Statistical Methods for Mediation, Confounding and Moderation Analysis Using R and SAS

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Symbols
1. Introduction
1.1. Types of Third-Variable Effects
1.2. Motivate Examples for Making Inferences on Third-Variable Effects
1.2.1. Evaluate Policies and Interventions
1.2.2. Explore Health Disparities
1.2.3. Exam the Trend of Disparities
1.3. Organization of the Book
2. A Review of Third-Variable Effect Inferences
2.1. The General Linear Model Framework
2.1.1. Baron and Kenny Method to Identify a Third-Variable Effect
2.1.2. The Coefficient-Difference Method
2.1.3. The Coefficient-Product Method
2.1.4. Categorical Third-Variables
2.1.5. Generalized Linear Model for the Outcome
2.1.6. Cox Proportional Hazard Model for Time-to-Event Outcome
2.2. The Counterfactual Framework
2.2.1. Binary Exposures
2.2.2. Continuous Exposure
2.2.3. Discussion
3. Advanced Statistical Modeling and Machine Learning Methods Used in the Book
3.1. Bootstrapping
3.1.1. An Illustration of Bootstrapping
3.1.2. Bootstrapping for Linear Regression
3.2. Elastic Net
3.2.1. Ridge Regression and LASSO
3.2.2. Elastic Net
3.3. Multiple Additive Regression Trees
3.3.1. Classification and Regression Tree
3.3.2. MART Algorithm
3.3.3. Improvement of MART
3.3.4. A Simulation Example
3.3.5. Interpretation Tools for MART
3.4. Generalized Additive Model
3.4.1. Generalized Additive Model
3.4.2. Smoothing Spline
3.4.3. Revisit the Simulation Example
4. The General Third-Variable Effect Analysis Method
4.1. Notations
4.2. Definitions of Third-Variable Effects
4.2.1. Total Effect
4.2.2. Direct and Indirect Effects
4.2.3. Relative Effect
4.3. Third-Variable Effect Analysis with Generalized Linear Models
4.3.1. Multiple Third-Variable Analysis in Linear Regressions
4.3.2. Multiple Third-Variable Analysis in Logistic Regression
4.3.2.1. When M is Binary
4.3.2.2. When M is Multi-categorical
4.3.2.3. Delta Method to Estimate the Variances
4.4. Algorithms of Third-Variable Effect Analysis with General Predictive Models for Binary Exposure
4.5. Algorithms of Third-Variable Effect Analysis with General Predictive Models for Continuous Exposure
5. The Implementation of General Third-Variable Effect Analysis Method
5.1. The R Package mma
5.1.1. Identification of Potential Mediators/Confounders and Organization of Data
5.1.2. Third-Variable Effect Estimates
5.1.3. Statistical Inference on Third-Variable Effect Analysis
5.2. SAS Macros
5.2.1. Running R in SAS
5.2.2. Macros to Call the data.org Function
5.2.3. Macros to Call the med Function
5.2.4. Macros to Call the boot.med Function
5.2.5. Macros to Call the plot Function
5.3. Examples and Simulations on General Third-Variable Effect Analysis
5.3.1. Pattern of Care Study
5.3.2. To Explore the Racial Disparity in Breast Cancer Mortality Rate
5.3.3. To Explore the Racial Disparity in Breast Cancer Survival Rate
5.3.4. Simulation Study
5.3.4.1. Empirical Bias
5.3.4.2. Type I Error Rate and Power
6. Assumptions for the General Third-Variable Analysis
6.1. Assumption 1: No-Unmeasured-Confounder for the Exposure-Outcome Relationship
6.1.1. On the Direct Effect
6.1.2. On the Indirect Effect of M
6.1.3. On the Total Effect
6.1.4. Summary and the Correct Model
6.2. Assumption 2: No-Unmeasured-Confounder for the Exposure-Third Variable Relationship
6.2.1. On the Direct Effect
6.2.2. On the Indirect Effect of M
6.2.3. On the Total Effect
6.2.4. Summary and the Correct Model
6.3. Assumption 3: No-Unmeasured-Confounder for the Third Variable-Outcome Relationship
6.3.1. On the Total Effect
6.3.2. On the Direct Effect
6.3.3. On the Indirect Effect of M
6.3.4. Summary and the Correct Model
