  Predicting the impact of treatments from observational data only still
represents a majorchallenge despite recent significant advances in time series
modeling. Treatment assignments are usually correlated with the predictors of
the response, resulting in a lack of data support for counterfactual
predictions and therefore in poor quality estimates. Developments in causal
inference have lead to methods addressing this confounding by requiring a
minimum level of overlap. However,overlap is difficult to assess and usually
notsatisfied in practice. In this work, we propose Counterfactual ODE (CF-ODE),
a novel method to predict the impact of treatments continuously over time using
Neural Ordinary Differential Equations equipped with uncertainty estimates.
This allows to specifically assess which treatment outcomes can be reliably
predicted. We demonstrate over several longitudinal data sets that CF-ODE
provides more accurate predictions and more reliable uncertainty estimates than
previously available methods.
