Wald-Wolfowitz optimality of sequentially planned tests: Remarks and conjectures

Group sequential tests with variable group sizes are considered whose decision functions depend on the likelihood ratio in a similar way as those of SPRTs. For these tests, Cressie and Morgan asserted an optimum property. The paper shows that their conjecture is not true in general, and that no direct counterpart to the famous Wald-Wolfowitz theorem is available for sequentially planned tests. Moreover, a modified optimality conjecture is formulated.