Network meta-analysis (NMA) combines direct and indirect comparisons across a connected treatment network to estimate relative treatment effects. However, there is a lack of exact contribution decompositions that reproduce NMA estimates, particularly in the presence of multi-arm trials that induce within-study correlations. We address this reproducibility gap by developing a contrast-space projection formulation of NMA. Working in the space of all estimable pairwise treatment contrasts, we express the NMA estimator as an explicit linear mapping of the observed contrasts onto the consistency-constrained contrast space induced by orthogonal projection. Building on this representation, we introduce a rigorous study-based definition of direct and indirect evidence through a canonical within-study reduction that removes algebraic redundancy and yields a unique, invariant decomposition. This leads to exact covariance-aware decompositions of the NMA estimator into study-level direct and indirect contributions, with indirect evidence further resolved into path-level components. The resulting weights are directly analogous to inverse-variance weights in pairwise meta-analysis and enable, to our knowledge, the first forest-plot representation that exactly reconstructs the NMA estimator. The framework also yields projection-based diagnostic and graphical tools, including forest plots, tension plots, and path-based visualizations. Applications to empirical datasets demonstrate how the proposed approach provides a reproducible and interpretable framework for understanding evidence contributions in network meta-analysis, supporting transparent interpretation and reporting.

翻译：网络荟萃分析（NMA）通过整合关联治疗网络中的直接与间接比较来估计相对治疗效果。然而，现有方法缺乏能够重现NMA估计值的精确贡献分解，尤其在存在多臂试验（会引入研究内部相关性）时这一问题更为突出。为解决这一可重现性缺口，我们提出了一种基于对比空间投影的NMA形式体系。通过在所有可估计的配对处理对比空间中展开工作，我们将NMA估计量表示为观测对比值到正交投影诱导的一致性约束对比空间上的显式线性映射。基于此表示，我们通过一种消除代数冗余的规范研究内部约简，提出了直接与间接证据的严格研究层面定义，并得到唯一且不变的分解。由此产生NMA估计量在考虑协方差条件下研究层面直接与间接贡献的精确分解，其中间接证据可进一步分解为路径层级分量。所得权重直接类比于配对荟萃分析中的逆方差权重，并据我们所知首次实现了能精确重建NMA估计量的森林图表示。该框架还衍生出基于投影的诊断与图形工具，包括森林图、张力图及路径可视化。实证数据集的应用表明，所提方法为理解网络荟萃分析中的证据贡献提供了可重现且可解释的框架，支持透明化解释与报告。