🤖 AI Summary
Conventional causal inference methods, designed for discretized time and finite-dimensional assumptions, fail to handle infinite-dimensional treatment–confounder feedback in functional longitudinal data—where outcomes, treatments, and confounders are observed as continuous-time trajectories—as arises in real-time health monitoring. Method: We integrate stochastic process theory, measure theory, and net convergence into causal identification, systematically generalizing g-computation, inverse probability weighting (IPW), and doubly robust formulae to accommodate time-varying outcomes subject to censoring and truncation by death. Contribution/Results: This work establishes the first nonparametric causal identification framework for functional longitudinal data, providing rigorous theoretical foundations for causal effect estimation without parametric or dimensionality constraints. Simulation studies validate its effectiveness, filling a critical theoretical gap and enabling future development of nonparametric causal estimators for functional data.
📝 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.