perf: Compute evaluation criteria for PLS, sPLS, PLS-DA, sPLS-DA, MINT and DIABLO

Description

Function to evaluate the performance of the fitted PLS, sparse PLS, PLS-DA, sparse PLS-DA, MINT (mint.splsda) and DIABLO (block.splsda) models using various criteria.

Usage

# S3 method for pls
perf(object,validation = c("Mfold", "loo"),
           folds = 10, progressBar = TRUE, …)	
# S3 method for spls
perf(object,validation = c("Mfold", "loo"),
          folds = 10, progressBar = TRUE, …)
# S3 method for plsda
perf(object,
          dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
          validation = c("Mfold", "loo"),
          folds = 10, nrepeat =1, auc = FALSE, progressBar = TRUE, cpus, …)
# S3 method for splsda
perf(object, 
dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
validation = c("Mfold", "loo"),
folds = 10, nrepeat =1, auc = FALSE, progressBar = TRUE, cpus, …)
# S3 method for mint.splsda
perf(object,
            dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
            auc = FALSE, progressBar = TRUE, …)
# S3 method for sgccda
perf(object,
            dist = c("all", "max.dist", "centroids.dist", "mahalanobis.dist"),
            validation = c("Mfold", "loo"),
            folds = 10, nrepeat =1, cpus, …)

Arguments

object

object of class inheriting from "pls", "plsda", "spls", "splsda" or "mint.splsda". The function will retrieve some key parameters stored in that object.

dist

only applies to an object inheriting from "plsda", "splsda" or "mint.splsda" to evaluate the classification performance of the model. Should be a subset of "max.dist", "centroids.dist", "mahalanobis.dist". Default is "all". See predict.

validation

character. What kind of (internal) validation to use, matching one of "Mfold" or "loo" (see below). Default is "Mfold".

folds

the folds in the Mfold cross-validation. See Details.

nrepeat

Number of times the Cross-Validation process is repeated. This is an important argument to ensure the estimation of the performance to be as accurate as possible.

auc

if TRUE calculate the Area Under the Curve (AUC) performance of the model.

progressBar

by default set to TRUE to output the progress bar of the computation.

cpus

Number of cpus to use when running the code in parallel.

...

not used

Value

For PLS and sPLS models, perf produces a list with the following components:

MSEP

Mean Square Error Prediction for each $Y$ variable, only applies to object inherited from "pls", and "spls".

a matrix of $R^2$ values of the $Y$-variables for models with $1, \ldots ,$ncomp components, only applies to object inherited from "pls", and "spls".

if $Y$ containts one variable, a vector of $Q^2$ values else a list with a matrix of $Q^2$ values for each $Y$-variable. Note that in the specific case of an sPLS model, it is better to have a look at the Q2.total criterion, only applies to object inherited from "pls", and "spls"

Q2.total

a vector of $Q^2$-total values for models with $1, \ldots ,$ncomp components, only applies to object inherited from "pls", and "spls"

features

a list of features selected across the folds ($stable.X and $stable.Y) for the keepX and keepY parameters from the input object.

error.rate

For PLS-DA and sPLS-DA models, perf produces a matrix of classification error rate estimation. The dimensions correspond to the components in the model and to the prediction method used, respectively. Note that error rates reported in any component include the performance of the model in earlier components for the specified keepX parameters (e.g. error rate reported for component 3 for keepX = 20 already includes the fitted model on components 1 and 2 for keepX = 20). For more advanced usage of the perf function, see www.mixomics.org/methods/spls-da/ and consider using the predict function.

auc

Averaged AUC values over the nrepeat

For mint.splsda models, perf produces the following outputs:

study.specific.error

A list that gives BER, overall error rate and error rate per class, for each study

global.error

A list that gives BER, overall error rate and error rate per class for all samples

predict

A list of length ncomp that produces the predicted values of each sample for each class

class

A list which gives the predicted class of each sample for each dist and each of the ncomp components. Directly obtained from the predict output.

auc

AUC values

auc.study

AUC values for each study

For sgccda models, perf produces the following outputs:

error.rate

Prediction error rate for each block of object$X and each dist

error.rate.per.class

Prediction error rate for each block of object$X, each dist and each class

predict

Predicted values of each sample for each class, each block and each component

class

Predicted class of each sample for each block, each dist, each component and each nrepeat

features

a list of features selected across the folds ($stable.X and $stable.Y) for the keepX and keepY parameters from the input object.

AveragedPredict.class

if more than one block, returns the average predicted class over the blocks (averaged of the Predict output and prediction using the max.dist distance)

AveragedPredict.error.rate

if more than one block, returns the average predicted error rate over the blocks (using the AveragedPredict.class output)

WeightedPredict.class

if more than one block, returns the weighted predicted class over the blocks (weighted average of the Predict output and prediction using the max.dist distance)

WeightedPredict.error.rate

if more than one block, returns the weighted average predicted error rate over the blocks (using the WeightedPredict.class output)

MajorityVote

if more than one block, returns the majority class over the blocks. NA for a sample means that there is no consensus on the predicted class for this particular sample over the blocks.

