Table 1.

Details of ECLUST algorithm

Step	Description, Softwarea and Reference
1a)	i)Calculate $TOM$ separately for observations with $E=0$ and $E=1$ using WGCNA::TOMsimilarityFromExpr (Langfelder & Horvath, 2008) ii)Euclidean distance matrix of $|TO{M}_{E=1}-TO{M}_{E=0}|$ using stats::dist iii)Run the dynamicTreeCut algorithm (Langfelder et al., 2008; Langfelder, P., Zhang, B., & with contributions from Steve Horvath, 2016) on the distance matrix to determine the number of clusters and cluster membership using dynamicTreeCut::cutreeDynamic with minClusterSize = 50
1b)	i)1st PC or average for each cluster using stat::prcomp or base::mean ii)Penalized regression model: create a design matrix of the derived cluster representatives and their interactions with E using stats::model.matrix iii)MARS model: create a design matrix of the derived cluster representatives and E
2)	i)For linear models, run penalized regression on design matrix from Step 1b using glmnet::cv.glmnet (Friedman et al., 2010). Elasticnet mixing parameter alpha=1 corresponds to the lasso and alpha=0.5 corresponds to the value we used in our simulations for elasticnet. The tuning parameter lambda is selected by minimizing 10 fold cross‐validated mean squared error (MSE). ii)For nonlinear effects, run MARS on the design matrix from Step 1b using earth::earth (Milborrow. Derived from mda:mars by T. Hastie and R. Tibshirani., 2011) with pruning method pmethod = “backward” and maximum number of model terms nk = 1000. The degree=1,2 is chosen using 10 fold cross validation (CV), and within each fold the number of terms in the model is the one that minimizes the generalized cross validated (GCV) error.

^aAll functions are implemented in R (R Core Team, 2016). The naming convention is as follows: package_name::package_function. Default settings used for all functions unless indicated otherwise.