Treatment Effect Estimation in Survival Analysis Using Copula-Based Deep Learning Models for Causal Inference

This paper presents the use of Copula-based deep learning with Horvitz–Thompson (HT) weights and inverse probability of treatment weighting (IPTW) for estimating propensity scores in causal inference problems. This study compares the performance of the statistical methods—Copula-based deep learning with HT and IPTW weights, propensity score matching (PSM), and logistic regression—in estimating the treatment effect (ATE) using both simulated and real-world data. Our results show that the Copula-based recurrent neural network (RNN) with the method of HT weights provides the most precise and robust treatment effect estimate, with narrow confidence intervals indicating high confidence in the results. The PSM model yields the largest treatment effect estimate, but with greater uncertainty, suggesting sensitivity to data imbalances. In contrast, logistic regression and causal forests produce a substantially smaller estimate, potentially underestimating the treatment effect, particularly in structured datasets such as COMPAS scores. Overall, copula-based methods (HT and IPTW) tend to produce higher and more precise estimates, making them effective choices for treatment effect estimation in complex settings. Our findings emphasize the importance of method selection based on both the magnitude and precision of the treatment effect for accurate analysis.