Bayesian approaches to mediation analysis in complex causal structures

다국어 초록 (Multilingual Abstract)

Causal mediation analysis is a powerful statistical framework that not only identifies the total causal effect of exposure on outcome, but also decomposes the total effect into indirect effects that occur through mediators and direct effect that affect outcome without going through the mediators, providing more detailed insights into the underlying causal mechanisms.

However, existing methods have limitations in that they do not sufficiently reflect the structure of complex mediators. In particular, many traditional methods assume a single mediator or independence between mediators, so bias can occur in estimating causal effects and selecting variables in situations where there are correlated multiple mediators. Moreover, the interpretation of indirect effects is likely to be distorted by ignoring the potential causal structure between mediators.

To overcome this, this dissertation proposes new Bayesian mediation analysis methods. First, we present a method to consider the correlation structure in both model fitting and variable selection process by combining the factor analytic (FA) model and the Markov random field (MRF) prior. Second, a generalized linear model (GLM) was introduced to develop a framework that can be extended to non-continuous outcome. Third, we propose a new procedure to relax the assumption of independence between mediators by estimating the causal structure between mediators with a directed acyclic graph (DAG). These contributions make it possible to estimate direct and indirect effects more realistically and precisely even under complex mediators.

국문 초록 (Abstract)

인과 매개 분석은 전반적인 인과효과를 매개 변수를 통해 발생하는 간접 효과와 결과에 직접적으로 영향을 미치는 직접 효과로 분해하여 근본적인 인과 메커니즘에 대한 보다 자세한 통찰을 제공하는 강력한 통계 프레임워크입니다.

그러나 기존 방법은 복잡한 매개변수의 구조를 충분히 반영하지 못한다는 한계가 있습니다. 특히 많은 전통적인 방법은 단일 매개변수 또는 매개변수 간의 독립성을 가정하기 때문에 상관관계가 있는 여러 매개변수가 있는 상황에서 인과효과를 추정하고 변수를 선택하는 데 오류가 발생할 수 있습니다. 또한 매개변수 간의 잠재적 인과관계를 무시함으로써 간접 효과의 경로 해석이 왜곡될 가능성이 높습니다.

이를 극복하기 위해 본 논문에서는 새로운 베이지안 매개 분석 방법을 제안합니다. 첫째, 요인 분석 (FA) 모델과 마르코프 랜덤 필드 (MRF) 사전분포를 도입하여 모델 추정과 변수 선택 과정 모두에서 상관 구조를 고려하는 방법을 제시합니다. 둘째, 비연속적인 결과로 확장할 수 있는 프레임워크를 개발하기 위해 일반화된 선형 모델을 도입했습니다. 셋째, 방향성 비순환 그래프(DAG)를 사용하여 매개변수 간의 인과 구조를 추정함으로써 매개변수 간 독립성 가정을 완화하는 새로운 절차를 제안합니다.

목차 (Table of Contents)

