The causal dose response curve is commonly selected as the statistical parameter of interest in studies where the goal is to understand the effect of a continuous exposure on an outcome.Most of the available methodology for statistical inference on the dose-response function in the continuous exposure setting requires strong parametric assumptions on the probability distribution. Such parametric assumptions are typically untenable in practice and lead to invalid inference. It is often preferable to instead use nonparametric methods for inference, which only make mild assumptions about the data-generating mechanism. We propose a nonparametric test of the null hypothesis that the dose-response function is equal to a constant function. We argue that when the null hypothesis holds, the dose-response function has zero variance. Thus, one can test the null hypothesis by assessing whether there is sufficient evidence to claim that the variance is positive. We construct a novel estimator for the variance of the dose-response function, for which we can fully characterize the null limiting distribution and thus perform well-calibrated tests of the null hypothesis. We also present an approach for constructing simultaneous confidence bands for the dose-response function by inverting our proposed hypothesis test. We assess the validity of our proposal in a simulation study. In a data example, we study, in a population of patients who have initiated treatment for HIV, how the distance required to travel to an HIV clinic affects retention in care.

翻译：因果剂量反应曲线通常被选为研究连续暴露对结果影响时的统计感兴趣参数。在连续暴露设置下，大多数关于剂量反应函数统计推断的现有方法需要对概率分布强加参数假设。这类参数假设在实践中通常站不住脚，并导致无效推断。相比之下，使用非参数方法进行推断通常更可取，因为它仅对数据生成机制施加温和假设。我们提出了一种非参数检验，用于检验剂量反应函数等于常数函数的零假设。我们论证当零假设成立时，剂量反应函数的方差为零。因此，可以通过评估是否有足够证据表明方差为正来检验零假设。我们构建了一个新颖的剂量反应函数方差估计量，能够完全刻画其零极限分布，从而执行校准良好的零假设检验。我们还提出了一种通过反转我们提出的假设检验来构建剂量反应函数同时置信带的方法。我们在模拟研究中评估了该方法的有效性。在一个数据示例中，我们研究了接受HIV治疗启动的患者群体中，前往HIV诊所所需的通勤距离如何影响护理 retention。