6.4. Assumption 4: Any Third-Variable Mi is not Causally Prior to Other Third-Variables in M_i
6.4.1. On the Direct Effect
6.4.2. On the Indirect Effect of M
6.4.3. On the Total Effect
6.4.4. Conclusion
7. Multiple Exposures and Multivariate Responses
7.1. Multivariate Multiple TVEA
7.1.1. Non/Semi-Parametric TVEA for Multi-Categorical Exposures
7.1.2. Non/Semi-Parametric TVEA for Multiple Continuous Exposures
7.2. Confidence Ball for Estimated Mediation Effects
7.2.1. A Simulation Study to Check the Coverage Probability of the Confidence Ball
7.3. The R Package mma
7.4. Racial and Ethnic Disparities in Obesity and BMI
7.4.1. Variables
7.4.2. Disparities
7.4.3. Descriptive Analysis
7.4.4. Results on Racial Disparities
7.4.5. Results on Ethnic Disparities
8. Regularized Third-Variable Effect Analysis for High-Dimensional Dataset
8.1. Regularized Third-Variable Analysis in Linear Regression Setting
8.2. Computation: The Algorithm to Estimate Third-variable Effects with Generalized Linear Models
8.3. The R Package: mmabig
8.3.1. Simulate a Dataset
8.3.2. Function data.org.big
8.3.2.1. Univariate Exposure and Univariate Outcome
8.3.2.2. Survival Outcome
8.3.2.3. Multivariate Predictors and/or Outcomes
8.3.3. Function med.big
8.3.4. Function mma.big
8.3.5. Generic Functions
8.3.6. Call mmabig from SAS
8.4. Sensitivity and Specificity Analysis
8.5. Simulations to Illustrate the Use of the Method
8.5.1. X_TV Relationship is Nonlinear
8.5.2. TV_Y Relationship is Nonlinear
8.5.3. When Third-Variables are Highly Correlated
8.6. Explore Racial Disparity in Breast Cancer Survival
9. Interaction/Moderation Analysis with Third-Variable Effects
9.1. Inference on Moderation Effect with Third-Variable Effect Analysis
9.1.1. Types of Interaction/Moderation Effects
9.1.2. Moderation Effect Analysis with MART
9.1.3. The R Package mma
9.2. Illustration of Moderation Effects
9.2.1. Direct Moderation
9.2.2. Exposure-Moderated TVE
9.2.3. Third-Variable-Moderated TVE
9.3. Explore the Trend of Racial Disparity in ODX Utilization among Breast Cancer Patients
9.3.1. Data Description
9.3.2. Third-Variable Effects and the Trend
9.4. Conclusions
10. Third-Variable Effect Analysis with Multilevel Additive Models
10.1. Third-Variable Analysis with Multilevel Additive Models
10.1.1. Definitions of Third-Variable Effects with Data of Two Levels
10.1.2. Multilevel Additive Models
10.1.3. Third-Variable Effects with Multilevel Additive Model
10.1.4. Bootstrap Method for Third-Variable Effect Inferences
10.2. The mlma R Package
10.2.1. A Simulated Dataset
10.2.2. Data Transformation and Organization
10.2.3. Multilevel Third-Variable Analysis
10.2.3.1. The mlma Function
10.2.3.2. The Summary Function for Multilevel Third-Variable Analysis
10.2.3.3. The Plot Function for the mlma Object
10.2.4. Make Inferences on Multilevel Third-Variable Effect
10.3. Explore the Racial Disparity in Obesity
11. Bayesian Third-Variable Effect Analysis
11.1. Why Bayesian Method?
11.2. Continuous Exposure Variable
11.2.1. Continuous Outcome and Third-Variables
11.2.1.1. Method 1: Functions of Estimated Coefficients
11.2.1.2. Method 2: Product of Partial Differences
11.2.1.3. Method 3: A Resampling Method
11.2.2. Different Format of Outcome and Third-Variables
11.2.2.1. Outcomes of Different Format
11.2.2.2. Binary Third-Variables
11.2.2.3. Categorical Third-Variables
11.3. Binary Exposure Variable
11.4. Multiple Exposure Variables and Multivariate Outcomes
12. Other Issues
12.1. Explaining Third-Variable Effects
12.2. Power Analysis and Sample Sizes
12.2.1. Linear Models
12.2.2. Simulation Method
12.3. Sequential Third-Variable Analysis and Third-Variable Analysis with Longitudinal Data
Appendices
Bibliography
Index