Statistical Analysis
Zhiqiang Pang, Jasmine Chong, Jeff Xia
2023-07-24
1. Introduction
MetaboAnalystR, in parallel with the webserver, provides a
comprehensive suite of statistical analyses to perform on a
user-uploaded data set. While researchers may have several goals for
their metabolomics data, the ultimate goal is to identify any
significant metabolite/s indicitive of a disease state, drugs, diet,
environment, geographical location, etc.
The standard workflow for statistical analysis is as follows:
Processed metabolomic data -> Univariate analysis ->
Multivariate analysis -> Biological interpretation
Univariate tests differ from multivariate tests in that they assess
the importance of each variable seperately. Meanwhile, multivariate
tests assess two or more variables at once, while also taking into
consideration the relationship between the variables. Finally,
biological interpretation provides a biological context for the
significant metabolites identified using univariate/multivariate
methods. Below, we will discuss the various statistical methods in
greater detail. For the tutorial, we will be using a dataset consisting
of concentrations of 77 urine samples from cancer patients (cachexic
vs. control) measured by 1H NMR - Eisner
et al. 2010.
2. Univariate Methods
To begin the SA module, we will start with identifying important
features from the data set using various univariate tests, including
classical methods such as the Student’s t-test and ANOVA, as well as
other methods such as the volcano plot and correlation analysis.
# Load MetaboAnalystR
library(MetaboAnalystR)
# Clean global environment
rm(list = ls())
library(MetaboAnalystR)
mSet<-InitDataObjects("conc", "stat", FALSE);
## Starting Rserve:
## /opt/R/4.2.2/lib/R/bin/R CMD /opt/R/4.2.2/lib/R/library/Rserve/libs//Rserve --no-save
##
## [1] "MetaboAnalyst R objects initialized ..."
mSet<-Read.TextData(mSet, "https://www.xialab.ca/api/download/metaboanalyst/human_cachexia.csv", "rowu", "disc");
mSet<-SanityCheckData(mSet);
## [1] "Successfully passed sanity check!"
## [2] "Samples are not paired."
## [3] "2 groups were detected in samples."
## [4] "Only English letters, numbers, underscore, hyphen and forward slash (/) are allowed."
## [5] "<font color=\"orange\">Other special characters or punctuations (if any) will be stripped off.</font>"
## [6] "All data values are numeric."
## [7] "A total of 0 (0%) missing values were detected."
## [8] "<u>By default, missing values will be replaced by 1/5 of min positive values of their corresponding variables</u>"
## [9] "Click the <b>Proceed</b> button if you accept the default practice;"
## [10] "Or click the <b>Missing Values</b> button to use other methods."
mSet<-ReplaceMin(mSet);
mSet<-PreparePrenormData(mSet);
mSet<-Normalization(mSet, "NULL", "LogNorm", "MeanCenter", "S10T0", ratio=FALSE, ratioNum=20);
## [1] 77 63
mSet<-PlotNormSummary(mSet, "norm_0_", format ="png", dpi=72, width=NA);
mSet<-PlotSampleNormSummary(mSet, "snorm_0_", format = "png", dpi=72, width=NA);
2.1 Fold-change analysis
The goal of fold-change (FC) analysis is to compare the absolute
value of change between two group means. Since column-wise normalization
(i.e. log transformation, mean-centering) will significantly alter
absolute values, FC is calculated as the ratio between two group means
using the data before column-wise normalization was applied.
For paired analysis, the program first counts the number of pairs
with consistent change above the given FC threshold. If this number
exceeds a given count threshold, the variable will be reported as
significant.
