Response-adaptive designs in clinical trials are schemes for patient a
ssignment to treatment, the goal of which is to place more patients on
the better treatment based on patient responses already accrued in th
e trial. While ethically attractive at first glance, these designs hav
e had very little use in practice; yet the statistical literature is r
ich on this subject. We discuss procedures and properties of these des
igns. Particular focus is given to the randomized play-the-winner rule
of Wei and Durham, which was used in the ECMO trial. We also discuss
reasons for the lack of use of these models, and areas of current and
future research to address the weaknesses of these methods. We conclud
e that these designs may be applicable in some situations and describe
conditions under which such a trial may be feasible.