Optimal asymmetric one-sided group sequential tests

Stuart Barber & Christopher Jennison.
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; unequal type I and type II error rates and different emphases on expected sample sizes at the null and alternative hypotheses. We use our optimal designs to assess the family of tests with parametric boundaries proposed by Pampallona & Tsiatis (1994) and two families of one-sided group sequential 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.

Some key words:
Asymmetric tests; backwards induction; Bayes decision problem; error spending tests; one-sided tests; optimal group sequential tests; unequal error rates.

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