# Perform fold-change analysis on uploaded data, unpaired
mSet<-FC.Anal(mSet, 2.0, 0, FALSE)
# Plot fold-change analysis
mSet<-PlotFC(mSet, "fc_0_", "png", 72, width=NA)
# To view fold-change
mSet$analSet$fc$fc.log
## 1,6-Anhydro-beta-D-glucose 1-Methylnicotinamide
## 0.888690 -0.052019
## 2-Aminobutyrate 2-Hydroxyisobutyrate
## 1.312700 0.633520
## 2-Oxoglutarate 3-Aminoisobutyrate
## 1.098400 1.329100
## 3-Hydroxybutyrate 3-Hydroxyisovalerate
## 1.563700 1.164900
## 3-Indoxylsulfate 4-Hydroxyphenylacetate
## 0.857170 0.263810
## Acetate Acetone
## 1.266100 0.664560
## Adipate Alanine
## 1.952900 1.141300
## Asparagine Betaine
## 0.852650 1.004000
## Carnitine Citrate
## 0.994090 0.883620
## Creatine Creatinine
## 1.763900 0.932160
## Dimethylamine Ethanolamine
## 1.120000 0.729170
## Formate Fucose
## 1.150600 0.918770
## Fumarate Glucose
## 1.262700 2.553000
## Glutamine Glycine
## 1.166100 0.869890
## Glycolate Guanidoacetate
## 0.657790 0.506100
## Hippurate Histidine
## 1.075800 1.013100
## Hypoxanthine Isoleucine
## 0.375470 0.420550
## Lactate Leucine
## 1.726900 1.205400
## Lysine Methylamine
## 0.442780 0.901220
## Methylguanidine N,N-Dimethylglycine
## 0.517770 1.342900
## O-Acetylcarnitine Pantothenate
## 1.270300 -0.397700
## Pyroglutamate Pyruvate
## 1.180400 1.096200
## Quinolinate Serine
## 1.090600 1.007700
## Succinate Sucrose
## 1.416200 1.432600
## Tartrate Taurine
## 0.720000 1.032700
## Threonine Trigonelline
## 0.990220 1.460400
## Trimethylamine N-oxide Tryptophan
## 1.077700 0.967880
## Tyrosine Uracil
## 0.953700 0.207270
## Valine Xylose
## 1.178900 1.194000
## cis-Aconitate myo-Inositol
## 1.589400 1.537500
## trans-Aconitate pi-Methylhistidine
## 0.811730 0.771640
## tau-Methylhistidine
## 0.708800
2.2 T-Test
MetaboAnalystR supports various options for performing T-test
analysis. Users can select the analysis type (paired), the
group variance (equal.var), whether the test is parametric or
non-parametric (nonpar), and the adjusted p-value (FDR) cut-off
(threshp).
Note, for a large data set (> 1000 variables), both the paired
information and the group variance will be ignored, and the default
parameters will be used for t-tests to save computational time. If you
choose non-parametric tests (Wilcoxon rank-sum test), the group variance
will be ignored.
# Perform T-test (parametric)
mSet<-Ttests.Anal(mSet, nonpar=F, threshp=0.05, paired=FALSE, equal.var=TRUE, "fdr", FALSE)
## Loading required package: memoise
## [1] "Performing regular t-tests ...."
## [1] "A total of 53 significant features were found."
# Plot of the T-test results
mSet<-PlotTT(mSet, imgName = "tt_0_", format = "png", dpi = 72, width=NA)
The t test results for MS1 feature table can be used for function
analysis.
2.3 Volcano Plot
The volcano plot is a combination of fold change and t-test values.
Note, for unpaired samples, the x-axis is log2(FC). For paired analysis,
the x-axis is number of significant counts. The y-axis is
-log10(p.value) for both cases, and can be based on raw or FDR adjusted
p values from the t-tests. In Volcano.Anal, users can specify
if the data are paired, the FC threshold, the comparison type, the
signigicant count threshold if data are paired, whether the test is
parametric or non-parametric, the p-value threshold, and the group
variance.
