Approximating the Operating Characteristics of Bayesian Uncertainty Directed Trial Designs

TL;DR

This paper develops large sample approximations for key operating characteristics of Bayesian Uncertainty Directed trials, enabling faster evaluation of trial performance without extensive simulations.

Contribution

It introduces asymptotic analysis methods for Bayesian Uncertainty Directed trial designs, providing practical approximations for operating characteristics like power.

Findings

Asymptotic normality of treatment allocation in BUDs.

Accurate approximation of trial power using large sample methods.

Validation of approximations through simulations across various outcome models.

Abstract

Bayesian response adaptive clinical trials are currently evaluating experimental therapies for several diseases. Adaptive decisions, such as pre-planned variations of the randomization probabilities, attempt to accelerate the development of new treatments. The design of response adaptive trials, in most cases, requires time consuming simulation studies to describe operating characteristics, such as type I/II error rates, across plausible scenarios. We investigate large sample approximations of pivotal operating characteristics in Bayesian Uncertainty directed trial Designs (BUDs). A BUD trial utilizes an explicit metric u to quantify the information accrued during the study on parameters of interest, for example the treatment effects. The randomization probabilities vary during time to minimize the uncertainty summary u at completion of the study. We provide an asymptotic analysis (i) of the allocation of patients to treatment arms and (ii) of the randomization probabilities. For BUDs with outcome distributions belonging to the natural exponential family with quadratic variance function, we illustrate the asymptotic normality of the number of patients assigned to each arm and of the randomization probabilities. We use these results to approximate relevant operating characteristics such as the power of the BUD. We evaluate the accuracy of the approximations through simulations under several scenarios for binary, time-to-event and continuous outcome models.