Are flexible designs sound?

Flexible designs allow large modifications of a design during an experiment. In particular, the sample size can be modified in response to interim data or external information. A standard flexible methodology combines such design modifications with a weighted test, which guarantees the type I error level. However, this inference violates basic inference principles. In an example with independent N(mu, 1) observations, the test rejects the null hypothesis of mu <= 0 while the average of the observations is negative. We conclude that flexible design in its most general form with the corresponding weighted test is not valid. Several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests.