Causal identification for continuous-time stochastic processes

TL;DR

This paper develops a framework for causal inference in continuous-time stochastic processes, addressing the limitations of discrete-time methods and establishing identification results under continuous-time confounding.

Contribution

It introduces new causal identification techniques for continuous-time data, extending existing methods to handle uncountably infinite variables and continuous confounding.

Findings

Established causal identification results for continuous-time processes.

Connected continuous-time identification to discrete-time g-methods.

Demonstrated assumptions with practical examples.

Abstract

Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data collection have yielded near continuous-time measurements, from e.g. physiological monitors, wearable digital devices, and environmental sensors. 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, due to the entanglement of uncountably infinite variables. 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, through orthogonalization and weighting. We use three concrete running examples to demonstrate the plausibility of our identification assumptions, as well as their connections to the discrete-time g methods literature.