title: Better prediction by use of co-data: adaptive group-regularized ridge regression.
abstract: For many high-dimensional studies, additional information on the variables, like (genomic) annotation or external p-values, is available. In the context of binary and continuous prediction, we develop a method for adaptive group-regularized (logistic) ridge regression, which makes structural use of such 'co-data'. Here, 'groups' refer to a partition of the variables according to the co-data. We derive empirical Bayes estimates of group-specific penalties, which possess several nice properties: (i) They are analytical. (ii) They adapt to the informativeness of the co-data for the data at hand. (iii) Only one global penalty parameter requires tuning by cross-validation. In addition, the method allows use of multiple types of co-data at little extra computational effort. We show that the group-specific penalties may lead to a larger distinction between 'near-zero' and relatively large regression parameters, which facilitates post hoc variable selection. The method, termed GRridge, is implemented in an easy-to-use R-package. It is demonstrated on two cancer genomics studies, which both concern the discrimination of precancerous cervical lesions from normal cervix tissues using methylation microarray data. For both examples, GRridge clearly improves the predictive performances of ordinary logistic ridge regression and the group lasso. In addition, we show that for the second study, the relatively good predictive performance is maintained when selecting only 42 variables.
authors.affiliation: Department of Epidemiology and Biostatistics, VU University Medical Center, Amsterdam, The Netherlands.|Department of Mathematics, VU University, Amsterdam, The Netherlands.
authors.forename: Mark A
authors.initials: MA
authors.lastname: van de Wiel
authors.affiliation: Department of Mathematics, University of Oslo, Oslo, Norway.
authors.forename: Tonje G
authors.initials: TG
authors.lastname: Lien
authors.affiliation: Department of Pathology, VU University Medical Center, Amsterdam, The Netherlands.
authors.forename: Wina
authors.initials: W
authors.lastname: Verlaat
authors.affiliation: Department of Epidemiology and Biostatistics, VU University Medical Center, Amsterdam, The Netherlands.|Department of Mathematics, VU University, Amsterdam, The Netherlands.
authors.forename: Wessel N
authors.initials: WN
authors.lastname: van Wieringen
authors.affiliation: Department of Pathology, VU University Medical Center, Amsterdam, The Netherlands.
authors.forename: Saskia M
authors.initials: SM
authors.lastname: Wilting
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D019175:DNA Methylation / Q000235:genetics; D005260:Female; D005820:Genetic Testing / Q000379:methods / Q000706:statistics & numerical data*; D006801:Humans; D016015:Logistic Models; D011230:Precancerous Conditions / Q000175:diagnosis* / Q000235:genetics; D011237:Predictive Value of Tests; D015203:Reproducibility of Results; D012107:Research Design / Q000592:standards / Q000706:statistics & numerical data*; D002583:Uterine Cervical Neoplasms / Q000175:diagnosis* / Q000235:genetics
keywords: classification; empirical Bayes; logistic ridge regression; methylation; random forest; variable selection