A longitudinal Bayesian framework for estimating causal dose-response relationships

TL;DR

This paper introduces a scalable Bayesian framework for estimating causal dose-response relationships with continuous exposures over time, addressing limitations of existing methods that focus on binary treatments.

Contribution

It develops a nonparametric Bayesian approach that models marginal longitudinal causal dose-response functions using Dirichlet processes within GEE, handling time-varying confounding and continuous exposures.

Findings

Identified causal dose-response patterns between metro ridership and COVID-19 cases.

Demonstrated the method's ability to characterize relationships with minimal assumptions.

Applied to real-world data from international cities, revealing actionable insights.

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.