Structured variable selection with q-values

Abstract

When some of the regressors can act on both the response and other explanatory variables, the already challenging problem of selecting variables when the number of covariates exceeds the sample size becomes more difficult. A motivating example is a metabolic study in mice that has diet groups and gut microbial percentages that may affect changes in multiple phenotypes related to body weight regulation. The data have more variables than observations and diet is known to act directly on the phenotypes as well as on some or potentially all of the microbial percentages. Interest lies in determining which gut microflora influence the phenotypes while accounting for the direct relationship between diet and the other variables A new methodology for variable selection in this context is presented that links the concept of q-values from multiple hypothesis testing to the recently developed weighted Lasso.

Associations between dairy foods, diabetes, and metabolic health: Potential mechanisms and future directions

“…It remains to be seen if these results translate to the human condition, and the mechanisms underlying the dairy effects are not known. Based on initial observations that a NFDM-based diet significantly alters gut microbial populations in DIO mice [57], a strong possibility is that dairy components (e.g., oligosaccharides: [58, 59]) alter the microbiome. This could change host-gut microbe signals that impact host metabolism, as originally speculated by the Cani group [56].…”

Integrated analysis of DNA-methylation and gene expression using high-dimensional penalized regression: a cohort study on bone mineral density in postmenopausal women

“…If the external data set possesses important information, the data integrated weights will strengthen the prediction, regardless of the results from the classical lasso. In [ 23 ], they build upon this and use p -values corrected for multiple testing as a basis. But in that paper they focus on dividing the covariates into two groups, where the first group should not be subject to selection and are given weights small enough to ensure their inclusion in the model.…”

Identification of important regressor groups, subgroups and individuals via regularization methods: application to gut microbiome data

“…The above procedure selects well for a fixed 1 , 2 , and now we describe how to optimally select 1 and 2 . We propose selecting the optimal 1 , 2 based on repeated 10-fold cross-validation as advocated by Garcia et al (2013) and Martinez et al (2011). For a fixed 1 ¼ 10 and 2 ¼ 20 , a single application of 10-fold cross-validation works as follows: (i) randomly partition the data into 10 non-overlapping equal-sized subsets; (ii) remove data subset d, and apply the algorithm in Section 2.2.1 at 10 , 20 and over the range of , and select the model that minimizes Mallow's C p criterion.…”

“…Analogous to the work done in Garcia et al (2013) and Martinez et al (2011), we did two additional steps to the above 10-fold cross-validation. First, when the minimizer of the cross-validation score was not unique, we took 1 , 2 as the average of the minimizers.…”

“…A prior analysis in Garcia et al (2013) demonstrated that diet has a significant impact on expression of mRNA for CD68. To accommodate this diet effect, we took the response variable (y) as the residuals from regressing expression of mRNA for CD68 on diet.…”