Studying causal effects of continuous treatments is important for gaining a deeper understanding of many interventions, policies, or medications, yet researchers are often left with observational studies for doing so. In the observational setting, confounding is a barrier to the estimation of causal effects. Weighting approaches seek to control for confounding by reweighting samples so that confounders are comparable across different treatment values. Yet, for continuous treatments, weighting methods are highly sensitive to model misspecification. In this paper we elucidate the key property that makes weights effective in estimating causal quantities involving continuous treatments. We show that to eliminate confounding, weights should make treatment and confounders independent on the weighted scale. We develop a measure that characterizes the degree to which a set of weights induces such independence. Further, we propose a new model-free method for weight estimation by optimizing our measure. We study the theoretical properties of our measure and our weights, and prove that our weights can explicitly mitigate treatment-confounder dependence. The empirical effectiveness of our approach is demonstrated in a suite of challenging numerical experiments, where we find that our weights are quite robust and work well under a broad range of settings.

翻译：研究连续处理变量的因果效应对于深入理解许多干预措施、政策或药物至关重要，但研究人员往往只能依赖观察性研究进行此类分析。在观察性环境下，混杂因素是因果效应估计的主要障碍。加权方法试图通过对样本进行重新加权来控制混杂因素，使混杂变量在不同处理值之间具有可比性。然而，对于连续处理变量，加权方法对模型误设高度敏感。本文阐明了使权重能够有效估计涉及连续处理变量因果量的关键性质。我们证明，要消除混杂效应，权重应使处理变量与混杂变量在加权尺度上相互独立。我们开发了一种度量标准，用于表征一组权重实现此类独立性的程度。进一步，我们提出了一种通过优化该度量标准来估计权重的无模型新方法。我们研究了该度量标准及所提权重的理论性质，并证明我们的权重能明确减轻处理变量与混杂变量之间的依赖关系。通过一系列具有挑战性的数值实验，我们验证了该方法在实际应用中的有效性，发现我们的权重具有高度稳健性，能在广泛的情景下表现出色。