Summary: We extend the optimal symmetric group sequential tests of J.D. Eales
and C. Jennison
[ibid. 79, No. 1, 13-24 (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 S. Pampallona
and A.A. Tsiatis
[J. Stat. Plann. Inference 42, No. 1-2, 19-35 (1994; Zbl 0805.62078
)] 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 and 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.