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 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 our doubly robust dose response test in the R package DRDRtest on CRAN.

翻译：基于观测数据评估处理效应显著性的绝大多数文献局限于离散处理。这些方法无法用于推断连续处理效应，而连续处理在许多重要应用中广泛存在。在评估连续处理效应时，为调整混杂因素，现有推断方法通常依赖于对处理变量进行离散化或使用（可能误设的）参数模型拟合效应曲线。近年来，Kennedy等人（2017）提出了观测研究中连续处理效应的非参数双稳健估计方法。然而，连续处理效应的推断是一个更具挑战性的问题。据我们所知，目前尚不存在完全非参数的双稳健推断方法。本文构建了此类非参数双稳健流程，用于对连续处理效应曲线进行推断。通过运用局部U过程和V过程的经验过程技术，我们建立了检验统计量的渐近分布。此外，我们提出了一种野自助法以在实践中实现该检验。通过数值模拟以及关于护士配置时数对医院绩效影响的构造数据集分析，我们验证了新方法的有效性。我们已将所提出的双稳健剂量反应检验方法在CRAN平台的R包DRDRtest中实现。