AE Hoerl

AM Halawa

CI Amos

CJ Hoggart

D Altman

E Riboli

E Vago

Erika Cule

G Golub

H Zou

IE Frank

J Lawless

J McKay

JC Whittaker

JY Tzeng

K Ayers

M Chadeau-Hyam

M Park

M Zucknick

Maria De Iorio

N Malo

N Meinshausen

P Armitage

P Yang

Paolo Vineis

R Development Core Team

R Tibshirani

RJ Hung

SL Cessie

T Hastie

T Hsiang

T Truong

TA Manolio

The 1000 Genomes Project Consortium

WTCCC

Y Sun

Y Wang

PubMed

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.</p

De Iorio Maria

Vineis Paolo

Cule Erika

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Significance testing in ridge regression for genetic data

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Cule, E

Vineis, P

De Iorio, M

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English

Significance testing in ridge regression for genetic data.

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Significance testing in ridge regression for genetic data.

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