# Perform the volcano analysis
mSet<-Volcano.Anal(mSet, FALSE, 2.0, 0, F, 0.1, TRUE, "raw")
## [1] "A total of 57 significant features were found."
# Create the volcano plot
mSet<-PlotVolcano(mSet, "volcano_0_", 1, 0, format ="png", dpi=72, width=NA)
## Loading required package: ggplot2
## Warning: Removed 30 rows containing missing values (`geom_text_repel()`).
2.4 One-way Analysis of Variance (ANOVA) - ONLY FOR MULTI-GROUP
ANALYSIS!
ANOVA can only be computed on data with more than one group.
Please note that the below example uses data from a different
example dataset, which contains more than 2 groups.
# Perform ANOVA
mSet <- ANOVA.Anal(mSet, F, 0.05, "fisher")
# Plot ANOVA
mSet <- PlotANOVA(mSet, "aov_0_", "png", 72, width=NA)
2.5 Correlation Analysis
To perform correlation analysis to evaluate the correlation between
all features or samples, use PlotCorrHeatMap. Here, users must
specify the mSet object, the dimensions to be correlated, the name of
the heatmap that will be created, the output, dpi, and width of the
image, the distance measure (Pearson, Spearman, or Kendall), to view the
heatmap as an overview or detailed view, to fix the colour distribution,
the colors, and whether or not to perform clustering. Please refer to
the user manual for more details.
Note, the heatmap will only show correlations for a maximum of 1000
features. For larger datasets, only top 1000 features will be selected
based on their interquantile range (IQR). When color distribution is
fixed, you can potentially compare the correlation patterns among
different data sets. In this case, you can choose “do not perform
clustering” for all data set, or only to perform clustering on a single
reference data set, then manually re-arranged other data sets according
to the clustering pattern of the reference data set.
### OPTION 1 - Heatmap specifying pearson distance and an overview
mSet<-PlotCorrHeatMap(mSet, "corr_0_", "png", 72, width=NA, "col", "pearson", "bwm", "overview", F, F, 0.0)
The following command shows the detailed view (zoomed-in) of the
above heatmap.
### OPTION 2 - Heatmap specifying pearson correlation and a detailed view
mSet<-PlotCorrHeatMap(mSet, "corr_1_", format = "png", dpi=72, width=NA, "col", "spearman", "bwm", "detail", F, F, 999)
2.6 Pattern Searching
Correlation analysis can be performed either against a given feature
or against a given pattern. The pattern is specified as a series of
numbers separated by “-”. Each number corresponds to the expected
expression pattern in the corresponding group. For example, a 1-2-3-4
pattern is used to search for features that increase linearly with time
in a time-series data with four time points (or four groups). The order
of the groups is given as the first item in the predefined patterns.
Indicate the mSet object, the distance measure (Pearson, Spearman, or
Kendall), and the pattern to use.
# Perform correlation analysis on a pattern (a feature of interest in this case)
mSet<-FeatureCorrelation(mSet, "pearson", "1,6-Anhydro-beta-D-glucose")
# Plot the correlation analysis on a pattern
mSet<-PlotCorr(mSet, "ptn_3_", format="png", dpi=72, width=NA)
2.7 Principal Component Analysis (PCA)
To perform PCA, first use PCA.Anal. MetaboAnalystR has the
options to create a scree plot (PlotPCAScree), score plot
(PlotPCA2DScore or PlotPCA3DScore), loadings plot
(PlotPCALoading), and biplot (PlotPCABiplot). For the
score plots, users will create both a static as well as interactive 3D
score plot. To view the interactive plot, type “mSet$imgSet$pca.3d” into
your R console. Please refer to the user manual for details about each
function.
