Network analysis

As an alternative to SNMU, a network analysis is proposed. The outcome of a network analysis is graphically displayed by a network. This is a collection of nodes, that may have pairwise relationships. Each node represents a substance, and an edge represents pairwise dependence between substances (e.g. correlation or partial correlation). In MCRA, the network is estimated using a Gaussian graphical model (GLASSO) based on partial correlation and a sparseness penalty to control the number of nonzero edges (Friedman et al. (2008)). Parameters are automatically tuned. The communities are detected using a Walkman algorithm. In Figure 80, using HBM data, a network is displayed with 6 communities. The largest community contains 5 substances: mbzp, A, B, C and D. Compared to the results of the SNMU mixture analysis, the communities are almost identical to the components found in the SNMU approach.

The exposure data may be log transformed before the network analysis. Zeros are replaced by the logarithm of the minimum of the non-zero exposure values per substance multiplied by a factor 0.01.

Figure 80 Network analysis.

Figure 81 SNMU solution with 6 components. Sparsity = 0.8.