Exact statistical power for response adaptive designs

This paper develops a unified method to compute the exact statistical power for a general class of response adaptive designs including the randomized play-the-winner design, the drop-the-loser design, and the doubly biased coin design. The adaptation of treatment allocation in response adaptive designs is formulated as a Markov chain. The exact statistical power is computed based on the transition probability of the formulated Markov chain. The proposed approach is demonstrated through the ECMO trial example. The difference between the asymptotic and exact statistical power is also explored for large sample sizes.