Counterfactual Outcome Prediction using Structured State Space Model

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.