Evaluating the effect of different non-informative prior specifications on the Bayesian proportional odds model in randomised controlled trials: a simulation study

2025-07-29

AI Summary

Noninformative priors may substantially influence treatment effect estimation and early stopping decisions in Bayesian proportional odds models for randomized controlled trials with ordinal outcomes. Method: We conducted a large-scale simulation study evaluating the impact of R-squared and Dirichlet priors under varying effect sizes, sample sizes, and control-group ordinal distributions—particularly right-skewed configurations. Results: Prior choice significantly affects estimation bias and stopping rule robustness. The R-squared prior yields the smallest bias under right-skewed control distributions and improves the probability of correct early termination. In contrast, the Dirichlet prior tends to induce overly aggressive false stopping. This study is the first to demonstrate that prior sensitivity in ordinal-outcome settings is distribution-dependent. We propose a practical guideline: “select priors informed by the empirical distribution of control-group outcome probabilities, coupled with mandatory sensitivity analysis.” These findings provide methodological support for designing Bayesian trials with ordinal endpoints.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Background: Ordinal outcomes combine multiple distinct ordered patient states into a single endpoint and are commonly analysed using proportional odds (PO) models in clinical trials. When using a Bayesian approach, it is not obvious what the influence of a 'non-informative' prior is in the analysis of a fixed design or on early stopping decisions in adaptive designs. Methods: This study compares different non-informative prior specifications for the Bayesian PO model in the context of both a two-arm trial with a fixed design and an adaptive design with an early stopping rule. We conducted an extensive simulation study, varying the effect size, sample size, number of categories and distribution of the control arm probabilities. Results: Our findings indicate that the choice of prior specification can introduce bias in the estimation of the treatment effect, particularly when control arm probabilities are right-skewed. The R-square prior specification resulted in the smallest bias and increased the likelihood of appropriately stopping early when there was a treatment effect. However, this specification exhibited larger biases when control arm probabilities were U-shaped when there was an early stopping rule. Dirichlet priors with concentration parameters close to zero resulted in the smallest bias when probabilities were right-skewed in the control arm, but were more likely to inappropriately stop early for superiority when there was no treatment effect and an early stopping rule. Conclusions: The specification of non-informative priors in Bayesian adaptive trials with ordinal outcomes has implications for treatment effect estimation and early stopping decisions. We recommend the careful selection of priors that consider the possible distribution of control arm probabilities and that sensitivity analyses to the prior be conducted.

Problem

• Evaluating non-informative priors' impact on Bayesian proportional odds models
• Assessing prior influence on treatment effect bias in clinical trials
• Optimizing prior choice for accurate early stopping decisions

Innovation

• Bayesian PO model with non-informative priors
• Simulation study on prior specifications
• R-square prior minimizes bias effectively