Causal Identification for Complex Functional Longitudinal Studies

TL;DR

This paper introduces a nonparametric causal identification framework for complex functional longitudinal data in medical research, addressing feedback loops and time-varying outcomes with advanced mathematical tools.

Contribution

It generalizes classical causal inference methods to handle uncountably infinite feedbacks in functional longitudinal data using measure theory and stochastic processes.

Findings

Framework successfully handles uncountably infinite feedbacks.

Simulation results demonstrate the method's effectiveness.

Addresses gaps in current causal inference methodologies.

Abstract

Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite treatment-confounder feedbacks, which traditional causal inference methodologies cannot handle. Inspired by the coarsened data framework, we adopt stochastic process theory, measure theory, and net convergence to propose a nonparametric causal identification framework. This framework generalizes classical g-computation, inverse probability weighting, and doubly robust formulas, accommodating time-varying outcomes subject to mortality and censoring for functional longitudinal data. We examine our framework through Monte Carlo simulations. Our approach addresses significant gaps in current methodologies, providing a solution for functional longitudinal data and paving the way for future estimation work in this domain.