as 200 groups and, for small numbers of groups, facilitate optimization over the choice of group sizes. We present a new method for constructing near-optimal tests when group sizes are unpredictable, based on interpolating the error spending function of an optimal test with a large number of groups.

Key Words: Baycs decision problem • Clinical trial • Efficiency • Group sequential tests • Unequal and unpredictable group sizes


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