A robust Bayesian bias-adjusted random effects model for consideration of uncertainty about bias terms in evidence synthesis

TL;DR

This paper introduces a robust Bayesian approach to meta-analysis that explicitly accounts for uncertainty and bias in study effects, using imprecise bias characterization and coherent probability sets.

Contribution

It proposes a novel method combining robust Bayesian analysis with bias quantification to improve evidence synthesis in meta-analyses.

Findings

Applied to Rituximab meta-analysis, demonstrating the method's practical utility.

Provides a framework for incorporating bias uncertainty into effect estimates.

Enhances the robustness of meta-analytic conclusions against bias assumptions.

Abstract

Meta-analysis is a statistical method used in evidence synthesis for combining, analyzing and summarizing studies that have the same target endpoint and aims to derive a pooled quantitative estimate using fixed and random effects models or network models. Differences among included studies depend on variations in target populations (i.e. heterogeneity) and variations in study quality due to study design and execution (i.e. bias). The risk of bias is usually assessed qualitatively using critical appraisal, and quantitative bias analysis can be used to evaluate the influence of bias on the quantity of interest. We propose a way to consider ignorance or ambiguity in how to quantify bias terms in a bias analysis by characterizing bias with imprecision (as bounds on probability) and use robust Bayesian analysis to estimate the overall effect. Robust Bayesian analysis is here seen as Bayesian updating performed over a set of coherent probability distributions, where the set emerges from a set of bias terms. We show how the set of bias terms can be specified based on judgments on the relative magnitude of biases (i.e., low, unclear and high risk of bias) in one or several domains of the Cochrane's risk of bias table. For illustration, we apply a robust Bayesian bias-adjusted random effects model to an already published meta-analysis on the effect of Rituximab for rheumatoid arthritis from the Cochrane Database of Systematic Reviews.