We consider a GWAMA-based polygenic score and three penalized regression methods, Ridge Regression (RR) (30), the Least Absolute Shrinkage and Selection Operator (LASSO) (31) and the Elastic Net (EN) (32).
To investigate the ability of our variables to jointly predict onset of MOH, we considered a multivariable prediction model obtained by least absolute shrinkage and selection operator (LASSO) regression.
All three feature selection techniques we consider; the Lasso, SNSS, and RDA; involve regularization parameters that we must select.
In addition to this optimal model, we also considered a parsimonious LASSO model with a higher penalty parameter (hereafter called LASSO-se) so that the mean deviance of the model was within one standard error of the LASSO-max average deviance [ 28, 32].
For this, we consider three techniques: Lasso [ 4].
In this study, we considered the LASSO variable selection for the marker effect estimation step of the multilevel approach and a Bayesian spike and slab prior approach for the linear mixed model (henceforth abbreviated as BLMM).
In particular, we consider the performance of LASSO to be representative of what would be the best prediction accuracy of a routine biomarker approach.
Recall that we consider three different feature selection techniques, the Lasso, SNSS, and RDA, in combination with three different classification approaches: (1) using the same model for classification as for feature selection, (2) using the selected features in a KNN classifier, or (3) using the selected features in a Random Forests classifier.
We consider the grouping of SNPs and apply the group-lasso penalty to B (Yuan and Lin, 2006): (2) where and g∈ represents a group of SNPs (inputs).
Here we consider the coordinate descent (CD) algorithm, which has been successfully used to solve lasso regression problems [ 20, 39].
