# Linear models Using limma

### Description

Differential expression analysis using the linear model features implemented in the limma package. A linear model is fitted to each miRNA gene so that the fold change between different experimental conditions and their standard errors can be estimated. Empirical Bayes methods are applied to obtain moderated statistics

### Usage

1 | ```
basicLimma(eset, design, CM,verbose = FALSE)
``` |

### Arguments

`eset` |
ExpressionSet containing the processed log-expression values |

`design` |
design matrix |

`CM` |
contrast matrix |

`verbose` |
logical, if |

### Details

In our data example (see the target file in Table 1 in vignette), we have used a paired design (by subject) to assess the differential expression between two treatments B and C vs a control treatment A. That is, we want to obtain the microRNAS that are differentially expressed between conditions A vs B and A vs C. The linear model that we are going to fit to every miRNA is defined by equation: y = Treatment + Subject + error term. This model is going to estimate the treatment effect and then, the comparison between the different treatments are done in terms of contrasts between the estimates of the treatment effects. To fit the model, we need first to define a design matrix. The design matrix is an incidence matrix that relates each array/sample/file to its given experimental conditions, in our case, relates each file to one of the three treatments and with its particular subject. If treatment is a factor variable, we can define de desing matrix using model.matrix(~ -1 + treatment + subject). Then the linear model can be fitted using fit=lmFit(eset,design). This will get the treatment estimates for each microRNA in the eset object:

treatmentA treatmentB treatmentC subject2 hsa-miR-152 7.5721 7.656 7.566 -0.1157 hsa-miR-15a* 0.9265 1.066 1.211 -0.2242 hsa-miR-337-5p 6.2448 7.298 7.084 -0.4489

We can define the contrasts of interest using a contrast matrix as in CM=cbind(MSC\_AvsMSC\_B=c(1,-1,0), MSC\_AvsMSC\_C=c(1,0,-1))

And then, we can estimate those contrats using fit2=contrasts.fit(fit,CM). Finally, we can obtain moderated statistics using fit2=eBayes(fit2).

The function 'basicLimma' implemented in AgiMicroRna produces the last fit2 object, that has in fit2\$coeff the M values, in fit\$t the moderated-t statistic of the contrasts, and in fit2\$p.value the corresponding p value of each particular contrasts. Be aware that these p values must be corrected by multiple testing.

MSC\_AvsMSC\_B MSC\_AvsMSC\_C hsa-miR-152 0.67567761 0.977326746 hsa-miR-15a* 0.68019442 0.413657270 hsa-miR-337-5p 0.03737814 0.075248741

See limmaUsersGuide() for a complete description of the limma package.

### Value

An MArrayLM object of the package limma

### Author(s)

Pedro Lopez-Romero

### References

Smyth, G. K. (2005). Limma: linear models for microarray data. In: 'Bioinformatics and Computational Biology Solutions using R and Bioconductor'. R. Gentleman, V. Carey, S. Dudoit, R. Irizarry, W. Huber (eds), Springer, New York, pages 397–420.

Smyth, G. K. (2004). Linear models and empirical Bayes methods for assessing diferential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology, Vol. 3, No. 1, Article 3. http://www.bepress.com/sagmb/vol3/iss1/art3

### See Also

An 'RGList' example containing proccesed data is in
`ddPROC`

and an overview of how the processed data is produced
is given in `filterMicroRna`

. The ExpressionSet object can be
generated using `esetMicroRna`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
## Not run:
data(targets.micro)
data(ddPROC)
esetPROC=esetMicroRna(ddPROC,targets.micro,makePLOT=FALSE,verbose=FALSE)
levels.treatment=levels(factor(targets.micro$Treatment))
treatment=factor(as.character(targets.micro$Treatment),
levels=levels.treatment)
levels.subject=levels(factor(targets.micro$Subject))
subject=factor(as.character(targets.micro$Subject),
levels=levels.subject)
design=model.matrix(~ -1 + treatment + subject )
CM=cbind(MSC_AvsMSC_B=c(1,-1,0,0),
MSC_AvsMSC_C=c(1,0,-1,0))
fit2=basicLimma(esetPROC,design,CM,verbose=TRUE)
names(fit2)
head(fit2$coeff)
head(fit2$p.value)
plot(fit2\$Amean,fit2$coeff[,1],xlab="A",ylab="M")
abline(h=0)
abline(h=c(-1,1),col="red")
plot(fit2$coeff[,1],fit2$p.value[,1], xlab="M",ylab="p value")
## End(Not run)
``` |