The use of vector bootstrapping to improve variable selection precision in Lasso models

The Lasso is a shrinkage regression method that is widely used for variable selection in statistical genetics. Commonly, K-fold cross-validation is used to fit a Lasso model. This is sometimes followed by using bootstrap confidence intervals to improve precision in the resulting variable selections. Nesting cross-validation within bootstrapping could provide further improvements in precision, but this has not been investigated systematically. We performed simulation studies of Lasso variable selection precision (VSP) with and without nesting cross-validation within bootstrapping. Data were simulated to represent genomic data under a polygenic model as well as under a model with effect sizes representative of typical GWAS results. We compared these approaches to each other as well as to software defaults for the Lasso. Nested cross-validation had the most precise variable selection at small effect sizes. At larger effect sizes, there was no advantage to nesting. We illustrated the nested approach with empirical data comprising SNPs and SNP-SNP interactions from the most significant SNPs in a GWAS of borderline personality symptoms. In the empirical example, we found that the default Lasso selected low-reliability SNPs and interactions which were excluded by bootstrapping.