  Clinical trials are an instrument for making informed decisions based on
evidence from well-designed experiments. Here we consider adaptive designs
mainly from the perspective of multi-arm Phase II clinical trials, in which one
or more experimental treatments are compared to a control. Treatment allocation
of individual trial participants is assumed to take place according to a fixed
block randomization, albeit with an important twist: The performance of each
treatment arm is assessed after every measured outcome, in terms of the
posterior distribution of a corresponding model parameter. Different treatments
arms are then compared to each other, according to pre-defined criteria and
using the joint posterior as the basis for such assessment. If a treatment is
found to be sufficiently clearly inferior to the currently best candidate, it
can be closed off either temporarily or permanently from further participant
accrual. The latter possibility provides a method for adaptive treatment
selection, including early stopping of the trial. The main development in the
paper is in terms of binary outcomes, but some extensions, notably for handling
time-to-event data, are discussed as well. The presentation is to a large
extent comparative and expository.
