Estimating the joint effect of a multivariate, continuous exposure is crucial, particularly in environmental health where interest lies in simultaneously evaluating the impact of multiple environmental pollutants on health. We develop novel methodology that addresses two key issues for estimation of treatment effects of multivariate, continuous exposures. We use nonparametric Bayesian methodology that is flexible to ensure our approach can capture a wide range of data generating processes. Additionally, we allow the effect of the exposures to be heterogeneous with respect to covariates. Treatment effect heterogeneity has not been well explored in the causal inference literature for multivariate, continuous exposures, and therefore we introduce novel estimands that summarize the nature and extent of the heterogeneity, and propose estimation procedures for new estimands related to treatment effect heterogeneity. We provide theoretical support for the proposed models in the form of posterior contraction rates and show that it works well in simulated examples both with and without heterogeneity. We apply our approach to a study of the health effects of simultaneous exposure to the components of PM$_{2.5}$ and find that the negative health effects of exposure to these environmental pollutants is exacerbated by low socioeconomic status and age.

翻译：估计多元连续暴露的联合效应至关重要，尤其是在环境健康领域，需要同时评估多种环境污染物对健康的影响。我们开发了新的方法论，以解决多元连续暴露治疗效果估计中的两个关键问题。采用非参数贝叶斯方法确保其灵活性，从而能够捕捉广泛的数据生成过程。此外，我们允许暴露效应随协变量呈现异质性。在因果推断文献中，针对多元连续暴露的治疗效果异质性尚未得到充分探索，因此我们引入了新的估计量来总结异质性的性质与程度，并提出了与治疗效果异质性相关的新估计量的估计程序。我们从后验收缩速率的角度为所提出的模型提供了理论支持，并通过含与不含异质性的模拟示例验证了其良好性能。我们将该方法应用于一项研究PM$_{2.5}$组分同时暴露对健康影响的研究中，发现低社会经济地位和年龄会加剧这些环境污染物暴露对健康的负面影响。