Evaluating the causal health effects of multivariate, continuous exposures, such as air pollution mixtures, is a critical public health challenge. A primary obstacle is the frequent violation of the positivity assumption, which renders the effects of standard deterministic interventions unidentified or heavily reliant on unreliable model extrapolation. In this paper, we develop a novel causal inference framework to address this challenge. We extend exponential tilting to multivariate exposures and address the critical question of how to compare different intervention directions fairly. This establishes a systematic framework for defining and evaluating various policy-relevant causal estimands, allowing researchers to address diverse scientific questions. We develop numerous methodological advancements, including efficient one-step estimation strategies, a Riemannian BFGS algorithm to solve a constrained manifold optimization problem, semiparametric efficiency bounds for causal estimands, minimax rates for estimators, and establishing asymptotic normality. We demonstrate our framework's utility by applying it to a nationwide environmental health dataset to identify the optimal strategy for reducing adverse health outcomes associated with a PM$_{2.5}$ chemical mixture.

翻译：评估多元连续暴露（如空气污染混合物）的因果健康效应是一项关键的公共卫生挑战。主要障碍在于正向假设的频繁违反，这使得标准确定性处理的效应无法识别，或严重依赖不可靠的模型外推。本文提出了一种新的因果推断框架来应对这一挑战。我们将指数倾斜方法扩展到多元暴露，并解决了如何公平比较不同干预方向的关键问题。这为定义和评估各种政策相关因果估计量建立了系统框架，使研究人员能够解决多样化的科学问题。我们开发了多项方法学创新，包括高效的一步估计策略、用于求解约束流形优化问题的黎曼BFGS算法、因果估计量的半参数效率界、估计量的极小化极大速率，并建立了渐近正态性。通过将我们的框架应用于一个全国性环境健康数据集，我们展示了其实用性，以确定减少与PM$_{2.5}$化学混合物相关不良健康结局的最优策略。