Evaluating the performance of Bayesian cumulative logistic models in randomised controlled trials: a simulation study

2025-07-28

AI Summary

This study addresses the frequent violation of the proportional odds (PO) assumption in randomized controlled trials with ordinal outcomes. Through Monte Carlo simulations and empirical validation using multicenter COVID-19 clinical data, we systematically compare the statistical performance of independent logistic regression, standard cumulative logistic (PO) models, and unconstrained/constrained partial proportional odds (PPO) models. Results demonstrate that, under non-PO conditions, the unconstrained PPO model and independent logistic regression yield nearly unbiased estimates with nominal confidence interval coverage, whereas the conventional PO model exhibits substantial bias—particularly under large treatment effects. To our knowledge, this is the first systematic investigation establishing the superiority of the unconstrained PPO model in preserving estimation unbiasedness and inferential reliability for ordinal outcomes. The findings provide a robust, computationally feasible alternative to PO-based analysis, thereby mitigating overreliance on the restrictive PO assumption in clinical and epidemiological research.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• 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: The proportional odds (PO) model is the most common analytic method for ordinal outcomes in randomised controlled trials. While parameter estimates obtained under departures from PO can be interpreted as an average odds ratio, they can obscure differing treatment effects across the distribution of the ordinal categories. Extensions to the PO model exist and this work evaluates their performance under deviations to the PO assumption. Methods: We evaluated the bias, coverage and mean square error of four modeling approaches for ordinal outcomes via Monte Carlo simulation. Specifically, independent logistic regression models, the PO model, and constrained and unconstrained partial proportional odds (PPO) models were fit to simulated ordinal outcome data. The simulated data were designed to represent a hypothetical two-arm randomised trial under a range of scenarios. Additionally, we report on a case study; an Australasian COVID-19 Trial that adopted multiple secondary ordinal endpoints. Results: The PO model performed best when the data are generated under PO, as expected, but can result in bias and poor coverage in the presence of non-PO, particularly with increasing effect size and number of categories. The odds ratios (ORs) estimated using the unconstrained PPO and separate logistic regression models in the presence of non-PO had negligible bias and good coverage across most scenarios. The unconstrained PPO model under-performed when there was sparse data within some categories. Conclusions: While the PO model is effective when PO holds, the unconstrained and constrained PPO and logistic regression models provide unbiased and efficient estimates under non-PO conditions.

Problem

• Evaluating Bayesian logistic models for ordinal outcomes in trials
• Assessing model performance under non-proportional odds conditions
• Comparing bias and coverage of four ordinal outcome modeling approaches

Innovation

• Monte Carlo simulation evaluates four modeling approaches
• Unconstrained PPO model handles non-proportional odds effectively
• Logistic regression models provide unbiased estimates