A longitudinal Bayesian framework for estimating causal dose-response relationships
Abstract
Existing causal methods for time-varying exposure and time-varying confounding focus on estimating the average causal effect of a time-varying binary treatment on an end-of-study outcome, offering limited tools for characterizing marginal causal dose-response relationships under continuous exposures. We propose a scalable, nonparametric Bayesian framework for estimating marginal longitudinal causal dose-response functions with repeated outcome measurements. Our approach targets the average potential outcome at any fixed dose level and accommodates time-varying confounding through the generalized propensity score. The proposed approach embeds a Dirichlet process specification within a generalized estimating equations structure, capturing temporal correlation while making minimal assumptions about the functional form of the continuous exposure. We apply the proposed methods to monthly metro ridership and COVID-19 case data from major international cities, identifying causal relationships and the dose-response patterns between higher ridership and increased case counts.
Cite
@article{arxiv.2505.20893,
title = {A longitudinal Bayesian framework for estimating causal dose-response relationships},
author = {Yu Luo and Kuan Liu and Ramandeep Singh and Daniel J. Graham},
journal= {arXiv preprint arXiv:2505.20893},
year = {2026}
}