• 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