Abstract
The Gittins index provides a well established, computationally attractive, optimal solution to a class of resource allocation problems known collectively as the multi-arm bandit problem. Its development was originally motivated by the problem of optimal patient allocation in multi-arm clinical trials. However, it has never been used in practice, possibly for the following reasons: (1) it is fully sequential, i.e., the endpoint must be observable soon after treating a patient, reducing the medical settings to which it is applicable; (2) it is completely deterministic and thus removes randomization from the trial, which would naturally protect against various sources of bias. We propose a novel implementation of the Gittins index rule that overcomes these difficulties, trading off a small deviation from optimality for a fully randomized, adaptive group allocation procedure which offers substantial improvements in terms of patient benefit, especially relevant for small populations. We report the operating characteristics of our approach compared to existing methods of adaptive randomization using a recently published trial as motivation.
Highlights
Consider a clinical trial to test the effectiveness of several treatments on a group of patients
It has never been used in practice, possibly for the following reasons: (1) it is fully sequential, i.e., the endpoint must be observable soon after treating a patient, reducing the medical settings to which it is applicable; (2) it is completely deterministic and removes randomization from the trial, which would naturally protect against various sources of bias
We propose a novel implementation of the Gittins index rule that overcomes these difficulties, trading off a small deviation from optimality for a fully randomized, adaptive group allocation procedure which offers substantial improvements in terms of patient benefit, especially relevant for small populations
Summary
Consider a clinical trial to test the effectiveness of several treatments on a group of patients. A rational observer, who is unfamiliar with established medical convention, might well suppose that patients would be allocated to treatments with the aim of optimizing their collective health. Using this idea as the initial motivation, Gittins and Jones (1979) first proposed an optimal, deterministic rule to perform such a task within a multi-arm clinical trial, which is termed the Gittins index. Bandits, and the Gittins index, have never been used in clinical practice (to the best of the authors’ knowledge) due to certain realities of medical research These are discussed at length in a recent review by Villar et al (2015), the main findings of which are summarized
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