prince {swamp}

Linear models of prinicipal conponents dependent on sample annotations

Description

The function calculates the principal components of the data and finds associations between the prinicpal components and the sample annotations using linear regressions.

Usage

prince(g, o, top = 25, imputeknn = F, center = T, permute = F)

Arguments

g

the input data in form of a matrix with features as rows and samples as columns.

o

the corresponding sample annotations in the form of a data.frame. rownames (o) must be identical to colnames (g). o can contain factors with 2 or more levels and numeric variables; no character variables are allowed. NAs are allowed (these samples are ommited in lm()).

top

the number of top principal components to be analyzed, default is set to 25.

imputeknn

default=FALSE. missing values in the data matrix can be imputed by imputeknn=TRUE. The function knn.impute from the package impute is used with default settings.

center

default=TRUE. the features are mean-centered before singular value decompositon. this is a pre-requisite for principal component analysis, change only if you are really convinced that centering is not necessary.

permute

default=FALSE. if set to TRUE a permuted data matrix is generated with the values for each feature shuffled. The linear models are also calculated for this permuted dataset.

Details

To calculate the principal components of a data matrix, the function prcomp is used. The function prcomp uses singular value decomposition instead of eigen decomposition of the covariance matrix, the actual principal component analysis. As prcomp cannot handle missing values they have to be imputed beforehands, imputeknn=TRUE can be used for k-nearest neighbor imputation from package impute, k is 10. A linear model is perfomed to find associations of the principal components with a dataframe of sample annotations. The f-statistics of lm(principal component i ~ sample annotation j) is used to derive the p-value for these associations. The results can be plotted using the prince.plot() function. If permute=TRUE the analysis will be repeated on permuted data, in which for each feature the values have been randomly shuffled.

Value

a list as a prince object with components

pr

the output list of the prcomp function with the principal components contained in pr$x.

linp

matrix containing the F-test p-values from lm(principal component~sample annotation).

rsquared

matrix containing the R-squared values from lm(principal component~sample annotation).

prop

numeric vector containing the percentage of the overall variation for each principal component.

o

the input data.frame containing the patient annotations.

pr.perm

if permute=T it contains the outcome list from prcomp for the permuted data.

linpperm

if permute=T it contains the p-values for the permuted data.

rsquaredperm

if permute=T it contains the R-squared values for the permuted data.

propperm

if permute=T it contains the percentages of variation for the permuted data.

imputed

if imputeknn=T it contains the data matrix with the imputed values.

Note

requires the package impute

Author(s)

Martin Lauss

Examples

## data as a matrix
set.seed(100)
g<-matrix(nrow=1000,ncol=50,rnorm(1000*50),dimnames=list(paste("Feature",1:1000),
          paste("Sample",1:50)))
g[1:100,26:50]<-g[1:100,26:50]+1 # the first 100 features show
# higher values in the samples 26:50
## patient annotations as a data.frame, annotations should be numbers and factor
# but not characters.
## rownames have to be the same as colnames of the data matrix 
set.seed(200)
o<-data.frame(Factor1=factor(c(rep("A",25),rep("B",25))),
              Factor2=factor(rep(c("A","B"),25)),
              Numeric1=rnorm(50),row.names=colnames(g))
              
## calculate principal components and use linear models to calculate 
## their dependence on sample annotations
res1<-prince(g,o,top=10,permute=TRUE)
str(res1)
res1$linp # to see the p values