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

TL;DR

This study compares the performance of different statistical models for ordinal outcomes in randomized trials, highlighting the robustness of partial proportional odds models when the proportional odds assumption is violated.

Contribution

It provides a comprehensive simulation-based evaluation of PO, PPO, and logistic regression models, demonstrating their strengths and limitations under various conditions.

Findings

PO model performs best under true PO conditions.

PPO and logistic regression models are unbiased under non-PO scenarios.

Unconstrained PPO underperforms with sparse data.

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.