New adaptive designs for delayed response models

Adaptive designs are effective mechanisms for flexibly allocating experimental resources. In clinical trials particularly, such designs allow researchers to balance short- and long-term goals. Unfortunately, fully sequential strategies require outcomes from all previous allocations prior to the next allocation. This can prolong an experiment unduly. As a result, we seek designs for models that specifically incorporate delays. We utilize a delay model in which patients arrive according to a Poisson process and their response times are exponential. We examine three designs with an eye towards minimizing patient losses: a delayed two-armed bandit rule which is optimal for the model and objective of interest; a newly proposed hyperopic rule; and a randomized play-the-winner rule. The results show that, except when the delay rate is several orders of magnitude different than the patient arrival rate, the delayed response bandit is nearly as efficient as the immediate response bandit. The delayed hyperopic design also performs extremely well throughout the range of delays, despite the fact that the rate of delay is not one of its design parameters. The delayed randomized lay-the-winner rule is far less efficient than either of the other methods.