Identification for Treatment Effects of General Continuous-Time Stochastic Processes

• Activity Number: 116 - Epidemiological Models for Longitudinal Studies, Time-to-Event Outcomes, and Functional Data
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Jinghao Sun* and Forrest W. Crawford
• Companies: Yale University and Yale University
• Keywords: longitudinal data; g methods; time-varying confounding; causal inference; observational studies; temporal discretization

Abstract

Many real-world processes are trajectories that may be regarded as continuous-time "functional data". For example, a patient’s biomarker concentrations and physiological states change continuously in time. Corresponding advances in data collection have yielded near continuous-time measurement, from e.g. physiological monitors and wearable digital devices. Statistical methodology for estimating the causal effect of a time-varying treatment, measured discretely in time, is well developed. But discrete-time methods like the g-formula, structural nested models, and marginal structural models do not generalize easily to continuous time. Moreover, researchers have shown that the choice of discretization time scale can seriously affect the quality of causal inferences about the effects of an intervention. In this paper, we establish causal identification results for continuous-time treatment-outcome relationships for general cadlag stochastic processes under continuous-time confounding. We use concrete running examples to demonstrate the plausibility of our identification assumptions, as well as their connections to the discrete-time g methods literature.