In this chapter, we describe group sequential test procedures that are designed for equal sample sizes per stage of the group sequential trial, i.e., \(n_1=\ldots =n_K=n\) . The procedures that were originally developed in the literature (which we refer to as classical group sequential designs) make this assumption. In practice, the situation with equally sized stages often occurs. Namely, in all cases when there is no specific reason for assuming different stage sizes the sample sizes per stage should be the same. Nevertheless, it might be questionable if equal sample sizes are practically feasible. Particularly, regardless of whether equal stage sizes are planned, the concrete implementation of an interim analysis will rarely be based on equally sized groups of observations. A more or less slight departure will occur in nearly all cases since usually all observations at hand are used for the interim stage. Especially from an organisational perspective, the theoretical requirement is therefore hard to fulfill. We will see, however, that the assumption of equally sized stages can be weakened, or other designs are perhaps better suited. These more general designs will be studied in Chap. 3.

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Procedures with Equally Sized Stages

  • Gernot Wassmer,
  • Werner Brannath

摘要

In this chapter, we describe group sequential test procedures that are designed for equal sample sizes per stage of the group sequential trial, i.e., \(n_1=\ldots =n_K=n\) . The procedures that were originally developed in the literature (which we refer to as classical group sequential designs) make this assumption. In practice, the situation with equally sized stages often occurs. Namely, in all cases when there is no specific reason for assuming different stage sizes the sample sizes per stage should be the same. Nevertheless, it might be questionable if equal sample sizes are practically feasible. Particularly, regardless of whether equal stage sizes are planned, the concrete implementation of an interim analysis will rarely be based on equally sized groups of observations. A more or less slight departure will occur in nearly all cases since usually all observations at hand are used for the interim stage. Especially from an organisational perspective, the theoretical requirement is therefore hard to fulfill. We will see, however, that the assumption of equally sized stages can be weakened, or other designs are perhaps better suited. These more general designs will be studied in Chap. 3.