The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the effect curve. Recently, Kennedy et al. (2017) proposed nonparametric doubly robust estimation for a continuous treatment effect in observational studies. However, inference for the continuous treatment effect is a significantly harder problem. To the best of our knowledge, a completely nonparametric doubly robust approach for inference in this setting is not yet available. We develop such a nonparametric doubly robust procedure in this paper for making inference on the continuous treatment effect curve. Using empirical process techniques for local U- and V-processes, we establish the test statistic's asymptotic distribution. Furthermore, we propose a wild bootstrap procedure for implementing the test in practice. We illustrate the new method via simulations and a study of a constructed dataset relating the effect of nurse staffing hours on hospital performance. We implement and share code for our doubly robust dose response test in the R package DRDRtest on CRAN.

翻译：关于根据观察数据评价治疗效应重要性的绝大多数文献都局限于根据观察数据评估治疗效应重要性的绝大多数文献,这些方法不适用于在许多重要应用中出现的连续治疗的推断,这些方法不适用于为连续治疗作出推断,而这种连续治疗在许多重要应用中产生。为了在评价连续治疗时适应混乱者,现有的推断方法往往依赖离析治疗或使用(可能误判)影响曲线参数模型。最近,肯尼迪等人(2017年)提议对观测研究中的连续治疗效应进行非参数性双重强估。然而,对连续治疗效应的推断是一个更困难得多的问题。我们最了解的是,目前尚不具备一种完全非对准的双重稳健的连续治疗推断方法。我们在本文件中制定这样一种非对连续治疗效应曲线作出推断的不完全对称的双重稳健健程序。我们利用当地U和V-处理工艺的经验性过程,建立了测试性统计分布的系统。此外,我们建议采用野生靴捕捉程序来进行试验。我们通过模拟和研究在RAR-DR测试中进行稳健的测试时分数的测试,我们测试了在医院中进行测试时数要求的状态。