AI 中文总结
针对观察性数据因果推断中未测量混杂因素的敏感性分析问题，提出逆混杂分析（ICA）方法，扩展E值方法，通过逆问题重构联合分布集并推导混杂显著性的精确解析度量。
AI 中文摘要
在观察性数据收集过程中，未测量混杂因素的存在可能导致暴露对结局效应的估计产生偏差。因此，基于观察性数据的因果推断中，一个核心问题是针对未测量混杂因素的敏感性分析。现有敏感性分析通常聚焦于最坏情况界。我们提出了一种量化混杂显著性的精确方法，这里的混杂显著性定义为在所有与观测特征兼容的联合分布集合上，基于分层的风险比分析估计值的完整范围。我们将该方法命名为逆混杂分析（Inverse Confounding Analysis, ICA）。所提出的ICA方法扩展了广泛使用的E值方法，但与E值方法不同，它不将分析限制在最坏情况下界，而是在所有可容许配置上提供精确估计。这需要几个额外的输入参数，即暴露、混杂因素和结局的频率。ICA方法基于一个逆问题：从指定的频率和成对关联中重构可容许联合分布的集合。我们将该重构问题表述为非线性方程组，并得到了解析解。令人惊讶的是，完整的解集可以通过单个自由参数进行线性参数化。对应的基于分层的风险比随后被表示为该参数的分式线性函数。这种表示使得能够在所有可容许统计配置上推导混杂显著性的精确解析度量。
英文摘要
The presence of unmeasured confounding factors during the collection of observational data may lead to biased estimates of the effect of an exposure on an outcome. Consequently, a central problem in causal inference based on observational data is sensitivity analysis with respect to unmeasured confounding. Existing sensitivity analyses generally focus on worst-case bounds. We propose an exact method for quantifying the significance of confounding, defined here in terms of the complete range of analytical estimates of the stratification-based Risk Ratio over the set of all joint distributions compatible with the observed characteristics. We refer to the proposed method as Inverse Confounding Analysis (ICA). The proposed ICA method extends the widely used E-value approach but, in contrast to it, does not restrict the analysis to a worst-case lower bound. Instead, it provides exact estimates over the entire set of admissible configurations. This requires several additional input parameters, namely the frequencies of the exposure, the confounder, and the outcome. The ICA method is based on an inverse problem: reconstructing the set of admissible joint distributions from specified frequencies and pairwise associations. We formulate this reconstruction problem as a system of nonlinear equations and obtain an analytical solution. Surprisingly, the complete solution set can be parameterized linearly by a single free parameter. The corresponding stratification-based Risk Ratio is then represented as a fractional-linear function of this parameter. This representation makes it possible to derive exact analytical measures of the significance of confounding over the entire set of admissible statistical configurations.
