  The question of selecting the "best" amongst different choices is a common
problem in statistics. In drug development, our motivating setting, the
question becomes, for example: what is the dose that gives me a pre-specified
risk of toxicity or which treatment gives the best response rate. Motivated by
a recent development in the weighted information measures theory, we propose an
experimental design based on a simple and intuitive criterion which governs arm
selection in the experiment with multinomial outcomes. The criterion leads to
accurate arm selection without any parametric or monotonicity assumption. The
asymptotic properties of the design are studied for different allocation rules
and the small sample size behaviour is evaluated in simulations in the context
of Phase I and Phase II clinical trials with binary endpoints. We compare the
proposed design to currently used alternatives and discuss its practical
implementation.
