Evidence inconsistency degrees of freedom in Bayesian network meta-analysis
1Department of Statistics, Florida State University, Tallahassee, Florida, USA.
Abstract:
Network meta-analysis (NMA) is a popular tool to synthesize direct and indirect evidence for simultaneously comparing multiple treatments, while evidence inconsistency greatly threatens its validity. One may use the inconsistency degrees of freedom (ICDF) to assess the potential that an NMA might suffer from inconsistency. Multi-arm studies provide intrinsically consistent evidence and complicate the ICDF's calculation; they commonly appear in NMAs. The existing ICDF measure may not feasibly handle multi-arm studies. Motivated from the effective numbers of parameters of Bayesian hierarchical models, we propose new ICDF measures in generic NMAs that may contain multi-arm studies. Under the fixed- or random-effects setting, the new ICDF measure is the difference between the effective numbers of parameters of the consistency and inconsistency NMA models. We used artificial NMAs created based on an illustrative example and 39 empirical NMAs to evaluate the performance of the existing and new measures. In NMAs with two-arm studies only, the proposed ICDF measure under the fixed-effects setting was nearly the same with the existing measure. Among the empirical NMAs, 27 (69%) contained at least one multi-arm study. The existing measure was not applicable to them, while the proposed measures led to interpretable ICDFs in all NMAs.
Insights
New inconsistency degrees of freedom (ICDF) measures effectively assess network meta-analysis (NMA) validity, even with complex multi-arm studies. These novel methods improve upon existing measures, offering interpretable results across diverse NMA scenarios.
Area of Science:
- Biostatistics
- Health Research Methodology
- Evidence Synthesis
Background:
- Network meta-analysis (NMA) synthesizes evidence from multiple treatments.
- Evidence inconsistency poses a significant threat to NMA validity.
- Existing inconsistency degrees of freedom (ICDF) measures struggle with multi-arm studies.
Purpose of the Study:
- To propose novel ICDF measures for NMAs, particularly those including multi-arm studies.
- To enhance the assessment of evidence inconsistency in complex NMA settings.
Main Methods:
- Developed new ICDF measures based on the effective number of parameters in Bayesian hierarchical models.
- Compared proposed measures against existing ones using artificial and empirical NMAs.
- Evaluated performance in both fixed- and random-effects models.
Main Results:
- The proposed fixed-effects ICDF measure closely matched the existing measure in two-arm study-only NMAs.
- 27 out of 39 (69%) empirical NMAs contained multi-arm studies, rendering existing measures inapplicable.
- The new ICDF measures provided interpretable results for all tested NMAs, including those with multi-arm studies.
Conclusions:
- The proposed ICDF measures are applicable and effective for NMAs with multi-arm studies.
- These new measures enhance the reliability of evidence synthesis by addressing limitations in inconsistency assessment.
- The findings support the adoption of these improved ICDF measures in NMA practice.
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