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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