Reduce dimension or reduce weights? Comparing two approaches to multi-arm studies in network meta-analysis

Area of Science:

• Biostatistics
• Medical Research Methodology

Background:

• Network meta-analysis integrates data from multiple randomized trials for comprehensive treatment comparisons.
• Multi-arm studies within networks present correlated pairwise comparisons requiring specific statistical handling.

Purpose of the Study:

• To mathematically prove the equivalence of two distinct methods for analyzing multi-arm studies in network meta-analysis.
• To demonstrate how these methods simplify the estimation of treatment effects and heterogeneity.

Main Methods:

• Weighted least squares regression is employed for estimating consistent treatment effects across all comparisons.
• Two approaches for multi-arm studies were analyzed: 'reduce dimension' (standard regression) and 'reduce weights' (graph theory-based).
• A mathematical proof established the identity of estimates derived from both the 'reduce dimension' and 'reduce weights' methods.

Main Results:

• Both the 'reduce dimension' and 'reduce weights' approaches yield identical treatment effect estimates.
• The 'reduce weights' method can be viewed as creating a network of independent two-arm studies.
• This unification leads to a simplified random-effects model with a single heterogeneity variance parameter.

Conclusions:

• The equivalence of the two methods simplifies network meta-analysis, particularly for studies with multi-arm trials.
• The findings facilitate a more straightforward application of random-effects models in complex meta-analytic settings.
• The approach was successfully applied to a systematic review in depression, demonstrating practical utility.