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：评估多变量连续暴露（如空气污染混合物）的因果健康效应是公共卫生领域的关键挑战。主要障碍在于正性假设常被违反，导致标准确定性干预措施的效应无法识别或严重依赖不可靠的模型外推。本文提出一种新颖的因果推断框架来解决这一问题。我们将指数倾斜方法扩展到多变量暴露场景，并解决了如何公平比较不同干预方向的关键问题。这建立了系统框架用于定义和评估各类政策相关的因果估计量，使研究者能够解决多样化的科学问题。我们发展了多项方法论创新，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、估计量的极小极大速率，并建立了渐近正态性。通过将框架应用于全国性环境健康数据集，我们识别出减少PM$_{2.5}$化学混合物相关不良健康结局的最优策略，从而证明了其实用价值。