Estimation of Long-Term Dose-Response via Longitudinal Surrogacy under Time-Varying Confounders

Estimating long-term treatment effects is critical in many domains, yet randomized experiments with long follow-up periods are often costly and ethically challenging. Such studies also typically involve dynamic treatment and evolving disease states, and single-visit observation provides little predictive signal for the chronic outcome, such as 90-day mortality given daily treatment for a chronic disease. Existing methods either average the dose, ignore time-dependent confounders, or rely on stringent assumptions. In this paper, we propose a Window-based Sequential Causal Framework (WSCF) that exploits longitudinal surrogates and the treatment path to identify long-term effects across sequential analysis windows. To address time-dependent confounding bias, we learn representations of the history to balance current treatment assignment, while aligning long-term observational data with auxiliary experimental data via optimal transport weighting to adjust for unmeasured confounding. Theoretically, we derive sequential g-formula for identification under a mean exchangeability assumption weaker than prior work, control the rollout error due to estimated surrogates, and establish a generalization bound on counterfactual prediction error. Experiments on synthetic and semi-synthetic datasets from real-world healthcare and online industrial data demonstrate both the effectiveness and long-depth robustness.