Causal Mediation Analysis for Zero-inflated Mixture Mediators

2025-07-20

AI Summary

Existing causal mediation analysis methods struggle with mixed-type mediators exhibiting zero-inflation, multimodality, and outliers. This paper proposes a novel causal mediation framework based on finite mixture distributions, jointly modeling zero-inflation, multimodality, and heterogeneity. It uniquely decomposes the mediated effect into two distinct components: a binary “zero-jump” effect (capturing transitions between zero and nonzero states) and a continuous “nonzero-value shift” effect (quantifying magnitude changes among nonzero values). The method integrates zero-inflated log-normal, Poisson, or negative binomial mixture models; employs an EM algorithm to jointly estimate latent mixture components, distinguish true zeros from structural zeros, and identify outliers; and selects the optimal number of mixture components via information criteria. Simulation studies and a neuroscience application demonstrate that the proposed approach significantly outperforms conventional mediation methods in both model fit and accuracy of dual-effect decomposition.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Causal mediation analysis is an important statistical tool to quantify effects transmitted by intermediate variables from a cause to an outcome. There is a gap in mediation analysis methods to handle mixture mediator data that are zero-inflated with multi-modality and atypical behaviors. We propose an innovative way to model zero-inflated mixture mediators from the perspective of finite mixture distributions to flexibly capture such mediator data. Multiple data types are considered for modeling such mediators including the zero-inflated log-normal mixture, zero-inflated Poisson mixture and zero-inflated negative binomial mixture. A two-part mediation effect is derived to better understand effects on outcomes attributable to the numerical change as well as binary change from 0 to 1 in mediators. The maximum likelihood estimates are obtained by an expectation maximization algorithm to account for unobserved mixture membership and whether an observed zero is a true or false zero. The optimal number of mixture components are chosen by a model selection criterion. The performance of the proposed method is demonstrated in a simulation study and an application to a neuroscience study in comparison with standard mediation analysis methods.

Problem

• Handling zero-inflated mixture mediators in causal analysis
• Modeling multi-modal mediator data with atypical behaviors
• Deriving two-part mediation effects for binary and numerical changes

Innovation

• Uses finite mixture distributions for zero-inflated mediators
• Derives two-part mediation effect for numerical and binary changes
• Employs EM algorithm for maximum likelihood estimation