# pathway.var.test

0th

Percentile

##### Testing the concentration matrices of a pathway.

Test the equality of concentration matrices in two experimental conditions for a pathway

##### Usage
pathway.var.test(y1,y2,dag,alpha,variance=FALSE,s1=NULL,s2=NULL)
##### Arguments
y1
a matrix with n1 individuals (rows) in the first experimental condition and p genes (columns).
y2
a matrix with n2 individuals (rows) in the second experimental condition and p genes (columns). The genes in the two experimental conditions must be the same.
dag
graphNEL object, directed acyclic graph (DAG) corresponding to the pathway of interest. See package gRbase for more details.
alpha
significance level of the test.
variance
logical flag. If TRUE the estimates of the covariance matrices are included in the result.
s1
y1 covariance matrix estimation.
s2
y2 covariance matrix estimation.
##### Details

The graph of a pathway is first converted into a DAG and then into a moral graph. The data is modelled with two Gaussian graphical models with zero mean and graph provided by the moral graph. The function tests the equality of the two concentration matrices (inverse of the covariance matrices).

The expression data may contain some genes differing from those in the pathway: in such case the function automatically takes the intersection between the two gene sets.

A necessary condition for the existence of the covariance estimates is that the number of statistical units (samples) is greater than the number of variables. If this is not the case, penalized techniques for estimating $s1^(-1)$ and $s2^(-1)$ have to be employed, that are currently not provided by the package. In theses cases, one can perform penalized estimation of $s1^(-1)$ and $s2^(-1)$ outside topologyGSA, and then provide such estimates as input arguments to the function pathway.var.test to compute the value of the test for homogeneity. In this case, computation of the p-value deserves attention, as standard results on the asymptotic distribution of the test statistic may no longer be valid. Therefore, computation of the p-value has to be dealt with by the user.

This function requires gRBase and qpgraph packages.

##### Value

lambda.value
the observed value of the test statistic.
qchisq.value
the 1 - alpha quantile value of the null distribution of the test statistic on the variance.
p.value
the observed value of the significance level of the test.
cli.moral
a list containing the cliques of the moral graph.
var.equal
logical flag. If TRUE variances are heteroschedastic.
graph
a graphNEL object representing the moral graph.
df
the degrees of freedom of the null distribution.
s1
if variance=TRUE, the estimate of y1 covariance.
s2
if variance=TRUE, the estimate of y2 covariance.

##### References

Massa, M.S., Chiogna, M., Romualdi, C. (2010). Gene set analysis exploiting the topology of a pathway. BMC Systems Biology, 4:121 http://www.biomedcentral.com/1752-0509/4/121

Lauritzen, S.L. (1996). Graphical models. Clarendon Press, Oxford.

pathway.mean.test, clique.var.test, clique.mean.test.

##### Aliases
• pathway.var.test
##### Examples
data(examples)

pathway.var.test(y1, y2, dag_bcell, 0.05)

Documentation reproduced from package topologyGSA, version 1.4.5, License: GPL-3

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