Resumen
Urn models are popular for response adaptive designs in clinical studies. Among different urn models, Ivanova's drop-the-loser rule is capable of producing superior adaptive treatment allocation schemes. Ivanova [2003. A play-the-winner-type urn model with reduced variability. Metrika 58, 1–13] obtained the asymptotic normality only for two treatments. Recently, Zhang et al. [2007. Generalized drop-the-loser urn for clinical trials with delayed responses. Statist. Sinica, in press] extended the drop-the-loser rule to tackle more general circumstances. However, their discussion is also limited to only two treatments. In this paper, the drop-the-loser rule is generalized to multi-treatment clinical trials, and delayed responses are allowed. Moreover, the rule can be used to target any desired pre-specified allocation proportion. Asymptotic properties, including strong consistency and asymptotic normality, are also established for general multi-treatment cases.