Integrating artificial neural network-based propensity score and outcome regression information into a multi-index propensity score framework for average causal effect estimation

In observational studies, the average causal effect (ACE) is commonly estimated using inverse probability weighting (IPW) or G-computation. However, these methods often rely on a single propensity score (PS) model or outcome regression (OcR) model and are therefore sensitive to model misspecification. Our previously proposed multi-index propensity score (MiPS) method can integrate information from multiple parametric models, but its robustness may still be limited when all candidate parametric models are misspecified. This study proposed a nonparametric model information-integrated MiPS (npMiPS) method. The method incorporates information from artificial neural network (ANN)-based nonparametric PS and OcR models together with multiple parametric PS and OcR models to construct an integrated propensity score for IPW estimation of the ACE. For single-dataset implementation, the integration ANN architecture was selected using three-fold out-of-fold mean absolute standardized mean difference (OOF-MASMD). Targeted simulations compared OOF-MASMD with the original prediction accuracy for treatment (PAT) criterion, and a three-fold cross-fitted Super Learner augmented inverse-probability weighting estimator (SL-AIPW) was included as an ensemble causal-learning benchmark. We also applied npMiPS to CLHLS data to estimate the ACE of active social participation on depression scores among older adults. In the tested simulation scenarios, npMiPS maintained low bias when the candidate model set contained either a correctly specified parametric model or an ANN model. In the targeted criterion comparison, OOF-MASMD reduced out-of-fold covariate imbalance relative to PAT while maintaining similar bias, RMSE, and confidence interval coverage. Cross-fitted SL-AIPW provided a strong ensemble benchmark; in representative scenarios without correctly specified parametric candidate models, npMiPS showed lower bias with similar RMSE. In the empirical analysis using OOF-MASMD tuning, npMiPS ACE estimates remained approximately − 1.0 points and were stable across model specifications and covariate-selection strategies. By integrating information from both parametric models and ANN-based nonparametric models, npMiPS showed robust ACE estimation across the settings examined. OOF-MASMD provides a balance-oriented approach for selecting the integration ANN architecture in a single dataset, although the current estimator is not fully cross-fitted. npMiPS may provide a useful information-integration strategy for observational studies with complex confounding structures and uncertain model forms. Not applicable. This study does not contain any clinical trial data in any form.