An approach to nonparametric inference on the causal dose–response function

Hudson Aaron (), Geng Elvin H., Odeny Thomas A., Bukusi Elizabeth A., Petersen Maya L. and J. van der Laan Mark
Additional contact information
Hudson Aaron: Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA
Geng Elvin H.: Division of Infectious Diseases, Department of Medicine, Washington University in St. Louis, St. Louis, Missouri, USA
Odeny Thomas A.: Research Care Training Program, Centre for Microbiology Research, Kenya Medical Research Institute, Nairobi, Kenya
Bukusi Elizabeth A.: Research Care Training Program, Centre for Microbiology Research, Kenya Medical Research Institute, Nairobi, Kenya
Petersen Maya L.: Division of Biostatistics, School of Public Health, University of California, Berkeley, California, United States
J. van der Laan Mark: Division of Biostatistics, School of Public Health, University of California, Berkeley, California, United States

Journal of Causal Inference, 2024, vol. 12, issue 1, 28

Abstract: 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.

Keywords: dose–response function; continuous exposure; nonparametric testing; targeted minimum loss-based estimation (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/jci-2024-0001 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:12:y:2024:i:1:p:28:n:1001

DOI: 10.1515/jci-2024-0001

Access Statistics for this article

Journal of Causal Inference is currently edited by Elias Bareinboim, Jin Tian and Iván Díaz

More articles in Journal of Causal Inference from De Gruyter
Bibliographic data for series maintained by Peter Golla ().