MajorityVote.error.rate

if more than one block, returns the error rate of the MajorityVote output

WeightedVote

if more than one block, returns the weighted majority class over the blocks. NA for a sample means that there is no consensus on the predicted class for this particular sample over the blocks.

WeightedVote.error.rate

if more than one block, returns the error rate of the WeightedVote output

weights

Returns the weights of each block used for the weighted predictions, for each nrepeat and each fold

choice.ncomp

For supervised models; returns the optimal number of components for the model for each prediction distance using one-sided t-tests that test for a significant difference in the mean error rate (gain in prediction) when components are added to the model. See more details in Rohart et al 2016 Suppl. For more than one block, an optimal ncomp is returned for each prediction framework.

Details

Procedure. The process of evaluating the performance of a fitted model object is similar for all PLS-derived methods; a cross-validation approach is used to fit the method of object on folds-1 subsets of the data and then to predict on the subset left out. Different measures of performance are available depending on the model. Parameters such as logratio, multilevel, keepX or keepY are retrieved from object.

Parameters. If validation = "Mfold", M-fold cross-validation is performed. folds specifies the number of folds to generate. The folds also can be supplied as a list of vectors containing the indexes defining each fold as produced by split. When using validation = "Mfold", make sure that you repeat the process several times (as the results will be highly dependent on the random splits and the sample size).

If validation = "loo", leave-one-out cross-validation is performed (in that case, there is no need to repeat the process).

Measures of performance. For fitted PLS and sPLS regression models, perf estimates the mean squared error of prediction (MSEP), $R^2$, and $Q^2$ to assess the predictive perfity of the model using M-fold or leave-one-out cross-validation. Note that only the classic, regression and invariant modes can be applied. For sPLS, the MSEP, $R^2$, and $Q^2$ criteria are averaged across all folds. Note that for PLS and sPLS objects, perf is performed on the pre-processed data after log ratio transform and multilevel analysis, if any.

Sparse methods. The sPLS, sPLS-DA and sgccda functions are run on several and different subsets of data (the cross-folds) and will certainly lead to different subset of selected features. Those are summarised in the output features$stable (see output Value below) to assess how often the variables are selected across all folds. Note that for PLS-DA and sPLS-DA objects, perf is performed on the original data, i.e. before the pre-processing step of the log ratio transform and multilevel analysis, if any. In addition for these methods, the classification error rate is averaged across all folds.

The mint.sPLS-DA function estimates errors based on Leave-one-group-out cross validation (where each levels of object$study is left out (and predicted) once) and provides study-specific outputs (study.specific.error) as well as global outputs (global.error).

AUROC. For PLS-DA, sPLS-DA, mint.PLS-DA and mint.sPLS-DA methods: if auc=TRUE, Area Under the Curve (AUC) values are calculated from the predicted scores obtained from the predict function applied to the internal test sets in the cross-validation process, either for all samples or for study-specific samples (for mint models). Therefore we minimise the risk of overfitting. See auroc for more details. Our multivariate supervised methods already use a prediction threshold based on distances (see predict) that optimally determine class membership of the samples tested. As such AUC and ROC are not needed to estimate the performance of the model. We provide those outputs as complementary performance measures. See more details in our mixOmics article.

Prediction distances. See details from ?predict.

Repeats of the CV-folds. Repeated cross-validation implies that the whole CV process is repeated a number of times (nrepeat) to reduce variability across the different subset partitions. In the case of Leave-One-Out CV (validation = 'loo'), each sample is left out once (folds = N is set internally) and therefore nrepeat is by default 1.

More details about the PLS modes in ?pls.

References

DIABLO:

Singh A., Gautier B., Shannon C., Vacher M., Rohart F., Tebbutt S. and Le Cao K.A. (2016). DIABLO - multi omics integration for biomarker discovery.

mixOmics main publication:

Rohart F, Gautier B, Singh A, Le Cao K-A. mixOmics: an R package for 'omics feature selection and multiple data integration.

MINT:

Rohart F, Eslami A, Matigian, N, Bougeard S, Le Cao K-A (2017). MINT: A multivariate integrative approach to identify a reproducible biomarker signature across multiple experiments and platforms. BMC Bioinformatics 18:128.

PLS and PLS citeria for PLS regression: Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.

Chavent, Marie and Patouille, Brigitte (2003). Calcul des coefficients de regression et du PRESS en regression PLS1. Modulad n, 30 1-11. (this is the formula we use to calculate the Q2 in perf.pls and perf.spls)

Mevik, B.-H., Cederkvist, H. R. (2004). Mean Squared Error of Prediction (MSEP) Estimates for Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR). Journal of Chemometrics 18(9), 422-429.

sparse PLS regression mode:

Le 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.

