Causal Identification for Complex Functional Longitudinal Studies

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.