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：研究连续治疗的因果效应对于深入理解许多干预措施、政策或药物具有重要意义，然而研究者往往依赖观察性研究进行此类分析。在观察性研究中，混杂因素是估计因果效应的主要障碍。加权方法通过重新加权样本使协变量在不同治疗值之间具有可比性，从而控制混杂偏倚。然而对于连续治疗，加权方法对模型设定错误高度敏感。本文阐明了使权重能够有效估计涉及连续治疗的因果量的关键性质。我们证明，为消除混杂效应，权重应使治疗与协变量在加权尺度上相互独立。我们开发了一种指标来刻画一组权重实现此种独立性的程度。进一步，我们通过优化该指标提出了一种新的无模型权重估计方法。我们研究了该指标及权重的理论性质，并证明我们的权重能够明确减轻治疗-协变量依赖性。通过一系列具有挑战性的数值实验验证了本方法的实证有效性，结果表明我们的权重具有较强鲁棒性，在广泛场景中均表现良好。