Urn models are popular and useful for adaptive designs in clinical studies. Among various urn models, the drop-the-loser rule is an e cient adaptive treatment allocation scheme, recently proposed for comparing di erent treatments in a clinical trial. This rule is superior to other randomization schemes in terms of variability and power. In this paper, the drop-the-loser rule is generalized to cope with more popular and practical circumstances, including (1) delayed responses when test results cannot be obtained immediately, (2) continuous responses, and (3) a prespeci ed target of allocation proportion. In addition, our proposed procedure has several favorable asymptotic properties such as strong consistency and asymptotic normality of the allocation proportions.