lkmt_test function

A function to calculate the p-values for kernel matrices.

For parameter 'satt' a pathway's influence on the probability of beeing a case is evaluated in the logistic kernel machine test and p-values are determined using a Sattherthwaite approximation as described by Dan Schaid.

For parameter 'davies' a pathways influence on the probability of beeing a case is evaluated using the p-value calculation method described by Davies. Here the function davies from package CompQuadForm is used.

lkmt_test(formula, kernel, GWASdata, method = c("satt", "davies"), ...)

## S4 method for signature 'matrix'
score_test(x1, x2)

## S4 method for signature 'matrix'
davies_test(x1, x2)

Arguments

• formula: The formula to be used for the regression nullmodel.
• kernel: An object of class kernel including the pathway representing kernel-matrix based on which the test statistic will be calculated.
• GWASdata: A GWASdata object stating the data used in analysis.
• method: A character specifying which method will be used for p-value calculation. Available are 'satt' for the Satterthwaite approximation and 'davies' for Davies' algorithm. For more details see the references.
• ...: Further arguments can be given to the function.
• x1: A matrix which is the similarity matrix calculated for the pathway to be tested.
• x2: An lm or glm object of the nullmodel with fixed effects covariates included, but no genetic random effects.

Returns

An lkmt object including the following test results

• The formula of the regression nullmodel used in the variance component test.
• An object of class kernel including the similarity matrix of the individuals based on which the pathways influence is evaluated.
• An object of class GWASdata stating the data on which the test was conducted.
• statistic A vector giving the value of the variance component test statistic.
• df A vector giving the number of degrees of freedom.
• p.value A vector giving the p-value calculated for the pathway in the variance component test.

Examples

data(hsa04020)
data(gwas)
net_kernel <- calc_kernel(gwas, hsa04020, knots=NULL, type='net', calculation='cpu')
lkmt_test(pheno ~ sex + age, net_kernel, gwas, method='satt')

References

For details on the variance component test

• Wu MC, Kraft P, Epstein MP, Taylor DM, Chanock SJ, Hunter DJ, Lin X: Powerful SNP-Set Analysis for Case-Control Genome-Wide Association Studies. Am J Hum Genet 2010, 86:929-42
• Liu D, Lin X, Ghosh D: Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 2007, 63(4):1079-88.

For details on the p-value calculation see

• Schaid DJ: Genomic Similarity and Kernel Methods I: Advancements by Building on Mathematical and Statistical Foundations. Hum Hered 2010, 70:109-31

• Davies R: Algorithm as 155: the distribution of a linear combination of chi-2 random variables. J R Stat Soc Ser C 1980, 29:323-333.

Author(s)

Stefanie Friedrichs, Juliane Manitz