multilevel: Multilevel analysis for repeated measurements (cross-over design)

Description

The analysis of repeated measurements is performed by combining a multilevel approach with multivariate methods: sPLS-DA (Discriminant Analysis) or sPLS (Integrative analysis). Both approaches embbed variable selection.

Usage

multilevel(X, Y = NULL, 
           cond = NULL,                  
           sample = NULL,
           ncomp = 1,
           keepX = rep(ncol(X), ncomp),
           keepY = NULL,
           method = NULL,
           tab.prob.gene=NULL, 
           max.iter = 500, 
           tol = 1e-06,...)

Arguments

numeric matrix of predictors. NAs are allowed.

if(method = 'spls') numeric vector or matrix of continuous responses (for multi-response models) NAs are allowed.

cond

a factor or a class vector for one-factor discrete outcome, a numeric matrix of 2 columns for two-factor discrete outcome. See Details

sample

a vector indicating the repeated measured on each individual.

ncomp

the number of components to include in the model (see Details).

keepX

numeric vector of length ncomp, the number of variables to keep in $X$-loadings. By default all variables are kept in the model.

keepY

if(method = 'spls'), numeric vector of length ncomp, the number of variables to keep in $Y$-loadings. By default all variables are kept in the model.

method

character string. Which multivariate method and type of analysis to choose, matching one of 'splsda' (Discriminant Analysis) or 'spls' (unsupervised integrative analysis). See Details.

tab.prob.gene

matrix of dimension ncol(X)x2 indicating the probes names (column 1) and corresponding gene names (column 2).

max.iter

integer, the maximum number of iterations.

tol

a positive real, the tolerance used in the iterative algorithm.

...

other internal arguments.

Value

For sPLS-DA analysis, multilevel returns either an object of class "splsda1fact" for one-factor analysis and "splsda2fact", a list that contains the following sPLS-DA outputs:
Xthe centered and standardized original predictor matrix.
Ythe centered and standardized indicator response vector or matrix.
ind.matthe indicator matrix.
ncompthe number of components included in the model.
keepXnumber of $X$ variables kept in the model on each component.
mat.cmatrix of coefficients to be used internally by predict.
variateslist containing the variates.
loadingslist containing the estimated loadings for the X and Y variates.
nameslist containing the names to be used for individuals and variables.
nzvlist containing the zero- or near-zero predictors information.
For sPLS analysis, multilevel returns either an object of class "splslevel" for one-factor analysis, a list that contains the following sPLS-DA components:
Xthe centered and standardized original predictor matrix.
Ythe centered and standardized original response vector or matrix.
ncompthe number of components included in the model.
modethe algorithm used to fit the model.
keepXnumber of $X$ variables kept in the model on each component.
keepYnumber of $Y$ variables kept in the model on each component.
mat.cmatrix of coefficients to be used internally by predict.
variateslist containing the variates.
loadingslist containing the estimated loadings for the $X$ and $Y$ variates.
nameslist containing the names to be used for individuals and variables.
nzvlist containing the zero- or near-zero predictors information.

encoding

latin1

Details

multilevel function first decomposes the variance in the data sets X (and Y) and applies either sPLS-DA (method = 'splsda') or sPLS ((method = 'spls')) on the within-subject deviation.

One or two-factor analyses are available for (method = 'splsda').

A sPLS-DA or sPLS model is performed with $1, \ldots ,$ncomp components to the factor or class vector cond. The appropriate indicator matrix is created for sPLS-DA.

Multilevel sPLS-DA enables the selection of discriminant variables between the conditions in cond.

Multilevel sPLS enables the integration of data measured on two different platforms on the same individuals. This approach differs from multilevel sPLS-DA as the aim is to select subsets variables from both data sets that are highly correlated (positively or negatively) across the samples. The approach is unsupervised: no prior knowledge about the samples groups is included.

References

On multilevel analysis: Liquet, B., Lê Cao, K.-A., Hocini, H. and Thiebaut, R. (2012) A novel approach for biomarker selection and the integration of repeated measures experiments from two platforms. BMC Bioinformatics 13:325.

