Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data

Estimating treatment effects over time is relevant in many real-world applications, such as precision medicine, epidemiology, economy, and marketing. Many state-of-the-art methods either assume the observations of all confounders or seek to infer the unobserved ones. We take a different perspective by assuming unobserved risk factors, i.e., adjustment variables that affect only the sequence of outcomes. Under unconfoundedness, we target the Individual Treatment Effect (ITE) estimation with unobserved heterogeneity in the treatment response due to missing risk factors. We address the challenges posed by time-varying effects and unobserved adjustment variables. Led by theoretical results over the validity of the learned adjustment variables and generalization bounds over the treatment effect, we devise Causal DVAE (CDVAE). This model combines a Dynamic Variational Autoencoder (DVAE) framework with a weighting strategy using propensity scores to estimate counterfactual responses. The CDVAE model allows for accurate estimation of ITE and captures the underlying heterogeneity in longitudinal data. Evaluations of our model show superior performance over state-of-the-art models.