Familywise error control in multi-armed response-adaptive two-stage designs

For comparing multiple treatments against a single control with normally distributed observations, we consider two-stage designs of the following form: During the first stage, control and treatments are allocated by response-adaptive randomization; after completion of the first stage, some treatments are selected to proceed to the second stage; during the second stage, control and selected treatments are allocated by block randomization. Tests for such designs that use the data from both stages have been based on simulation under the global null hypothesis. We present an approach that does not rely on simulation and protects the familywise error rate in the strong sense. The main idea is to view the trial as a data-dependent modification of a simpler design, for which we know the distributions of its test statistics. To account for the data-dependent modification, we use the conditional invariance principle (Brannath et al., 2007).