Preface
About the Author
1
Introduction
1.1
Environmental mixtures
1.2
Clarifying the research question
1.3
Broad classification(s) of statistical approaches
1.4
Introduction to R packaged and simulated data
2
Unsupervised analyses
2.1
Data pre-processing
2.2
Correlation analysis
2.2.1
Weighted correlation network analysis
2.3
Principal component analysis
2.3.1
Fitting a PCA in R
2.3.2
Choosing the number of components
2.3.3
Getting sense of components interpretation
2.3.4
Using principal components in subsequent analyses
2.3.5
PCA in practice
2.4
Cluster analysis
2.4.1
K-means clustering
2.4.2
K-means in R
2.4.3
Cluster analysis to simplify descriptive statistics presentation
3
Regression-based approaches
3.1
Ordinary Least Squares (OLS) regression
3.1.1
Chemical-specific regression (EWAS)
3.1.2
Multiple regression
3.1.3
The problem of multicollinearity
3.2
Penalized regression approaches
3.2.1
Bias-variance tradeoff
3.2.2
Ridge regression
3.2.3
LASSO
3.2.4
Elastic net
3.2.5
Additional notes
3.2.6
Elastic Net and environmental mixtures
3.3
Other regression-based approaches
3.3.1
Hierarchical linear models
3.3.2
Partial least square regression
3.4
Advantages and limitations of regression approaches
4
Assessing the overall (cumulative) effect of multiple exposures
4.1
Unsupervised summary scores
4.2
The Weighted Quantile Sum (WQS) and its extensions
4.2.1
Model definition and estimation
4.2.2
The unidirectionality assumption
4.2.3
Extensions of the original WQS regression
4.2.4
Quantile G-computation
4.2.5
WQS regression in R
4.2.6
Example from the literature
5
Flexible approaches for complex settings
5.1
Bayesian Kernel Machine Regression
5.1.1
Introduction
5.1.2
Estimation
5.1.3
Trace plots and burning phase
5.1.4
Visualizing results
5.1.5
Hierarchical selection
5.1.6
BKMR Extensions
5.1.7
Practical considerations and discussion
5.2
Assessing interactions
5.2.1
Tree-based modeling
5.2.2
Interaction screening and regression approaches
6
Additional topics and final remarks
6.1
Causal mixture effects
6.2
Binary and zero-inflated exposures
6.3
Integrating environmental mixtures in mediation analysis
6.4
Final remarks
References
Statistical Methods for Environmental Mixtures
Statistical Methods for Environmental Mixtures
Andrea Bellavia
November 2021
