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Biometrika 2002 89(1):49-60; doi:10.1093/biomet/89.1.49
© 2002 by Biometrika Trust
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Optimal asymmetric one-sided group sequential tests

Stuart Barber1 and Christopher Jennison2

1 Department of Mathematics, University of Bristol, Bristol, BS8 1TW, U.Kstuart.barber{at}bristol.ac.uk 2 Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, U.K.cj{at}maths.bath.ac.uk

We extend the optimal symmetric group sequential tests of Eales & Jennison (1992) to the broader class of asymmetric designs. Two forms of asymmetry are considered, involving unequal type I and type II error rates and different emphases on expected sample sizes at the null and alternative hypotheses.We discuss the properties of our optimal designs and use them to assess the efficiency of the family of tests proposed by Pampallona & Tsiatis (1994) and two families of one-sided tests defined through error spending functions. We show that the error spending designs are highly efficient, while the easily implemented tests of Pampallona & Tsiatis are a little less efficient but still not far from optimal. Our results demonstrate that asymmetric designs can decrease the expected sample size under one hypothesis, but only at the expense of a significantly larger expected sample size under the other hypothesis.

Key Words: Asymmetric test; Backwards induction; Bayes decision problem; Error spending; Interim analysis; One-sided test; Optimal group sequential test; Unequal error rates

Received February 2001. Revised July 2001


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