Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations

TL;DR

This paper introduces TE-CDE, a continuous-time neural differential equation model for estimating counterfactual outcomes from irregularly sampled longitudinal data, improving personalized healthcare decision-making.

Contribution

The paper presents a novel neural controlled differential equation framework for counterfactual modeling that handles irregular sampling and adjusts for confounding using adversarial training.

Findings

TE-CDE outperforms existing methods in simulated irregular sampling scenarios.

The approach effectively models continuous-time trajectories for counterfactual inference.

Adversarial training helps mitigate confounding in longitudinal data.

Abstract

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time-series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all simulated scenarios with irregular sampling.