,
John C. Marioni [aut] ,
Simon Tavar\'{e} [aut] | Title: | Statistical Inference about the Mean Matrix and the Covariance Matrices in High-Dimensional Transposable Data (HDTD) |
|---|---|
| Description: | Characterization of intra-individual variability using physiologically relevant measurements provides important insights into fundamental biological questions ranging from cell type identity to tumor development. For each individual, the data measurements can be written as a matrix with the different subsamples of the individual recorded in the columns and the different phenotypic units recorded in the rows. Datasets of this type are called high-dimensional transposable data. The HDTD package provides functions for conducting statistical inference for the mean relationship between the row and column variables and for the covariance structure within and between the row and column variables. |
| Authors: | Anestis Touloumis [cre, aut] ,
John C. Marioni [aut] ,
Simon Tavar\'{e} [aut] |
| Maintainer: | Anestis Touloumis <[email protected]> |
| License: | GPL-3 |
| Version: | 1.39.0 |
| Built: | 2024-07-03 04:01:30 UTC |
| Source: | https://github.com/bioc/HDTD |
The package HDTD offers functions to estimate and test the matrix parameters of transposable data in high-dimensional settings.
The term transposable data refers to datasets that are structured in a matrix form such that both the rows and columns correspond to variables of interest. For example, consider microarray studies in genetics where multiple RNA samples across different tissues are available per subject. In this case, a data matrix can be created with row variables the genes, column variables the tissues and measurements the corresponding expression levels.
The function meanmat.hat estimates the mean matrix of the
transposable data.
The mean relationship of the row and column variables can be tested using
the function meanmat.ts. The implemented test is nonparametric
and not seriously restricted by the dependence structure among and/or
between the row and column variables.
See Touloumis et al. (2015) for more details.
The function covmat.hat provides Stein-type shrinkage
estimators for the row covariance matrix and/or for the column covariance
matrix under a matrix-variate normal model.
See Touloumis et al. (2016) for more details.
The sphericity and identity hypothesis for the row or column covariance
matrix can be tested using the function covmat.ts. Both tests
are nonparametric, i.e., they do not rely on a normality assumption.
See Touloumis et al. (2017) for more details.
There are three utility functions that allow the user to change to
interchange the role of row and column variables
(transposedata), to center the transposable data
(centerdata) or to rearrange the order of the row and/or
column variables (orderdata).
Anestis Touloumis, John Marioni, Simon Tavare.
Maintainer: Anestis.Touloumis <[email protected]>
Touloumis, A., Tavare, S. and Marioni, J. C. (2015) Testing the Mean Matrix in High-Dimensional Transposable Data. Biometrics 71, 157–166.
Touloumis, A., Marioni, J. C. and Tavare, S. (2016) HDTD: Analyzing multi-tissue gene expression data. Bioinformatics 32, 2193–2195.
Touloumis, A., Marioni, J. C. and Tavare, S. (2021) Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure. Statistica Sinica 31, 1309–1329.
data(VEGFmouse) ## The sample mean matrix. sample_mean <- meanmat.hat(datamat = VEGFmouse, N = 40) sample_mean ## Testing conservation of the overall gene expression across tissues. tissues_mean_test <- meanmat.ts(datamat = VEGFmouse, N = 40, group.sizes = 9) tissues_mean_test # Estimating the gene and column covariance matrices. est_cov_mat <- covmat.hat(datamat = VEGFmouse, N = 40) est_cov_mat ## Hypothesis tests for the covariance matrix of the genes (rows). genes_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40) genes_cov_test ## Hypothesis tests for the covariance matrix of the tissues (columns). tissues_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40, voi = 'columns') tissues_cov_testdata(VEGFmouse) ## The sample mean matrix. sample_mean <- meanmat.hat(datamat = VEGFmouse, N = 40) sample_mean ## Testing conservation of the overall gene expression across tissues. tissues_mean_test <- meanmat.ts(datamat = VEGFmouse, N = 40, group.sizes = 9) tissues_mean_test # Estimating the gene and column covariance matrices. est_cov_mat <- covmat.hat(datamat = VEGFmouse, N = 40) est_cov_mat ## Hypothesis tests for the covariance matrix of the genes (rows). genes_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40) genes_cov_test ## Hypothesis tests for the covariance matrix of the tissues (columns). tissues_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40, voi = 'columns') tissues_cov_test
This function centers the transposable data around their sample mean matrix.
centerdata(datamat, N)centerdata(datamat, N)
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, e.g., the number of subjects. |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
Returns a matrix of the same size as datamat.
