# pathway.var.test

##### 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.

##### See Also

##### Examples

```
data(examples)
pathway.var.test(y1, y2, dag_bcell, 0.05)
```

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