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

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 (Conv...

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Main Author: Jong-Min Kim
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/15/2384
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author Jong-Min Kim
author_facet Jong-Min Kim
author_sort Jong-Min Kim
collection DOAJ
description 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.
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spelling doaj-art-c8f36c9220954ca2bbabf93dc02633532025-08-20T04:00:50ZengMDPI AGMathematics2227-73902025-07-011315238410.3390/math13152384A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate OutcomesJong-Min Kim0Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN 56267, USAEstimating 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.https://www.mdpi.com/2227-7390/13/15/2384heterogeneous treatment effectsempirical copulaCNN-LSTMmultitask learningcausal inferencesurvival analysis
spellingShingle Jong-Min Kim
A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes
Mathematics
heterogeneous treatment effects
empirical copula
CNN-LSTM
multitask learning
causal inference
survival analysis
title A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes
title_full A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes
title_fullStr A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes
title_full_unstemmed A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes
title_short A Copula-Driven CNN-LSTM Framework for Estimating Heterogeneous Treatment Effects in Multivariate Outcomes
title_sort copula driven cnn lstm framework for estimating heterogeneous treatment effects in multivariate outcomes
topic heterogeneous treatment effects
empirical copula
CNN-LSTM
multitask learning
causal inference
survival analysis
url https://www.mdpi.com/2227-7390/13/15/2384
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AT jongminkim copuladrivencnnlstmframeworkforestimatingheterogeneoustreatmenteffectsinmultivariateoutcomes