  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.
