# Testing for differential variability

### Description

Fit linear model on mean absolute or squared deviations for each CpG given a series of methylation arrays

### Usage

1 |

### Arguments

`data` |
object of class |

`design` |
the design matrix of the experiment, with rows corresponding to arrays/samples and columns to coefficients to be estimated. Defaults to the unit vector. |

`coef` |
The columns of the design matrix containing the comparisons to test for differential variability. |

`type` |
character string, |

`trend` |
logical, if true fits a mean variance trend on the absolute or squared deviations |

`robust` |
logical, if true performs robust empirical Bayes shrinkage of the variances for the moderated t statistics |

`weights` |
non-negative observation weights. Can be a numeric matrix of individual weights, of same size as the object matrix, or a numeric vector of array weights, or a numeric vector of gene/feature weights. |

### Details

This function depends on the `limma`

package and is used to rank features such as CpG sites or genes in order of evidence of differential variability between different comparisons corresponding to the columns of the design matrix. A measure of variability is calculated for each CpG in each sample by subtracting out the group mean and taking the absolute or squared deviation. A linear model is then fitted to the absolute or squared deviations. The residuals of the linear model fit are subjected to empirical Bayes shrinkage and moderated t statistics (Smyth, 2004) calculated. False discovery rates are calculated using the method of Benjamini and Hochberg (1995).

If `coef`

is not specified, then group means are estimated based on all the columns of the design matrix and subtracted out before testing for differential variability. If the design matrix contains nuisance parameters, then subsetting the design matrix columns by `coef`

should remove these columns from the design matrix. If the design matrix includes an intercept term, this should be included in `coef`

. The nuisance parameters are included in the linear model fit to the absolute or squared deviations, but should not be considered when subtracting group means to obtain the deviations. Note that design matrices without an intercept term are permitted, and specific contrasts tested using the function `contrasts.varFit`

.

For methylation data, the analysis is performed on the M-values, defined as the log base 2 ratio of the methylated signal to the unmethylated signal. If a `MethylSet`

object is supplied, M-values are extracted with an offset of 100 added to the numerator and denominator.

For testing differential variability on RNA-Seq data, a `DGEList`

object can be supplied directly to the function. A `voom`

transformation is applied before testing for differential variability. The weights calculated in `voom`

are used in the linear model fit.

Since the output is of class `MArrayLM`

, any functions that can be applied to fit objects from `lmFit`

and `eBayes`

can be applied, for example, `topTable`

and `decideTests`

.

### Value

produces an object of class `MArrayLM`

(see `MArrayLM-class`

) containing everything found in a fitted model object produced by `lmFit`

and `eBayes`

as well as a vector containing the sample CpG-wise variances and a matrix of LogVarRatios corresponding to the differential variability analysis.

### Author(s)

Belinda Phipson

### References

Phipson, B., and Oshlack, A. (2014). A method for detecting differential variability in methylation data shows CpG islands are highly variably methylated in cancers. *Genome Biology*, **15**:465.

Smyth, G.K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. *Statistical Applications in Genetics and Molecular Biology*, Volume **3**, Article 3.

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, 2005.

Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. *Journal of the Royal Statistical Society Series*, B, **57**, 289-300.

### See Also

`contrasts.varFit`

, `topVar`

, `getLeveneResiduals`

, `lmFit`

, `eBayes`

, `topTable`

, `decideTests`

, `voom`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# Randomly generate data for a 2 group problem with 100 CpG sites and 5 arrays in each group.
y<-matrix(rnorm(1000),ncol=10)
group<-factor(rep(c(1,2),each=5))
design<-model.matrix(~group)
# Fit linear model for differential variability
vfit<-varFit(y,design,coef=c(1,2))
# Look at top table of results
topVar(vfit,coef=2)
``` |

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