Advisor(s)
Nengjun Yi
Committee Member(s)
Justin Leach
Lama Ghazi
Leann Long
Melissa Smith
School
School of Public Health
Document Type
Dissertation
Department (new version)
Biostatistics
Date of Award
9-11-2025
Abstract
Mediation analysis is a fundamental tool in causal inference, enabling researchers to disentangle the pathways through which an exposure affects an outcome via intermediate variables (mediators). It has been widely applied in social sciences, psychology, and healthcare-related studies. Traditionally, mediation analysis has been conducted within the linear structural equation modeling (LSEM) framework. However, recent advances have shifted attention toward the counterfactual framework due to its flexibility in defining causal effects and its capacity to accommodate non-linear relationships, parametric and non-parametric models. Building on this foundation, methodological developments in mediation analysis have expanded to address more complex data structures, such as count data, longitudinal data, and data with multiple mediators. Nonetheless, limited attention was given to data involving zero-inflated variables, which are characterized by an excessive number of zeros beyond the standard statistical distributions. These data types are common in biomedical and public health research, particularly in microbiome studies, health service utilization, and rare event outcomes. In this dissertation, we introduce a novel Bayesian mediation analysis method tailored for both zero-inflated count and zero-inflated continuous data. This approach is built on the strengths of Bayesian framework, including the integration of prior information and the ability to quantify uncertainty in parameter estimates particularly when dealing with the complexities introduced by zero inflation. Our approach utilizes Bayesian models for both the mediator and outcome, utilizing Markov Chain Monte Carlo algorithms for parameter estimation. We decompose the mediation effects into components attributable to either the probability of zero or the mean of the non-zero distribution, providing nuanced insights into the causal mechanisms. To facilitate the application of this framework, we developed an open-source R package, mediationBayes, available at https://github.com/jhcuibst/mediationBayes. The package supports flexible model specifications, including various distributions for exposure and covariates, and includes functions for data simulation, model fitting, and mediation effect estimation. It is designed to be user-friendly for researchers with limited backgrounds in Bayesian statistics. In summary, this dissertation addresses a critical methodological gap by introducing a flexible and robust Bayesian mediation analysis framework for zero-inflated data. We additionally provide an accessible tool for applied researchers in biostatistics and related fields.
ProQuest ID
Recommended Citation
Cui, Jinhong, "Bayesian Mediation Analyses For Zero-Inflated Data" (2025). All ETDs from UAB. 7419.
https://digitalcommons.library.uab.edu/etd-collection/7419
