Description Usage Arguments Details Value References See Also Examples

`gates.test`

, `minP.test`

, `tTS.test`

and `tProd.test`

aim at performing gene-gene interaction analysis based on SNP-SNP interaction tests. The following methods are used to combine SNP-SNP interaction tests
into a single Gene-Gene Interaction p-value:

Minimum p-value in

`minP.test`

functionGene Association Test with Extended Simes procedure in

`gates.test`

Truncated Tail Strength in

`tTS.test`

functionTruncated p-value Product in

`tProd.test`

function

1 | ```
gates.test(Y, G1, G2, alpha = 0.05, me.est = c("ChevNy", "Keff", "LiJi","Galwey"))
``` |

`Y` |
numeric or factor vector with exactly two different values. |

`G1` |
SnpMatrix object.
Must have a number of rows equal to the length of |

`G2` |
SnpMatrix object.
Must have a number of rows equal to the length of |

`alpha` |
numeric value in [0, 1]. Threshold for GATES method when estimating the number of effective tests Me with Keff method. |

`me.est` |
character string for GATES method. |

In a first step, all methods start by applying a logistic regression model to test all pairs of SNPs between the two genes `G1`

and `G2`

. If `G1`

has *m1* SNPs and `G2`

*m2* SNPs, a total of *m1 * m2* SNP-SNP tests are performed. In a second step, the *m1 * m2* SNP-SNP tests are combined according to their covariance matrix *Σ*. *Σ* is computed as described in the method developped in Emily (2016). The covariance *Σ* is used in each method as follows:

minP test - minP test considered the significant of the observed minimum p-value. Significance is computed by integrating the multivariate normal distribution with covariance

*Σ*as proposed in Conneelly and Boehnke (2008).GATES test - The p-value for GATES is the minimum p-value obtained after a multiple testing correction of the SNP-SNP interaction p-values. Correction for multiple testing is defined as

*me * p[i]/me[i]*where

*me*is the effective number of independant tests,*p[i]*is the i-th top p-values and*me[i]*is the effective number of independant test among the top i p-values. Many methods exist to estimate*me*and*me[i]*terms:Cheverud-Nyholt method (Cheverud, 2001 and Nyholt, 2004)

Keff method (Moskovina and Schmidt, 2008)

Li & Ji method (Li and Ji, 2005)

Galwey method (Galwey, 2009)

Details of each method can be found in the references.

tTS test - tTS test does not consider only the strongest signal but all signals that are inferior to a given threshold

*τ*. For these p-values, the weighted sum of*tTS=∑ (1-p[i]*(m1*m2+1)/i)*is computed and represents the test statistic. The p-value is calculated using an empirical distribution of

*tTS*obtained by simulating multivariate normal statistics with a covariance*Σ*as proposed by Jiang et al. (2011).TProd test - The procedure is similar to

*tTS*with*tProd*defined as*tProd=∏ p[i].*See Zaykin et al. (2002) for details.

A list with class `"GGItest"`

containing the following components:

`statistic` |
The value of the statistic: the p-value kept as the minimum after GATES correction) |

`p.value` |
Tue p-value for the test |

`estimate` |
The estimation of the GATES p-value. |

`alternative` |
a character string describing the alternative. |

`method` |
a character string indicating the method used. |

`data.name` |
a character string giving the names of the data. |

M. Emily AGGrEGATOr: A Gene-based GEne-Gene interActTiOn test for case-control association studies, Statistical Application in Genetics and Molecular Biology, 15(2): 151-171, 2016.

L. Ma, A.G. Clark and A. Keinan Gene-Based Testing Of Interactions in Association Studies of Quantitative Traits. PLoS Genetics 9(2):e1003321, 2013.

V. Moskvina and K.M. Schmidt On multiple-testing correction in genome-wide association studies. Genetic Epidemiology, 32(6): 567-573, 2008.

J. Li and L. Ji. Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix. Heredity 95: 221-227, 2005.

N.W. Galwey. A new measure of the effective number of tests, a practical tool for comparing families of non-independent significance tests. Genetic Epidemiology 33(7): 559-568, 2009.

J.M. Cheverud. A simple correction for multiple comparisons in interval mapping genome scans. Heredity. 87(1):52-58, 2001.

D.R. Nyholt. A Simple Correction for Multiple Testing for Single-Nucleotide Polymorphisms in Linkage Disequilibrium with Each Other. American journal of human genetics. 74(4): 765-769, 2004.

K.N. Conneely and M. Boehnke. So many correlated tests, so little time! rapid adjustment of p values for multiple correlated tests. The American Journal of Human Genetics, 81: 1158-1168, 2008

B. Jiang, X. Zhang, Y. Zuo and G. Kang. A powerful truncated tail strength method for testing multiple null hypotheses in one dataset. Journal of Theoretical Biology 277: 67-73, 2011.

D.V. Zaykin, L.A. Zhivotovsky, P.H. Westfall and B.S. Weir. Truncated product method for combining P-values. Genetic epidemiology 22: 170-185, 2002.

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