• 1 Introduction 1
• 2 Preliminaries 7
• 2.1 Notation 7
• 2.2 Assumption of Independent Causal Pathways among Mediators 8
• 2.3 Frequentist Methods of HighDimensional Mediation Analysis 9
• 2.4 Existing Nonparametric Bayesian Methods 11
• 2.4.1 Bayesian additive regression trees (BART) 11
• 2.4.2 Multivariate Bayesian additive regression trees (mBART) 14
• 2.5 Gaussian Directed Acyclic Graph (DAG) Model and Bayesian Structure Learning 16
• 3 Bayesian Variable Selection for HighDimensional Mediation Analysis: Application to Metabolomics Data in Epidemiological Studies 21
• 3.1 Introduction 21
• 3.2 HighDimensional Mediation Analysis 25
• 3.2.1 Notations and estimands 25
• 3.2.2 Model formulations 26
• 3.3 Bayesian Variable Selection 28
• 3.3.1 Prior distributions 28
• 3.3.2 Practical considerations: phase transition and selection of variables 30
• 3.3.3 Computational scheme 31
• 3.4 Simulation Studies 32
• 3.4.1 Setup and data generation 33
• 3.4.2 Specification of hyperparameters and analysis settings 34
• 3.4.3 Results 35
• 3.4.4 Sensitivity analyses and comparison with a frequentist method 40
• 3.5 Application to Metabolomics Data 40
• 3.5.1 Health Professionals Followup Study and Nurses' Health Study II 40
• 3.5.2 Specification of hyperparameters and analysis settings 41
• 3.5.3 Results 41
• 4 BVS on HighDimensional Mediation Analysis with Noncontinuous Outcome 46
• 4.1 Introduction 46
• 4.2 Bayesian Variable Selection for HighDimensional Mediation Analysis 49
• 4.2.1 Notation and model specification 50
• 4.2.2 Correlation structure and MRF prior 52
• 4.2.3 Prior specification for variable selection 53
• 4.3 Causal Estimands and Effect Decomposition 55
• 4.4 Posterior Computation 57
• 4.4.1 Update of δ and ω 57
• 4.4.2 Refinement for δ 58
• 4.4.3 Update of α = (α0,α1,.,αp+1) 58
• 4.5 Simulation Studies 60
• 4.5.1 Setup and data generation 60
• 4.5.2 Specification of hyperparameters and analysis settings 62
• 4.5.3 Results 63
• 4.6 Application to Metabolomics Data 67
• 4.6.1 Data explanation 67
• 4.6.2 Hyperparameter settings 67
• 4.6.3 Results 68
• 5 Causal Mediation Analysis with DART using DAG 71
• 5.1 Introduction 71
• 5.2 Model Specification 74
• 5.2.1 Construct the models for mediation analysis 74
• 5.2.2 Incorporating DAG information into the outcome model 76
• 5.3 Causal Estimand 78
• 5.4 Simulation Study 81
• 5.4.1 Data generating process 81
• 5.4.2 Competing model 83
• 5.4.3 Hyperparameter setting 85
• 5.4.4 Evaluation and summary measures 86
• 5.4.5 Results 87
• 5.5 Real Data Analysis 92
• 5.5.1 Data explanation 92
• 5.5.2 Hyperparameters setting 94
• 5.5.3 Results 95
• 6 Discussion 97
• 6.1 Discussion for Chapter 3 97
• 6.2 Discussion for Chapter 4 101
• 6.3 Discussion for Chapter 5 103
• References 107
• A Appendix for 'Bayesian Variable Selection for HighDimensional Mediation Analysis: Application to Metabolomics Data in Epidemiological Studies (Chapter 3)' 119
• A.1 Computational Scheme for the Proposed Bayesian Framework 119
• A.1.1 Computational scheme 119
• A.1.2 Updating τ and γ 121
• A.1.3 Refinement of τ 123
• A.1.4 Updating δ and ω 124
• A.1.5 Refinement of δ 127
• A.1.6 Updating β0 128
• A.1.7 Updating βj for j = 1,.,q 128
• A.1.8 Updating α0 129
• A.1.9 Updating α = (α1,.,αp) 129
• A.1.10 Updating αp+1 129
• A.1.11 Updating λ 130
• A.1.12 Updating σ2Σ 131
• A.1.13 Updating σ2 131
• A.2 Additional Details Regarding Simulation Studies Presented in the Main Manuscript 132 A.2.1 Estimated indirect effects in Scenarios IIIV 132
• A.2.2 Results from NormalIBSSB model 136
• A.2.3 FDR control with adaptive BFDR thresholding 141
• A.2.4 Sensitivity analyses 142
• A.2.5 Comparison with nonBayesian method 144
• A.3 Additional Details about the HPFS/NHSII Data 146
• A.4 Additional Details from the Analysis of the HPFS/NHSII Data 147
• B Appendix for 'BVS on Highdimensional Mediation Analysis with Noncontinuous Outcome (Chapter 4)' 152
• B.1 Preliminaries 152
• B.1.1 Hamiltonian Monte Carlo (HMC) 152
• B.2 Additional Details Regarding Simulation Studies Presented in the Main Manuscript 153
• B.2.1 Estimated causal effects in Scenarios IIV 153
• B.2.2 Results from NormalIBSSB model 159
• B.3 Additional Details from the Analysis of the HPFS/NHSII Data 166
• C Appendix for 'Causal Mediation Analysis with BART using DAG (Chapter 5)' 168
• C.1 Additional Details About 400 CoalFired Power Plants Data 168