Clinical trials have traditionally followed a fixed randomized design, where patients are typically allocated once, at random, and usually equally to various treatments. Such designs provide a clean way of separating out the effects of alternate treatments. Response-adaptive designs, where assignment to treatments evolves as patient outcomes are observed, are gaining in popularity due to potential for improvements in both cost and efficiency over traditional designs. Such designs can be modeled as a Bayesian adaptive Markov decision process (BAMDP), essentially an MDP with unknown transition probabilities. Given the forward-looking nature of the underlying algorithms which solve BAMDP, the problem size grows as the trial becomes larger or more complex, often exponentially, making it computationally challenging to solve. In this study, we propose grid-based approximation as a way to reduce the problem dimensionality and the associated computationally burden. The proposed methods also open the possibility of implementing adaptive designs to large clinical trials. Further, we use numerical examples to demonstrate the effectiveness of our approach, including the effects of number of patient observations and the grid resolution.
['Vishal Ahuja', 'John R. Birge', 'Christopher W. Ryan']
Approximation Methods for Determining Optimal Allocations in Response Adaptive Clinical Trials