Estimating causal effects with multivariate continuous exposures is challenging because causal exposure-response surfaces can be high-dimensional, complicating estimation and interpretation of joint exposure effects. Such settings arise in environmental epidemiology, where interest centers on the health effects of chemical and pollutant mixtures. We develop causal sufficient dimension reduction (CSDR), a semiparametric framework for representing causal exposure-response surfaces through low-dimensional exposure summaries. We formalize the reduction target as the causal central mean subspace and propose a modular two-stage estimator that decouples nuisance-function estimation from subspace estimation, simplifying implementation relative to existing marginal structural model-based approaches. The reduced exposure preserves the information needed to characterize joint causal effects while enabling efficient downstream estimation. We establish a convergence rate for causal subspace recovery accounting for first-stage nuisance estimation error, show that the structural dimension can be estimated consistently, and introduce a subspace importance score that quantifies the contribution of each exposure to the reduction. In simulations, CSDR yielded more accurate estimation and uncertainty quantification of the exposure-response surface than methods using noncausal dimension reduction or the original exposure. We apply CSDR to study the effect of maternal exposure to PFAS chemical mixtures on infant birth weight in the Atlanta African American Maternal-Child Cohort.

翻译：多变量连续暴露的因果效应估计具有挑战性，因为因果暴露-反应曲面可能具有高维特征，这增加了联合暴露效应估计与解释的复杂性。此类情境常见于环境流行病学领域，研究重点在于化学物质和污染物混合物对健康的影响。本文提出因果充分降维（CSDR）方法——一种通过低维暴露摘要表征因果暴露-反应曲面的半参数框架。我们将降维目标形式化为因果中心均值子空间，并提出模块化两阶段估计器，将干扰函数估计与子空间估计解耦，从而简化了现有基于边缘结构模型方法的实现过程。降维后的暴露在保留联合因果效应表征所需信息的同时，可实现高效的下游估计。我们建立了考虑第一阶段干扰估计误差的因果子空间恢复收敛率，证明结构维度可被一致估计，并引入量化各暴露变量对降维贡献的子空间重要性评分。模拟实验表明，相较于使用非因果降维或原始暴露变量的方法，CSDR对暴露-反应曲面的估计与不确定性量化更为精准。我们将CSDR应用于亚特兰大非洲裔母婴队列，研究母体PFAS化学混合物暴露对新生儿出生体重的影响。