Significance testing in ridge regression for genetic data.

TitleSignificance testing in ridge regression for genetic data.
Publication TypeJournal Article
Year of Publication2011
AuthorsCule E, Vineis P, De Iorio M
JournalBMC Bioinformatics
Volume12
Pagination372
Date Published2011
ISSN1471-2105
KeywordsCase-Control Studies, Chromosome Mapping, Disease, Genetic Association Studies, Genetic Markers, Humans, Linkage Disequilibrium, Polymorphism, Single Nucleotide, Prospective Studies, Regression Analysis
Abstract

BACKGROUND: Technological developments have increased the feasibility of large scale genetic association studies. Densely typed genetic markers are obtained using SNP arrays, next-generation sequencing technologies and imputation. However, SNPs typed using these methods can be highly correlated due to linkage disequilibrium among them, and standard multiple regression techniques fail with these data sets due to their high dimensionality and correlation structure. There has been increasing interest in using penalised regression in the analysis of high dimensional data. Ridge regression is one such penalised regression technique which does not perform variable selection, instead estimating a regression coefficient for each predictor variable. It is therefore desirable to obtain an estimate of the significance of each ridge regression coefficient.

RESULTS: We develop and evaluate a test of significance for ridge regression coefficients. Using simulation studies, we demonstrate that the performance of the test is comparable to that of a permutation test, with the advantage of a much-reduced computational cost. We introduce the p-value trace, a plot of the negative logarithm of the p-values of ridge regression coefficients with increasing shrinkage parameter, which enables the visualisation of the change in p-value of the regression coefficients with increasing penalisation. We apply the proposed method to a lung cancer case-control data set from EPIC, the European Prospective Investigation into Cancer and Nutrition.

CONCLUSIONS: The proposed test is a useful alternative to a permutation test for the estimation of the significance of ridge regression coefficients, at a much-reduced computational cost. The p-value trace is an informative graphical tool for evaluating the results of a test of significance of ridge regression coefficients as the shrinkage parameter increases, and the proposed test makes its production computationally feasible.

DOI10.1186/1471-2105-12-372
Alternate JournalBMC Bioinformatics
PubMed ID21929786