Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the outcome law change substantially. This paper develops a topological causal framework based on persistent homology. We formalize a persistent-homology ignorability condition, define topological analogues of CATE and ATE, and prove that these estimands are identifiable up to an explicit error bound under approximate topological ignorability. We also clarify a subtle but important point: a marginal persistence-diagram effect is not identified from conditional topological ignorability alone because persistent homology does not in general commute with mixtures over covariates. To preserve the original intuition while ensuring scientific correctness, we retain the marginal effect as a motivating quantity, but place the mathematically sound conditional estimands at the center of the theory. A synthetic experiment with mean-preserving topology change shows that mean-based causal estimands remain near zero while the proposed topological effect increases sharply and remains recoverable after adjustment for confounding.

翻译：平均处理效应（ATE）和条件平均处理效应（CATE）是基础的因果估计量，但它们仅针对期望结果的变化，可能遗漏处理导致的结果分布形状变化。一个典型的失效情形是：对照组结果呈单峰分布，而处理组结果变为双峰分布，且两分布均值相同。此时，即使结果分布的几何与拓扑结构发生显著变化，基于均值的因果估计量仍为零。本文基于持续同调构建了一个拓扑因果框架。我们形式化定义了持续同调可忽略性条件，给出了CATE和ATE的拓扑类比估计量，并证明了在近似拓扑可忽略性下，这些估计量可识别且具有显式误差界。我们还阐明了一个细微但关键的问题：由于持续同调通常不与协变量混合运算可交换，仅凭条件拓扑可忽略性无法识别边缘持续同调图效应。为在保证科学严谨性的同时保留原始直觉，我们将边缘效应作为激励性概念，但以数学上严谨的条件估计量作为理论核心。一个保留均值不变的拓扑变化合成实验表明：基于均值的因果估计量始终接近零，而本文提出的拓扑效应则急剧增加，且在混杂调整后仍可恢复。