The potential outcomes framework serves as a fundamental tool for quantifying causal effects. The average dose-response function (also called the effect curve), denoted as (\mu(t)), is typically of interest when dealing with a continuous treatment variable (exposure). The focus of this work is to determine the impact of an extreme level of treatment, potentially beyond the range of observed values--that is, estimating (\mu(t)) for very large (t). Our approach is grounded in the field of statistics known as extreme value theory. We outline key assumptions for the identifiability of the extreme treatment effect. Additionally, we present a novel and consistent estimation procedure that can potentially reduce the dimension of the confounders to at most 3. This is a significant result since typically, the estimation of (\mu(t)) is very challenging due to high-dimensional confounders. In practical applications, our framework proves valuable when assessing the effects of scenarios such as drug overdoses, extreme river discharges, or extremely high temperatures on a variable of interest.

翻译：潜在结果框架是量化因果效应的基本工具。当处理连续治疗变量（暴露）时，通常关注平均剂量-反应函数（也称为效应曲线），记为(μ(t))。本研究旨在确定极端治疗水平的影响，该水平可能超出观测值范围——即估计极大(t)下的(μ(t))。我们的方法基于统计学中的极值理论领域。我们提出了极端治疗效果可识别性的关键假设。此外，我们提出了一种新颖且一致的估计程序，该程序可能将混杂变量的维度降至最多3维。这是一个重要成果，因为通常由于高维混杂变量的存在，估计(μ(t))极具挑战性。在实际应用中，我们的框架在评估药物过量、极端河道流量或极高温度等情景对感兴趣变量的影响时具有重要价值。