Causal inference literature has extensively focused on binary treatments, with relatively fewer methods developed for multi-valued treatments. In particular, methods for multiple simultaneously assigned treatments remain understudied despite their practical importance. This paper introduces two settings: (1) estimating the effects of multiple treatments of different types (binary, categorical, and continuous) and the effects of treatment interactions, and (2) estimating the average treatment effect across categories of multi-valued regimens. To obtain robust estimates for both settings, we propose a class of methods based on the Double Machine Learning (DML) framework. Our methods are well-suited for complex settings of multiple treatments/regimens, using machine learning to model confounding relationships while overcoming regularization and overfitting biases through Neyman orthogonality and cross-fitting. To our knowledge, this work is the first to apply machine learning for robust estimation of interaction effects in the presence of multiple treatments. We further establish the asymptotic distribution of our estimators and derive variance estimators for statistical inference. Extensive simulations demonstrate the performance of our methods. Finally, we apply the methods to study the effect of three treatments on HIV-associated kidney disease in an adult HIV cohort of 2455 participants in Nigeria.

翻译：因果推断文献主要关注二元处理，针对多值处理的方法相对较少。尽管具有实际重要性，但针对同时分配的多种处理的方法仍然研究不足。本文引入两种设定：（1）估计不同类型处理（二元、分类和连续）的效应以及处理交互效应，（2）估计多值方案各分类的平均处理效应。为获得两种设定的稳健估计，我们提出一类基于双重机器学习（DML）框架的方法。我们的方法适用于多重处理/方案的复杂场景，利用机器学习对混杂关系建模，同时通过奈曼正交性和交叉拟合克服正则化与过拟合偏差。据我们所知，这是首次将机器学习应用于存在多重处理时交互效应的稳健估计。我们进一步建立了估计量的渐近分布，并推导了用于统计推断的方差估计量。广泛模拟验证了所提方法的性能。最后，我们将该方法应用于尼日利亚一项包含2455名成年HIV感染者的队列研究，分析三种处理对HIV相关肾脏疾病的效应。