The Performance of Fixed-Horizon, Look-Ahead Procedures Compared to Backward Induction in Bayesian...

Designing optimal, Bayesian decision-theoretic trials has traditionally required the use of computationally-intensive backward induction. While methods for addressing this barrier have been put forward, few are both computationally tractable and non-myopic, with applications of the Gittins index being one notable example. Here we explore the look-ahead approach with adaptive-randomization, with designs ranging from the fully myopic to the fully informed. We compare the operating characteristics of the look-ahead designed trials, in which decision rules are based on a fixed number of future blocks, with those of trials designed using traditional backward induction. The less-myopic designs performed well. As the designs become more myopic or the trials longer, there were disparities in regions of the decision space that are transition zones between continuation and stopping decisions. The more myopic trials generally suffered from early stopping as compared to the less myopic and backward induction trials. Myopic trials with adaptive randomization also saw as many as 28 % of their continuation decisions change to a different randomization ratio as compared to the backward induction designs. Finally, early stages of myopic-designed trials may have disproportionate effect on trial characteristics.