1 The ropls package

The ropls R package implements the PCA, PLS(-DA) and OPLS(-DA) approaches with the original, NIPALS-based, versions of the algorithms (Wold, Sjostrom, and Eriksson 2001; Trygg and Wold 2002). It includes the R2 and Q2 quality metrics (Eriksson et al. 2001; Tenenhaus 1998), the permutation diagnostics (Szymanska et al. 2012), the computation of the VIP values (Wold, Sjostrom, and Eriksson 2001), the score and orthogonal distances to detect outliers (Hubert, Rousseeuw, and Vanden Branden 2005), as well as many graphics (scores, loadings, predictions, diagnostics, outliers, etc).

2 Context

2.1 Orthogonal Partial Least-Squares

Partial Least-Squares (PLS), which is a latent variable regression method based on covariance between the predictors and the response, has been shown to efficiently handle datasets with multi-collinear predictors, as in the case of spectrometry measurements (Wold, Sjostrom, and Eriksson 2001). More recently, Trygg and Wold (2002) introduced the Orthogonal Partial Least-Squares (OPLS) algorithm to model separately the variations of the predictors correlated and orthogonal to the response.

OPLS has a similar predictive capacity compared to PLS and improves the interpretation of the predictive components and of the systematic variation (Pinto, Trygg, and Gottfries 2012). In particular, OPLS modeling of single responses only requires one predictive component.

Diagnostics such as the Q2Y metrics and permutation testing are of high importance to avoid overfitting and assess the statistical significance of the model. The Variable Importance in Projection (VIP), which reflects both the loading weights for each component and the variability of the response explained by this component (Pinto, Trygg, and Gottfries 2012; Mehmood et al. 2012), can be used for feature selection (Trygg and Wold 2002; Pinto, Trygg, and Gottfries 2012).

2.2 OPLS software

OPLS is available in the SIMCA-P commercial software (Umetrics, Umea, Sweden; Eriksson et al. (2001)). In addition, the kernel-based version of OPLS (Bylesjo et al. 2008) is available in the open-source R statistical environment (R Development Core Team 2008), and a single implementation of the linear algorithm in R has been described (Gaude et al. 2013).

3 The sacurine metabolomics dataset

The sacurine metabolomics dataset will be used as a case study to describe the features from the ropls pacakge.

3.1 Study objective

The objective was to study the influence of age, body mass index (bmi), and gender on metabolite concentrations in urine, by analysing 183 samples from a cohort of adults with liquid chromatography coupled to high-resolution mass spectrometry (LC-HRMS; Thevenot et al. (2015)).

3.2 Pre-processing and annotation

Urine samples were analyzed by using an LTQ Orbitrap in the negative ionization mode. A total of 109 metabolites were identified or annotated at the MSI level 1 or 2. After retention time alignment with XCMS, peaks were integrated with Quan Browser. Signal drift and batch effect were corrected, and each urine profile was normalized to the osmolality of the sample. Finally, the data were log10 transformed (Thevenot et al. 2015).

3.3 Covariates

The volunteers’ age, body mass index (bmi), and gender were recorded.

4 Hands-on

4.1 Loading

We first load the ropls package:

library(ropls)

We then load the sacurine dataset which contains:

  1. The dataMatrix matrix of numeric type containing the intensity profiles (log10 transformed),

  2. The sampleMetadata data frame containg sample metadata,

  3. The variableMetadata data frame containg variable metadata

data(sacurine)
names(sacurine)
## [1] "dataMatrix"       "sampleMetadata"   "variableMetadata" "se"              
## [5] "eset"

We display a summary of the content of the dataMatrix, sampleMetadata and variableMetadata with the view method from the ropls package:

view(sacurine$dataMatrix)
##        dim  class    mode typeof   size NAs  min mean median max
##  183 x 109 matrix numeric double 0.2 Mb   0 -0.3  4.2    4.3   6
##        (2-methoxyethoxy)propanoic acid isomer (gamma)Glu-Leu/Ile ...
## HU_011                            3.019766011        3.888479324 ...
## HU_014                             3.81433889        4.277148905 ...
## ...                                       ...                ... ...
## HU_208                            3.748127215        4.523763202 ...
## HU_209                            4.208859398        4.675880567 ...
##        Valerylglycine isomer 2  Xanthosine
## HU_011             3.889078716 4.075879575
## HU_014             4.181765852 4.195761901
## ...                        ...         ...
## HU_208             4.634338821 4.487781609
## HU_209              4.47194762 4.222953354

view(sacurine$sampleMetadata)
##      age     bmi gender
##  numeric numeric factor
##  nRow nCol size NAs
##   183    3 0 Mb   0
##         age   bmi gender
## HU_011   29 19.75      M
## HU_014   59 22.64      F
## ...     ...   ...    ...
## HU_208   27 18.61      F
## HU_209 17.5 21.48      F
## 1 data.frame 'factor' column(s) converted to 'numeric' for plotting.

view(sacurine$variableMetadata)
##  msiLevel      hmdb chemicalClass
##   numeric character     character
##  nRow nCol size NAs
##   109    3 0 Mb   0
##                                        msiLevel      hmdb chemicalClass
## (2-methoxyethoxy)propanoic acid isomer        2                  Organi
## (gamma)Glu-Leu/Ile                            2                  AA-pep
## ...                                         ...       ...           ...
## Valerylglycine isomer 2                       2           AA-pep:AcyGly
## Xanthosine                                    1 HMDB00299        Nucleo
## 2 data.frame 'character' column(s) converted to 'numeric' for plotting.

Note:

  1. the view method applied to a numeric matrix also generates a graphical display

  2. the view method can also be applied to an ExpressionSet object (see below)

4.2 Principal Component Analysis (PCA)

We perform a PCA on the dataMatrix matrix (samples as rows, variables as columns), with the opls method:

sacurine.pca <- opls(sacurine$dataMatrix)

A summary of the model (8 components were selected) is printed:

## PCA
## 183 samples x 109 variables
## standard scaling of predictors
##       R2X(cum) pre ort
## Total    0.501   8   0

In addition the default summary figure is displayed:

Figure 1: PCA summary plot. Top left overview: the scree plot (i.e., inertia barplot) suggests that 3 components may be sufficient to capture most of the inertia; Top right outlier: this graphics shows the distances within and orthogonal to the projection plane (Hubert, Rousseeuw, and Vanden Branden 2005): the name of the samples with a high value for at least one of the distances are indicated (see the Comments section for the code used to compute these metrics and the thresholds); Bottom left x-score: the variance along each axis equals the variance captured by each component: it therefore depends on the total variance of the dataMatrix X and of the percentage of this variance captured by the component (indicated in the labels); it decreases when going from one component to a component with higher indice; Bottom right x-loading: the 3 variables with most extreme values (positive and negative) for each loading are black colored and labeled.

Note:

  1. Since dataMatrix does not contain missing value, the singular value decomposition was used by default; NIPALS can be selected with the algoC argument specifying the algorithm (Character),

  2. The predI = NA default number of predictive components (Integer) for PCA means that components (up to 10) will be computed until the cumulative variance exceeds 50%. If the 50% have not been reached at the 10th component, a warning message will be issued (you can still compute the following components by specifying the predI value).

Let us see if we notice any partition according to gender, by labeling/coloring the samples according to gender (parAsColFcVn) and drawing the Mahalanobis ellipses for the male and female subgroups (parEllipseL).

genderFc <- sacurine$sampleMetadata[, "gender"]
plot(sacurine.pca,
     typeVc = "x-score",
     parAsColFcVn = genderFc)