# Bayesian adaptive bandit-based designs using the Gittins index for multi-armed trials with normally distributed endpoints

## TL;DR

This paper develops and evaluates Bayesian adaptive trial designs based on the Gittins index for normally distributed endpoints, demonstrating their potential to improve clinical trial efficiency and patient outcomes.

## Contribution

It introduces a novel application of Gittins index-based bandit algorithms to normally distributed clinical trial endpoints, including a correction for type I error inflation.

## Key findings

- Bandit-based designs show favorable power and bias properties.
- Type I error inflation can be effectively controlled with a simulation-based correction.
- The approach is particularly advantageous in rare disease trials.

## Abstract

Adaptive designs for multi-armed clinical trials have become increasingly popular recently in many areas of medical research because of their potential to shorten development times and to increase patient response. However, developing response-adaptive trial designs that offer patient benefit while ensuring the resulting trial avoids bias and provides a statistically rigorous comparison of the different treatments included is highly challenging. In this paper, the theory of Multi-Armed Bandit Problems is used to define a family of near optimal adaptive designs in the context of a clinical trial with a normally distributed endpoint with known variance. Through simulation studies based on an ongoing trial as a motivation we report the operating characteristics (type I error, power, bias) and patient benefit of these approaches and compare them to traditional and existing alternative designs. These results are then compared to those recently published in the context of Bernoulli endpoints. Many limitations and advantages are similar in both cases but there are also important differences, specially with respect to type I error control. This paper proposes a simulation-based testing procedure to correct for the observed type I error inflation that bandit-based and adaptive rules can induce. Results presented extend recent work by considering a normally distributed endpoint, a very common case in clinical practice yet mostly ignored in the response-adaptive theoretical literature, and illustrate the potential advantages of using these methods in a rare disease context. We also recommend a suitable modified implementation of the bandit-based adaptive designs for the case of common diseases.