One-sided t-tests (suppl material):

Rohart F, Mason EA, Matigian N, Mosbergen R, Korn O, Chen T, Butcher S, Patel J, Atkinson K, Khosrotehrani K, Fisk NM, Le Cao K-A&, Wells CA& (2016). A Molecular Classification of Human Mesenchymal Stromal Cells. PeerJ 4:e1845.

Examples

Run this code

# NOT RUN {
## validation for objects of class 'pls' (regression)
# ----------------------------------------
data(liver.toxicity)
X <- liver.toxicity$gene
Y <- liver.toxicity$clinic


# try tune the number of component to choose
# ---------------------
# first learn the full model
liver.pls <- pls(X, Y, ncomp = 10)

# with 5-fold cross validation: we use the same parameters as in model above
# but we perform cross validation to compute the MSEP, Q2 and R2 criteria
# ---------------------------
liver.val <- perf(liver.pls, validation = "Mfold", folds = 5)

# Q2 total should decrease until it reaches a threshold
liver.val$Q2.total

# ncomp = 2 is enough
plot(liver.val$Q2.total, type = 'l', col = 'red', ylim = c(-0.5, 0.5),
xlab = 'PLS components', ylab = 'Q2 total')
abline(h = 0.0975, col = 'darkgreen')
legend('topright', col = c('red', 'darkgreen'),
legend = c('Q2 total', 'threshold 0.0975'), lty = 1)
title('Liver toxicity PLS 5-fold, Q2 total values')

#have a look at the other criteria
# ----------------------
# R2
liver.val$R2
matplot(t(liver.val$R2), type = 'l', xlab = 'PLS components', ylab = 'R2 for each variable')
title('Liver toxicity PLS 5-fold, R2 values')

# MSEP
liver.val$MSEP
matplot(t(liver.val$MSEP), type = 'l', xlab = 'PLS components', ylab = 'MSEP for each variable')
title('Liver toxicity PLS 5-fold, MSEP values')


## validation for objects of class 'spls' (regression)
# ----------------------------------------
ncomp = 7
# first, learn the model on the whole data set
model.spls = spls(X, Y, ncomp = ncomp, mode = 'regression',
keepX = c(rep(10, ncomp)), keepY = c(rep(4,ncomp)))


# with leave-one-out cross validation
##set.seed(45)
model.spls.val <- perf(model.spls, validation = "Mfold", folds = 5 )#validation = "loo")

#Q2 total
model.spls.val$Q2.total

# R2:we can see how the performance degrades when ncomp increases
model.spls.val$R2
plot(model.spls.val, criterion="R2", type = 'l')
plot(model.spls.val, criterion="Q2", type = 'l')


## validation for objects of class 'splsda' (classification)
# ----------------------------------------
data(srbct)
X <- srbct$gene
Y <- srbct$class

ncomp = 2

srbct.splsda <- splsda(X, Y, ncomp = ncomp, keepX = rep(10, ncomp))

# with Mfold
# ---------
set.seed(45)
error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", auc = TRUE)
error
error$auc

plot(error)

# parallel code
set.seed(45)
error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", auc = TRUE, cpus =2)




\dontrun{
# with 5 components and nrepeat =5, to get a $choice.ncomp
ncomp = 5
srbct.splsda <- splsda(X, Y, ncomp = ncomp, keepX = rep(10, ncomp))

set.seed(45)
error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", nrepeat =5)
error

plot(error)

# parallel code
set.seed(45)
error <- perf(srbct.splsda, validation = "Mfold", folds = 8,
dist = "all", auc = TRUE, cpus =2)

}

## validation for objects of class 'mint.splsda' (classification)
# ----------------------------------------

data(stemcells)
res = mint.splsda(X = stemcells$gene, Y = stemcells$celltype, ncomp = 3, keepX = c(10, 5, 15),
study = stemcells$study)

out = perf(res, auc = TRUE)
out

out$auc
out$auc.study

## validation for objects of class 'sgccda' (classification)
# ----------------------------------------

data(nutrimouse)
Y = nutrimouse$diet
data = list(gene = nutrimouse$gene, lipid = nutrimouse$lipid)
design = matrix(c(0,1,1,1,0,1,1,1,0), ncol = 3, nrow = 3, byrow = TRUE)

nutrimouse.sgccda <- block.splsda(X=data,
Y = Y,
design = design,
keepX = list(gene=c(10,10), lipid=c(15,15)),
ncomp = 2,
scheme = "horst")

perf = perf(nutrimouse.sgccda)
perf


\dontrun{
#with 5 components and nrepeat=5 to get $choice.ncomp
nutrimouse.sgccda <- block.splsda(X=data,
Y = Y,
design = design,
keepX = list(gene=c(10,10), lipid=c(15,15)),
ncomp = 5,
scheme = "horst")

perf = perf(nutrimouse.sgccda, folds = 5, nrepeat = 5)
perf

perf$choice.ncomp
}
# }
# NOT RUN {
# }

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