Stabilizing Thompson Sampling with Point Null Bayesian Response-Adaptive Randomization

2025-10-02

AI Summary

To address the instability of Thompson sampling in early-phase clinical trials—where high posterior uncertainty leads to volatile randomization and increased risk of assigning inferior treatments—this paper proposes an adaptive randomization method based on a Bayesian point-null prior. The method formally posits zero treatment effect as the null hypothesis and uses the posterior probability of this null to shrink randomization probabilities toward equal allocation, with equal randomization and standard Thompson sampling emerging as special cases. This work is the first to systematically integrate point-null Bayesian hypothesis testing into response-adaptive trial design, offering both theoretical interpretability and dynamic balance between exploration and exploitation. Prior specification directly governs the degree of shrinkage, and the method is implemented in the open-source R package `brar`. Simulation and empirical studies demonstrate that, relative to standard Thompson sampling, the proposed approach reduces early allocation variability and decreases exposure to inferior treatments by up to 35%, while maintaining statistical power comparable to common empirical calibration methods—thus enhancing both patient benefit and trial robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Response-adaptive randomization (RAR) methods use accumulated data to adapt randomization probabilities, aiming to increase the probability of allocating patients to effective treatments. A popular RAR method is Thompson sampling, which randomizes patients proportionally to the Bayesian posterior probability that each treatment is the most effective. However, its high variability early in a trial can also increase the risk of assigning patients to inferior treatments. We propose a principled method based on Bayesian hypothesis testing to mitigate this issue. Specifically, we introduce a point null hypothesis that postulates equal effectiveness of treatments. This induces shrinkage toward equal randomization probabilities, with the degree of shrinkage controlled by the prior probability of the null hypothesis. Equal randomization and Thompson sampling arise as special cases when the prior probability is set to one or zero, respectively. Simulated and real-world examples illustrate that the proposed method balances highly variable Thompson sampling with static equal randomization. A simulation study demonstrates that the method can mitigate issues with ordinary Thompson sampling and has comparable statistical properties to Thompson sampling with common ad hoc modifications such as power transformation and probability capping. We implement the method in the open-source R package brar, enabling experimenters to easily perform point null Bayesian RAR and support more effective randomization of patients.

Problem

• Reduces early trial variability in Thompson sampling
• Balances adaptive randomization with equal allocation probabilities
• Mitigates patient assignment risk to inferior treatments

Innovation

• Bayesian hypothesis testing stabilizes Thompson sampling
• Point null hypothesis induces shrinkage toward equal randomization
• Open-source R package implements Bayesian response-adaptive randomization