A multivariate approach to investigate the combined biological effects of multiple exposures

Abstract

Epidemiological studies provide evidence that environmental exposures may affect health through complex mixtures. Formal investigation of the effect of exposure mixtures is usually achieved by modelling interactions, which relies on strong assumptions relating to the identity and the number of the exposures involved in such interactions, and on the order and parametric form of these interactions. These hypotheses become difficult to formulate and justify in an exposome context, where influential exposures are numerous and heterogeneous. To capture both the complexity of the exposome and its possibly pleiotropic effects, models handling multivariate predictors and responses, such as partial least squares (PLS) algorithms, can prove useful. As an illustrative example, we applied PLS models to data from a study investigating the inflammatory response (blood concentration of 13 immune markers) to the exposure to four disinfection by-products (one brominated and three chlorinated compounds), while swimming in a pool. To accommodate the multiple observations per participant (n=60; before and after the swim), we adopted a multilevel extension of PLS algorithms, including sparse PLS models shrinking loadings coefficients of unimportant predictors (exposures) and/or responses (protein levels). Despite the strong correlation among co-occurring exposures, our approach identified a subset of exposures (n=3/4) affecting the exhaled levels of 8 (out of 13) immune markers. PLS algorithms can easily scale to high-dimensional exposures and responses, and prove useful for exposome research to identify sparse sets of exposures jointly affecting a set of (selected) biological markers. Our descriptive work may guide these extensions for higher dimensional data.

Keywords: OMICs data; exposome; multi-level sparse PLS models; multiple exposures; multivariate response.

Figure 1

Spearman correlation coefficients for exposures (top) and Pearson correlation coefficients for protein levels (bottom) before (first column) and after (second column) the swim. The third column represent the correlation coefficients between differences in exposures and proteins levels. BDCM, bromodichloromethane; CCL11, C-C motif chemokine 11, CCL2 motif, chemokine (C-C motif) ligand 2; CCL22, C-C motif chemokine 22; CHBr₃, bromoform; CRP, C reactive protein; CHCl₃, chloroform; CXCL10, C-X-C motif chemokine 10; DBCM, dibromochloromethane; EGF, epidermal growth factor, G-CSF, granulocyte colony-stimulating factor; IL, interleukin; MPO, myeloperoxidase; VEGF, vascular endothelial growth factor.

Figure 2

Variable importance in projection plots and proportion of variance explained by protein. Results are presented for PLS model (A), for sparse PLS performing variable selection on exposures (B), on proteins (C), and both on exposures and proteins (D). CCL11, C-C motif chemokine 11, CCL2 motif, chemokine (C-C motif) ligand 2; CCL22, C-C motif chemokine 22; CRP, C reactive protein; CXCL10, C-X-C motif chemokine 10; EGF, epidermal growth factor, G-CSF, granulocyte colony-stimulating factor; IL, interleukin; MPO, myeloperoxidase; PLS, partial least squares; sVEGF, vascular endothelial growth factor.

Figure 3

X-Y score plot representing the PLS scores for the first exposure PLS component (C_1X‴x-axis) as a function of the scores of the first PLS component for proteins (C_1Y‴, y-axis). Scores are presented for all (n=60) participants before (blue), and after (orange) the swimming session. Results are presented for the sparse PLS models performing variable selection of both exposures and proteins. PLS, partial least squares.

Figure 4

Per-protein coefficient of determination (R²) (A) and Akaike information criterion (B) for the four PLS models investigated: non-penalised, with variable selection on X, on Y and on both X and Y. Results are also represented for a linear mixed model using the participant ID as random effect, and the set of four exposure are fixed effects, in relation to each protein separately. CCL11, C-C motif chemokine 11, CCL2 motif, chemokine (C-C motif) ligand 2; CCL22, C-C motif chemokine 22; CRP, C reactive protein; CXCL10, C-X-C motif chemokine 10; EGF, epidermal growth factor, G-CSF, granulocyte colony-stimulating factor; IL, interleukin; MPO, myeloperoxidase; PLS, partial least squares; VEGF, vascular endothelial growth factor.