Westerhuis, J. A., van Velzen, E. J., Hoefsloot, H. C., and Smilde, A. K. (2010). Multivariate paired data analysis: multilevel PLSDA versus OPLSDA. Metabolomics, 6(1), 119-128.

On sPLS-DA: Lê Cao, K.-A., Boitard, S. and Besse, P. (2011). Sparse PLS Discriminant Analysis: biologically relevant feature selection and graphical displays for multiclass problems. BMC Bioinformatics 12:253.

On sPLS: Lê Cao, K.-A., Martin, P.G.P., Robert-Granie, C. and Besse, P. (2009). Sparse canonical methods for biological data integration: application to a cross-platform study. BMC Bioinformatics 10:34.

Lê Cao, K.-A., Rossouw, D., Robert-Granie, C. and Besse, P. (2008). A sparse PLS for variable selection when integrating Omics data. Statistical Applications in Genetics and Molecular Biology 7, article 35.

Examples

Run this code

## First example: one-factor analysis with sPLS-DA
data(vac18) # vac18 study
X <- vac18$genes
Y <- vac18$stimulation

res <- multilevel(X, cond = Y, ncomp = 3,
tab.prob.gene = vac18$tab.prob.gene,
sample = vac18$sample, method = "splsda",
keepX = c(30, 137, 123))

# color for plot3dIndiv
col_stim <- c("darkblue", "purple", "green4","red3")
cols <- Y
levels(cols) <- col_stim
cols <- as.character(cols)

plot3dIndiv(res, ind.names = Y, col = cols,
cex = 0.3, axes.box = "both")


## Second example: two-factor analysis with sPLS-DA
data(data.simu) # simulated data

time = factor(rep(c(rep('t1', 6), rep('t2', 6)), 4))
stimu.time = data.frame(cbind(as.character(data.simu$stimu), 
                        as.character(time)))
repeat.simu2 = rep(c(1:6), 8)

res.2level <- multilevel(data.simu$X, cond = stimu.time,
                         sample = repeat.simu2, ncomp = 2,
                         keepX = c(200, 200), tab.prob.gene = NULL, 
                         method = 'splsda')

# color for plotIndiv
col.stimu = as.numeric(data.simu$stimu)
# pch for plots
pch.time = rep(20, 48)
pch.time[time == 't2'] = 4

plotIndiv(res.2level, col = col.stimu, pch = pch.time, ind.names = FALSE)
legend('bottomright', col = unique(col.stimu), 
       legend = levels(data.simu$stimu),  pch = 20, cex = 0.8)
legend('topright', col = 'black', legend = levels(time),  
       pch = unique(pch.time), cex = 0.8)


## Third example: one-factor integrative analysis with sPLS
data(liver.toxicity)
repeat.indiv = c(1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 4, 3, 4, 3, 4, 4, 5, 6, 5, 5,
                 6, 5, 6, 7, 7, 8, 6, 7, 8, 7, 8, 8, 9, 10, 9, 10, 11, 9, 9, 
                 10, 11, 12, 12, 10, 11, 12, 11, 12, 13, 14, 13, 14, 13, 14, 
                 13, 14, 15, 16, 15, 16, 15, 16, 15, 16)

result.rat <- multilevel(X = liver.toxicity$gene, Y=liver.toxicity$clinic, 
                         cond = liver.toxicity$treatment$Dose.Group, 
                         sample = repeat.indiv, ncomp = 2, keepX = c(50, 50), 
                         keepY = c(5, 5), method = 'spls') 

# variable plots
plotVar(result.rat, comp = 1:2, X.label = TRUE, Y.label = TRUE, 
        cex = c(0.5, 0.9)) 

CIM <- cim(result.rat, comp = 1:2, xlab = "genes", ylab = "clinic var", 
           margins = c(5, 6), zoom = FALSE)


network(result.rat, comp = 1:2, threshold = 0.8, 
        Y.names = NULL, keep.var = TRUE,
        color.node = c( "lightcyan","mistyrose"),
        shape.node = c("circle", "rectangle"),
        color.edge = c("red", "green"),
        lty.edge = c("solid", "solid"), lwd.edge = c(1, 1), 
        show.edge.labels = FALSE, interactive = FALSE)

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