tProd.test {GeneGeneInteR} | R Documentation

## Gene-based Gene-Gene Interaction analysis by combining SNP-SNP interaction tests

### Description

`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` function

- Gene Association Test with Extended Simes procedure in `gates.test`

- Truncated Tail Strength in `tTS.test` function

- Truncated p-value Product in `tProd.test` function

### Usage

    tProd.test(Y, G1, G2, tau = 0.05, n.sim = 1000)

### Arguments

`Y` | numeric or factor vector with exactly two different values. `Y` is the response variable and should be of length equal to the number of rows of `G1` and `G2` arguments (number of individuals).
`G1` | SnpMatrix object. Must have a number of rows equal to the length of `Y`.
`G2` | SnpMatrix object. Must have a number of rows equal to the length of `Y`.
`tau` | numeric in [0, 1]. See details section for its use.
`n.sim` | positive integer. `n.sim` is the number of multivariate normal distribution simulations used to compute the significant level for tTS and tProd methods.

### Details

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.

### Value

A list with class `"GGItest"` containing the following components:

`statistic` | The value of the statistic tProd.
`p.value` | The p-value for the test
`estimate` | Estimation of tProd.
`parameter` | The threshold value tau.
`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.

### References

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.

### See Also

`GGI`

### Examples

    data(gene.pair)
    tProd.test(gene.pair$Y, gene.pair$G1, gene.pair$G2, tau = 0.5, n.sim = 500)

[Package GeneGeneInteR version 1.20.0 Index]