Doubly adaptive biased coin designs with de- layed responses

In clinical studies, patients are usually accrued sequentially, and, in such cases, response-adaptive designs are useful tools to generate treatment allocation schemes in which the assignment of a treatment to an incoming patient is a function of the observed treatment responses thus far. It has been shown that among the various classes of designs, doubly adaptive biased coin designs have several advantageous properties over other response-adaptive designs under the assumption that their responses can be obtained immediately after testing. However, it is a common occurrence that responses are observed only after a certain period of time. In this article, we examine the effect of delayed responses on doubly adaptive biased coin designs and derive some relevant asymptotic properties. A major finding is that doubly adaptive biased coin designs are relatively insensitive to delayed responses under widely satisfied conditions. A simulation study is also reported to provide a better understanding of the effects of delayed responses. Title in French: we can supply this Résumé : In clinical studies, patients are usually accrued sequentially, and, in such cases, response-adaptive designs are useful tools to generate treatment allocation schemes in which the assignment of a treatment to an incoming patient is a function of the observed treatment responses thus far. It has been shown that among the various classes of designs, doubly adaptive biased coin designs have several advantageous properties over other response-adaptive designs under the assumption that their responses can be obtained immediately after testing. However, it is a common occurrence that responses are observed only after a certain period of time. In this article, we examine the effect of delayed responses on doubly adaptive biased coin designs and derive some relevant asymptotic properties. A major finding is that doubly adaptive biased coin designs are relatively insensitive to delayed responses under widely satisfied conditions. A simulation study is also reported to provide a better understanding of the effects of delayed responses.