From Prediction to Intervention: Causal Inference in Time-to-Event and Time-Series Data

Abstract: Modeling time-to-event (TTE) and time-series (TS) data is essential for advancing scientific understanding and informing decision-making. For TTE data, example applications include predicting patients’ length of stay in healthcare facilities based on admission characteristics, or selecting personalized treatments for HIV patients to optimize survival. For TS data, a representative use case is modeling the effect of fluid infusion on the cardiovascular system. This work introduces three methodological advances, ranging from prediction models to intervention effect evaluation. First, we introduce a regression framework for discrete-time TTE data with competing risks, enabling principled modeling when event times are discrete. The approach allows for adding penalization or performing feature screening, offering flexibility unavailable in existing methods. Second, we develop MISTR (Multiple Imputation for Survival Treatment Response), a general non-parametric method for estimating heterogeneous treatment effects in TTE data. MISTR integrates recursively imputed survival trees with generalized random forests, producing robust estimates even under heavy censoring. Moreover, it extends to settings with unobserved confounding leveraging instrumental variables, providing the first non-parametric solution for this problem. Finally, we propose hybrid mechanistic-data-driven models for intervention outcome estimation in TS data. By integrating mechanistic knowledge expressed as ordinary differential equations with neural ODEs, these models combine the robustness of physics-based approaches with the adaptability of data-driven learning, achieving superior generalization to out-of-distribution interventions, especially when the mechanistic model is incomplete or simplified. Together, these contributions advance the methodological toolkit for TTE and TS domains, while advancing from prediction toward causal modeling.