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Estimating counterfactual outcomes over time has the potential to unlockpersonalized 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 henceare unable to naturally model irregularly sampled data, which is the commonsetting in practice. To handle arbitrary observation patterns, we interpret thedata as samples from an underlying continuous-time process and propose to modelits latent trajectory explicitly using the mathematics of controlleddifferential equations. This leads to a new approach, the Treatment EffectNeural Controlled Differential Equation (TE-CDE), that allows the potentialoutcomes to be evaluated at any time point. In addition, adversarial trainingis used to adjust for time-dependent confounding which is critical inlongitudinal settings and is an added challenge not encountered in conventionaltime-series. To assess solutions to this problem, we propose a controllablesimulation environment based on a model of tumor growth for a range ofscenarios with irregular sampling reflective of a variety of clinicalscenarios. TE-CDE consistently outperforms existing approaches in all simulatedscenarios with irregular sampling.

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