Anestis Touloumis
covmat.hat and covmat.ts.
data(VEGFmouse) ## Centering the VEGF dataset around the sample mean matrix. VEGFcen <- centerdata(datamat = VEGFmouse, N = 40)data(VEGFmouse) ## Centering the VEGF dataset around the sample mean matrix. VEGFcen <- centerdata(datamat = VEGFmouse, N = 40)
This function provides the row and/or column covariance matrix estimators.
covmat.hat(datamat, N, shrink = "both", centered = FALSE, voi = "both")covmat.hat(datamat, N, shrink = "both", centered = FALSE, voi = "both")
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, i.e., the number of subjects. |
shrink |
character indicating if shrinkage estimation should be
performed. Options include ' |
centered |
logical indicating if the transposable data are centered.
Options include |
voi |
character indicating if the row, column or both covariance
matrices should be printed. Options include ' |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
For identifiability reasons, the trace of the row covariance matrix is set
equal to its dimension. If you want to place the equivalent restriction on
the column covariance matrix, interchange the role of row and column
variables by utilizing the function transposedata.
Returns a list with components:
rows.covmat |
the estimated row covariance matrix. |
rows.intensity |
the estimated row intensity. |
cols.covmat |
the estimated column covariance matrix. |
cols.intensity |
the estimated column intensity. |
N |
the sample size. |
n.rows |
the number of row variables. |
n.cols |
the number of column variables. |
shrink |
character indicating if shrinkage estimation was performed. |
centered |
logical indicating if the transposable data were centered. |
Anestis Touloumis
Touloumis, A., Marioni, J. C. and Tavare, S. (2016) HDTD: Analyzing multi-tissue gene expression data, Bioinformatics 32, 2193–2195.
data(VEGFmouse) # Estimating the gene and tissue covariance matrices. est_cov_mat <- covmat.hat(datamat = VEGFmouse, N = 40) est_cov_matdata(VEGFmouse) # Estimating the gene and tissue covariance matrices. est_cov_mat <- covmat.hat(datamat = VEGFmouse, N = 40) est_cov_mat
Testing the sphericity, identity and diagonality hypotheses for the row or column covariance matrix.
covmat.ts(datamat = datamat, N = N, voi = "rows", centered = FALSE)covmat.ts(datamat = datamat, N = N, voi = "rows", centered = FALSE)
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, i.e., the number of subjects. |
voi |
character indicating if the test should be applied on the row or
column covariance matrix. Options include ' |
centered |
logical indicating if the transposable data are centered.
Options include |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
The tests are nonparametric and thus robust to some departures from the matrix-variate normal model.
It returns a list with components:
diagonality.ts |
a list containing the test statistic and p-value of the diagonality hypothesis test. |
sphericity.ts |
a list containing the test statistic and p-value of the sphericity hypothesis test. |
identity.ts |
a list containing the test statistic and p-value of the identity hypothesis test. |
N |
the sample size. |
n.rows |
the number of row variables. |
n.cols |
the number of column variables. |
variables |
character indicating if the tests were applied to the row or column covariance matrix. |
centered |
logical indicating if the transposable data were centered. |
Anestis Touloumis
Touloumis, A., Marioni, J.C. and Tavare, S. (2021) Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure. Statistica Sinica 31, 1309–1329.
data(VEGFmouse) ## Hypothesis tests for the covariance matrix of the genes (rows). genes_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40) genes_cov_test ## Hypothesis tests for the covariance matrix of the tissues (columns). tissues_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40, voi = 'columns') tissues_cov_testdata(VEGFmouse) ## Hypothesis tests for the covariance matrix of the genes (rows). genes_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40) genes_cov_test ## Hypothesis tests for the covariance matrix of the tissues (columns). tissues_cov_test <- covmat.ts(datamat = VEGFmouse, N = 40, voi = 'columns') tissues_cov_test
This function estimates the mean matrix.
meanmat.hat(datamat, N, group.sizes = NULL, group.vars = NULL)meanmat.hat(datamat, N, group.sizes = NULL, group.vars = NULL)
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, i.e., the number of subjects. |
group.sizes |
numeric vector indicating the size of the row or column
groups that share the same mean vector. It should be used only when
|
group.vars |
character indicating that the mean matrix can be
simplified over the row or column variables. Options include ' |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
Returns a list with components:
estmeanmat |
the estimated mean matrix. |
N |
the sample size. |
n.rows |
the number of row variables. |
n.cols |
the number of column variables. |
Anestis Touloumis
Touloumis, A., Marioni, J. C. and Tavare, S. (2016) HDTD: Analyzing multi-tissue gene expression data. Bioinformatics 32, 2193–2195.
data(VEGFmouse) ## The sample mean matrix of the VEGF mouse data. sample_mean <- meanmat.hat(datamat = VEGFmouse, N = 40) sample_mean sample_mean$estmeanmatdata(VEGFmouse) ## The sample mean matrix of the VEGF mouse data. sample_mean <- meanmat.hat(datamat = VEGFmouse, N = 40) sample_mean sample_mean$estmeanmat
This function performs hypothesis testing for the mean matrix.
