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.

翻译：连续时间下的治疗效果估计对个性化医疗至关重要。然而，现有方法仅限于潜在结果的点估计，忽略了不确定性估计。毋庸置疑，不确定性量化对医疗应用中的可靠决策至关重要。为填补这一空白，我们提出了一种新颖的贝叶斯神经受控微分方程（BNCDE），用于连续时间下的治疗效果估计。在BNCDE中，时间维度通过神经受控微分方程与神经随机微分方程的耦合系统进行建模，其中神经随机微分方程支持可处理的变分贝叶斯推断。因此，对于给定的治疗序列，我们的BNCDE能够提供潜在结果的有意义的后验预测分布。据我们所知，这是首个专门针对连续时间下治疗效果估计提供不确定性量化的神经方法。因此，该方法对促进医学中的可靠决策具有直接的实用价值。