Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation
This work addresses the need for uncertainty quantification in treatment effect estimation for medical decision-making, representing a novel tailored neural method in this domain.
The paper tackles treatment effect estimation in continuous time for personalized medicine by proposing a Bayesian neural controlled differential equation (BNCDE) that provides posterior predictive distributions of potential outcomes, addressing the lack of uncertainty estimates in existing methods.
Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless to say, uncertainty quantification is crucial for reliable decision-making in medical applications. To fill this gap, we propose a novel Bayesian neural controlled differential equation (BNCDE) for treatment effect estimation in continuous time. In our BNCDE, the time dimension is modeled through a coupled system of neural controlled differential equations and neural stochastic differential equations, where the neural stochastic differential equations allow for tractable variational Bayesian inference. Thereby, for an assigned sequence of treatments, our BNCDE provides meaningful posterior predictive distributions of the potential outcomes. To the best of our knowledge, ours is the first tailored neural method to provide uncertainty estimates of treatment effects in continuous time. As such, our method is of direct practical value for promoting reliable decision-making in medicine.