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arXiv · 2604.21994

Contrast-Space Projection for Network Meta-Analysis: An Exact and Invariant Study-Based Decomposition of Direct and Indirect Contributions

Chong Wang·Yanqi Zhang·Zhezhen Jin·Annette O'Connor
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Abstract

Network meta-analysis (NMA) combines direct and indirect comparisons across a treatment network, but exact contribution decompositions that reproduce NMA estimates are lacking, especially for multi-arm trials with correlated contrasts. We develop a contrast-space projection formulation of NMA that expresses the estimator as a linear mapping of observed pairwise contrasts onto the consistency-constrained contrast space. Building on this representation, we define direct and indirect evidence through a canonical within-study reduction that removes algebraic redundancy and yields a unique, invariant study-level decomposition. The resulting covariance-aware weights exactly reconstruct the NMA estimator and can be further resolved into indirect path-level components. Under fixed effects, the same projection also represents the generalized Cochran Q decomposition into within-design heterogeneity and between-design inconsistency. The framework yields diagnostic and graphical tools, including forest plots, tension plots, and path-based visualizations. Applications to empirical networks illustrate how the approach provides a reproducible and interpretable account of evidence contributions in NMA.

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Chong Wang, Yanqi Zhang, Zhezhen Jin, Annette O'Connor. 2026-04-23. Contrast-Space Projection for Network Meta-Analysis: An Exact and Invariant Study-Based Decomposition of Direct and Indirect Contributions. https://arxiv.org/abs/2604.21994

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