meanmat.ts(datamat, N, group.sizes, voi = "columns")meanmat.ts(datamat, N, group.sizes, voi = "columns")
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, i.e., the number of subjects. |
group.sizes |
numeric vector indicating the group sizes under the null hypothesis. |
voi |
character indicating if the test will be applied to the row or
column variables. Options include ' |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
Returns a list with components:
statistic |
the value of the test statistic. |
p.value |
the corresponding p-value. |
voi |
the set of variables that the test was applied to. |
n.groups |
the number of groups under the null hypothesis. |
group.sizes |
the size of each group under the null hypothesis. |
N |
the sample size. |
n.rows |
the number of row variables. |
n.cols |
the number of column variables. |
Anestis Touloumis
Touloumis, A., Tavare, S. and Marioni, J. C. (2015) Testing the Mean Matrix in High-Dimensional Transposable Data. Biometrics 71, 157–166.
data(VEGFmouse) ## Testing conservation of the overall gene expression across tissues. tissues_mean_test <- meanmat.ts(datamat = VEGFmouse, N = 40, group.sizes = 9) tissues_mean_test ## Testing if the adrenal and the cerebrum tissues have the same mean vector. test2 <- meanmat.ts(VEGFmouse, N = 40, group.sizes = c(2, rep(1,7))) test2data(VEGFmouse) ## Testing conservation of the overall gene expression across tissues. tissues_mean_test <- meanmat.ts(datamat = VEGFmouse, N = 40, group.sizes = 9) tissues_mean_test ## Testing if the adrenal and the cerebrum tissues have the same mean vector. test2 <- meanmat.ts(VEGFmouse, N = 40, group.sizes = c(2, rep(1,7))) test2
This utility function rearranges the row and/or the column variables in a desired order.
orderdata(datamat, N, order.rows = NULL, order.cols = NULL)orderdata(datamat, N, order.rows = NULL, order.cols = NULL)
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, i.e., the number of subjects. |
order.rows |
numeric vector displaying the desired order of the row variables. |
order.cols |
numeric vector displaying the desired order of the column variables. |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
Returns a matrix of the same size as datamat.
Anestis Touloumis
meanmat.ts and meanmat.hat.
data(VEGFmouse) set.seed(1) tissuesold <- colnames(VEGFmouse[ ,1:9]) ## Suppose that you want to order the tissues in the folowing order. tissuesnew <- colnames(VEGFmouse[ ,1:9])[sample(9)] tissuesnew ## To do this, create a numeric vector with the desired order. ordtis <- pmatch(tissuesnew, tissuesold) VEGFmousenew <- orderdata(datamat = VEGFmouse, N = 40, order.cols = ordtis) colnames(VEGFmousenew)[1:9]data(VEGFmouse) set.seed(1) tissuesold <- colnames(VEGFmouse[ ,1:9]) ## Suppose that you want to order the tissues in the folowing order. tissuesnew <- colnames(VEGFmouse[ ,1:9])[sample(9)] tissuesnew ## To do this, create a numeric vector with the desired order. ordtis <- pmatch(tissuesnew, tissuesold) VEGFmousenew <- orderdata(datamat = VEGFmouse, N = 40, order.cols = ordtis) colnames(VEGFmousenew)[1:9]
This function interchanges the row and column variables in transposable data so that the original row variables will be treated as column variables and the original column variables as row variables.
transposedata(datamat, N)transposedata(datamat, N)
datamat |
numeric matrix containing the transposable data. |
N |
positive integer number indicating the sample size, i.e., the number of subjects. |
It is assumed that there are nrow(datamat) row variables and
ncol(datamat)/N column variables in datamat. Further,
datamat should be written in such a way that every
ncol(datamat)/N consecutive columns belong to the same subject
and the order of the column variables in each block is preserved across
subjects.
Returns a matrix with ncol(datamat) rows and
nrow(datamat)/N columns.
Anestis Touloumis
centerdata and orderdata.
data(VEGFmouse) ## Transposing the VEGF dataset. VEGFtr <- transposedata(datamat = VEGFmouse, N = 40)data(VEGFmouse) ## Transposing the VEGF dataset. VEGFtr <- transposedata(datamat = VEGFmouse, N = 40)
Log2 normalized mouse gene expression data in the vascular endothelial growth factor signalling pathway across multiple tissues.
A data frame with 46 rows and 360 columns. The rows corresponds to 46 genes in the VEGF signalling pathway. The column names indicate the mouse and the tissue on which gene expression levels were measured. Since there are 40 mice and 9 tissues, we have a total of 360 columns. Every 9 consecutive columns belong to the same mouse and the tissues are ordered in the same way in each mouse.
Zahn et al. (2007). AGEMAP: A gene expression database for aging in mice. PLoS Genetics 3, e201.
data(VEGFmouse) ## Check the order of the tissues from the first mouse. colnames(VEGFmouse[,1:9])data(VEGFmouse) ## Check the order of the tissues from the first mouse. colnames(VEGFmouse[,1:9])