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. 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.