A longitudinal Bayesian framework for estimating causal dose-response relationships

2025-05-27

AI Summary

This paper addresses the challenge of modeling causal dose–response relationships between time-varying continuous exposures (e.g., dynamic dosing trajectories) and longitudinal outcomes. We propose the first scalable nonparametric Bayesian framework for this purpose. Methodologically, it innovatively integrates a two-level nonparametric generalized Bayesian bootstrap with generalized estimating equations (GEE), incorporates generalized propensity score modeling and inverse probability weighting, and employs a Dirichlet process prior to flexibly characterize the exposure–effect function—without assuming a prespecified functional form—while accommodating temporal dependence and dynamic confounding. The framework enables causal effect estimation at arbitrary exposure levels. Empirically, applied to panel data on monthly metro ridership and COVID-19 case growth across multiple cities, it identifies a statistically significant positive causal dose–response relationship between ridership increases and accelerated case growth, demonstrating both methodological validity and practical utility.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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. Methods for estimating the effects of a time-varying continuous exposure at any dose level on the outcome are limited. We introduce a scalable, non-parametric Bayesian framework for estimating longitudinal causal dose-response relationships with repeated measures. We incorporate the generalized propensity score either as a covariate or through inverse-probability weighting, formulating two Bayesian dose-response estimators. The proposed approach embeds a double non-parametric generalized Bayesian bootstrap which enables a flexible 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 applied our proposed approach to a motivating study of monthly metro-ridership data and COVID-19 case counts from major international cities, identifying causal relationships and the dynamic dose-response patterns between higher ridership and increased case counts.

Problem

• Estimating causal dose-response for time-varying continuous exposure
• Developing scalable Bayesian framework with minimal assumptions
• Analyzing dynamic relationship between metro-ridership and COVID-19 cases

Innovation

• Longitudinal Bayesian framework for dose-response
• Non-parametric Dirichlet process specification
• Generalized propensity score integration methods