Prediction of an outcome using NETwork Clusters (NET-C)

Abstract

Birth weight is a key consequence of environmental exposures and metabolic alterations and can influence lifelong health. While a number of methods have been used to examine associations of trace element (including essential nutrients and toxic metals) concentrations or metabolite concentrations with a health outcome, birth weight, studies evaluating how the coexistence of these factors impacts birth weight are extremely limited. Here, we present a novel algorithm NETwork Clusters (NET-C), to improve the prediction of outcome by considering the interactions of features in the network and then apply this method to predict birth weight by jointly modelling trace element and cord blood metabolite data. Specifically, by using trace element and/or metabolite subnetworks as groups, we apply group lasso to estimate birth weight. We conducted statistical simulation studies to examine how both sample size and correlations between grouped features and the outcome affect prediction performance. We showed that in terms of prediction error, our proposed method outperformed other methods such as (a) group lasso with groups defined by hierarchical clustering, (b) random forest regression and (c) neural networks. We applied our method to data ascertained as part of the New Hampshire Birth Cohort Study on trace elements, metabolites and birth outcomes, adjusting for other covariates such as maternal body mass index (BMI) and enrollment age. Our proposed method can be applied to a variety of similarly structured high-dimensional datasets to predict health outcomes.

Keywords: Dimensionality reduction; Gaussian graphical model; Lasso; Metabolic network; Outcome prediction; Trace element exposures.

Figure 1:

The matrix representation of three large clusters, three medium clusters and three small clusters. The strength of feature interactions in each square submatrix, C[i,j], in the matrix is randomly chosen between 0.1 and 0.7 or between −0.7 and −0.1, and the strength of other feature interactions outside submatrices of clusters is chosen between 0.01 and 0.012 or between −0.012 and −0.01. C[i,j] with integers i, j ∈ S₁ × T₁ where S₁ and T₁ are integers from 1 to 9, i, j ∈ S₂ × T₂ where S₂ and T₂ are integers from 10 to 18, and i, j ∈ S₃ × T₃ where S₃ and T₃ are integers from 19 to 27 represents 3 large clusters, C[i,j] with integers i, j ∈ S₄ × T₄ where S₄ and T₄ are integers from 28 to 33, i, j ∈ S₅ × T₅ where S₅ and T₅ are integers from 34 to 39, and i, j ∈ S₆ × T₆ where S₆ and T₆ are integers from 40 to 45 represents 3 medium clusters and C[i,j] with integers i, j ∈ S₇ × T₇ where S₇ and T₇ are integers from 46 to 48, i, j ∈ S₈ × T₈ where S₈ and T₈ are integers from 49 to 51, and i, j ∈ S₉ × T₉ where S₉ and T₉ are integers from 52 to 54 represents 3 small clusters

Figure 2:

Metabolites in this subnetwork including lysophosphatidylcholines were nonnegatively associated with birth weight. The metabolite nodes such as lysophosphadidylcholines colored green were positively associated with birth weight