A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes

Jong-Min Kim ()
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Jong-Min Kim: Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN 56267, USA

Mathematics, 2025, vol. 13, issue 15, 1-20

Abstract: Estimating heterogeneous treatment effects (HTEs) across multiple correlated outcomes poses significant challenges due to complex dependency structures and diverse data types. In this study, we propose a novel deep learning framework integrating empirical copula transformations with a CNN-LSTM (Convolutional Neural Networks and Long Short-Term Memory networks) architecture to capture nonlinear dependencies and temporal dynamics in multivariate treatment effect estimation. The empirical copula transformation, a rank-based nonparametric approach, preprocesses input covariates to better represent the underlying joint distributions before modeling. We compare this method with a baseline CNN-LSTM model lacking copula preprocessing and a nonparametric tree-based approach, the Causal Forest, grounded in generalized random forests for HTE estimation. Our framework accommodates continuous, count, and censored survival outcomes simultaneously through a multitask learning setup with customized loss functions, including Cox partial likelihood for survival data. We evaluate model performance under varying treatment perturbation rates via extensive simulation studies, demonstrating that the Empirical Copula CNN-LSTM achieves superior accuracy and robustness in average treatment effect (ATE) and conditional average treatment effect (CATE) estimation. These results highlight the potential of copula-based deep learning models for causal inference in complex multivariate settings, offering valuable insights for personalized treatment strategies.

Keywords: heterogeneous treatment effects; empirical copula; CNN-LSTM; multitask learning; causal inference; survival analysis; causal forest; multivariate outcomes; deep learning; nonparametric transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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