Title: Nonparametric methodology for causal inference with continuous exposures
Authors: Mark van der Laan - University of California at Berkeley (United States)
Aaron Hudson - Fred Hutchinson Cancer Center (United States) [presenting]
Abstract: In many scientific studies, it is of interest to assess whether there exists a causal relationship between an exposure variable and an outcome. When the exposure is continuous, a target statistical parameter that is commonly of interest is the dose-response function. Most of the available methodology for statistical inference on the dose-response function requires strong parametric assumptions on the probability distribution. Such parametric assumptions are typically untenable in practice and lead to an 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.