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.

连续时间中的治疗效果估计对个性化医学至关重要，现有方法只关注潜在结果的点估计而忽略了不确定性估计，因此本文提出了一种用于连续时间中治疗效果估计的新型贝叶斯神经控制微分方程（BNCDE），通过神经控制微分方程和神经随机微分方程的耦合系统来建模时间维度，其中神经随机微分方程可以进行可行的变分贝叶斯推断，从而为给定顺序的治疗提供了潜在结果的有意义的后验预测分布。据我们所知，这是首个用于连续时间中治疗效果的不确定性估计的定制神经方法，因此我们的方法对于促进可靠的医学决策具有直接的实用价值。