Counterfactual outcome prediction in longitudinal data has recently gained attention due to its potential applications in healthcare and social sciences. In this paper, we explore the use of the state space model, a popular sequence model, for this task. Specifically, we compare the performance of two models: Treatment Effect Neural Controlled Differential Equation (TE-CDE) and structured state space model (S4Model). While TE-CDE uses controlled differential equations to address time-dependent confounding, it suffers from optimization issues and slow training. In contrast, S4Model is more efficient at modeling long-range dependencies and easier to train. We evaluate the models on a simulated lung tumor growth dataset and find that S4Model outperforms TE-CDE with 1.63x reduction in per epoch training time and 10x better normalized mean squared error. Additionally, S4Model is more stable during training and less sensitive to weight initialization than TE-CDE. Our results suggest that the state space model may be a promising approach for counterfactual outcome prediction in longitudinal data, with S4Model offering a more efficient and effective alternative to TE-CDE.

翻译：纵向数据中的反事实结果预测因其在医疗健康和社会科学中的潜在应用而近来受到关注。本文探索了使用状态空间模型——一种流行的序列模型——来完成此任务。具体而言，我们比较了两种模型的性能：治疗效应神经受控微分方程（TE-CDE）和结构化状态空间模型（S4Model）。TE-CDE利用受控微分方程处理时间依赖性混杂因素，但其面临优化问题和训练速度慢的挑战。相比之下，S4Model在建模长程依赖关系方面更为高效，且更易训练。我们在模拟肺部肿瘤生长数据集上评估了这些模型，发现S4Model在每周期训练时间上相较于TE-CDE减少了1.63倍，归一化均方误差改善了10倍。此外，S4Model训练过程更加稳定，对权重初始化的敏感性低于TE-CDE。我们的结果表明，状态空间模型或可成为纵向数据中反事实结果预测的一种有前景的方法，而S4Model相较于TE-CDE提供了更高效且有效的替代方案。