AI 中文总结
本研究针对正性条件违反的连续处理，提出内移投影改进的部分识别框架，可稳健估计修正处理策略的因果效应，其置信区间在模拟及农药混合物应用中表现优于传统方法。
AI 中文摘要
修正处理策略（Modified Treatment Policies, MTPs）是基于每个个体自然处理值的干预措施，我们研究连续处理（包括暴露混合物）下MTP的平均结果。正性是在无需外推的情况下识别这些平均结果的标准充分条件：给定协变量时，策略生成的值仍处于支持范围内。对于多元处理或连续协变量，处理-协变量组合可能稀疏或不受支持。在保留该策略的前提下，我们的部分识别框架将其平均结果分解为正性区域内的点识别贡献与区域外的贡献。我们通过对条件潜在结果施加Lipschitz连续性而非参数外推模型来限定后者的范围。该限制将每个区域外的均值与区域内锚点处的均值进行比较。度量投影可最小化单锚区间的宽度，但会将锚点集中在低维边界上，导致端点不可路径可微。我们提出的新型内移投影将锚点向内移动，恢复了路径可微性。在已知区域的情况下，我们推导了影响函数，刻画了其有效时的条件，并得到了渐近正态估计量和置信区间。模拟结果显示，在假设正性条件的方法出现覆盖率不足的情况下，我们的区间仍能达到至少名义覆盖率。在农药混合物应用中，假设正性条件的方法所显示的保护性关联对超出估计区域的适度结果变化并不稳健。
英文摘要
Modified treatment policies (MTPs) are interventions based on each individual's natural treatment value. We study mean outcomes under MTPs for continuous treatments, including exposure mixtures. Positivity is the standard sufficient condition for identifying these mean outcomes without extrapolation: policy-generated values remain supported given covariates. With multivariate treatments or continuous covariates, treatment--covariate combinations can be sparse or unsupported. Retaining the policy, our partial-identification framework decomposes its mean outcome into a point-identified contribution inside a positivity region and one outside. We bound the latter by imposing Lipschitz continuity on conditional mean potential outcomes rather than a parametric extrapolation model. The restriction compares each outside mean with the mean at an anchor inside the region. Metric projection minimizes width among one-anchor intervals but concentrates anchors on a lower-dimensional boundary, making the endpoints not pathwise differentiable. Our novel interior-displaced projection moves anchors inward, restoring pathwise differentiability. With a known region, we derive influence functions, characterize when they are efficient, and obtain asymptotically normal estimators and confidence intervals. In simulations, our intervals attain at least nominal coverage where those assuming positivity undercover. In a pesticide-mixture application, protective associations suggested by methods assuming positivity are not robust to modest outcome variation beyond the estimated region.
