We consider the acute lymphocytic leukemia dataset, included with the **simPATHy** package, first published in (Chiaretti et al. 2005). This dataset contains expression of 3405 genes in two conditions with sample sizes \(n_1=37\) and \(n_2=41\).

```
library(simPATHy)
library(graph)
```

```
data("chimera")
dim(chimera)
```

`## [1] 3405 78`

`table(colnames(chimera))`

```
##
## 1 2
## 37 41
```

The column names indicate the condition (1 or 2) of each sample.

In this example, we restrict our attention to a subset of genes in this dataset, corresponding to genes participating in the KEGGâ€™s ``Acute Myeloid Leukemiaâ€™â€™ pathway.

The graph that we consider in what follows is a directed acyclic graph derived manually from this pathway.

```
graph<-gRbase::dag(~867:25+867:613+5295:867+5294:867+
207:5295+207:5294+4193:207+3551:207+
4792:3551+7157:4193+3265:6654+
3845:6654+6654:2885+2885:25+2885:613)
```

We take the first condition of this dataset as a reference condition for our example and begin by estimating the covariance matrix.

```
genes<-graph::nodes(graph)
data<-t(chimera[genes,colnames(chimera)==1])
S<-cov(data)
```

The matrix `S`

does not reflect conditional independence constraints imposed by the `graph`

. To impose these structural constraints **simPATHy** provides a function `fitSgraph`

for maximum likelihood estimation of covariance matrices in graphical models, for both Gaussian bayesian networks and Gaussian graphical models.

```
S<-fitSgraph(graph,S)
round(S[1:5,1:5],3)
```

```
## 867 25 613 5295 5294
## 867 0.115 -0.006 0.071 0.008 0.045
## 25 -0.006 0.240 0.000 0.000 -0.003
## 613 0.071 0.000 0.121 0.005 0.028
## 5295 0.008 0.000 0.005 0.317 0.003
## 5294 0.045 -0.003 0.028 0.003 0.246
```

The package also provides two plotting functions for graphical models. The first `plotGraphNELD3`

, focuses on the graphical structure, while the second one, `plotCorGraph`

, focuses on the correlation matrix. In both cases, the colors represent the strength of relation between nodes, where the user by setting the parameter `type`

chooses whether to show the pairwise correlation coefficient (`type= "cor"`

) or the partial correlation coefficient (`type= "pcor"`

).

`plotGraphNELD3(graph,type = "cor",S1 = S)`