# Perform PCA analysis
mSet<-PCA.Anal(mSet)
# Create PCA overview
mSet<-PlotPCAPairSummary(mSet, "pca_pair_0_", format = "png", dpi = 72, width=NA, 5)
# Create PCA scree plot
mSet<-PlotPCAScree(mSet, "pca_scree_0_", "png", dpi = 72, width=NA, 5)
# Create a 2D PCA score plot
mSet<-PlotPCA2DScore(mSet, "pca_score2d_0_", format = "png", dpi=72, width=NA, 1, 2, 0.95, 1, 0)
# Create a 3D PCA score plot
mSet<-PlotPCA3DScoreImg(mSet, "pca_score3d_0_", "png", 72, width=NA, 1,2,3, 40)
# Create a PCA loadings Plots
mSet<-PlotPCALoading(mSet, "pca_loading_0_", "png", 72, width=NA, 1,2);
# Create a PCA Biplot
mSet<-PlotPCABiplot(mSet, "pca_biplot_0_", format = "png", dpi = 72, width=NA, 1, 2)
# View the 3D interactive PLS-DA score plot
mSet$imgSet$pca.3d
2.8 Partial Least Squares - Discriminant Analysis (PLS-DA)
To perform PLS-DA, first use PLSR.Anal. MetaboAnalystR has
the options to create a plot component pairs
(PlotPLSPairSummary), score plot (PlotPLS2DScore),
loadings plot (PlotPLSLoading), perform cross-validation and
permutation (PLSDA.CV and PLSDA.Permut), and plot the
results of the cross-validation and permutation (PlotPLS.Imp
and PlotPLS.Permutation). For the score plots, users will
create both a static as well as interactive 3D score plot. To view the
interactive plot, type “mSet$imgSet$plsda.3d” into your R console.
Please refer to the user manual for details about each function.
mSet<-PLSR.Anal(mSet, reg=TRUE)
mSet<-PlotPLSPairSummary(mSet, "pls_pair_0_", "png", 72, width=NA, 5)
mSet<-PlotPLS2DScore(mSet, "pls_score2d_0_", "png", 72, width=NA, 1,2,0.95,1,0)
mSet<-PlotPLS3DScoreImg(mSet, "pls_score3d_0_", "png", 72, width=NA, 1,2,3, 40)
mSet<-PlotPLSLoading(mSet, "pls_loading_0_", "png", 72, width=NA, 1, 2);
mSet<-PLSDA.CV(mSet, "5", 5,5, "Q2")
## Loading required package: lattice
##
## Attaching package: 'caret'
## The following object is masked from 'package:MetaboAnalystR':
##
## splsda
## Loading required package: pls
##
## Attaching package: 'pls'
## The following object is masked from 'package:caret':
##
## R2
## The following object is masked from 'package:stats':
##
## loadings
mSet<-PlotPLS.Classification(mSet, "pls_cv_0_", "png", 72, width=NA)
mSet<-PlotPLS.Imp(mSet, "pls_imp_0_", "png", 72, width=NA, "vip", "Comp. 1", 15, FALSE)
mSet<-PLSDA.Permut(mSet, 100, "accu")
## [1] "performing 100 permutations ..."
## [1] "Empirical p value: p = 0.02 (2/100)"
mSet<-PlotPLS.Permutation(mSet, "pls_perm_1_", "png", 72, width=NA)
# View the 3D interactive PLS-DA score plot
mSet$imgSet$plsda.3d
2.9 Sparse Partial Least Squares - Discriminant Analysis
(sPLS-DA)
The sparse PLS-DA (sPLS-DA) algorithm can effectively reduce the
number of variables (metabolites) in high-dimensional metabolomics data
to produce robust and easy-to-interpret models. Users can control the
“sparseness” of the model by controlling the number of components
included in the model and the number of variables within each component.
More details can be found from Le Cao et. al 2011 (PMC3133555).
To begin, use SPLSR.Anal. MetaboAnalystR has the options to
create an overview of the sPLS-DA analysis
(PlotSPLSPairSummary), a score plot (PlotSPLS2DScore
or PlotSPLS3DScore), loadings plot (PlotSPLSLoading),
and classification plot (PlotSPLSDA.Classification). For the
score plots, users will create both a static as well as interactive 3D
score plot. To view the interactive plot, type “mSet$imgSet$splsda.3d”
into your R console. Please refer to the user manual for details about
each function. Note that the loadings plot shows the variables selected
by the sPLS-DA model for a given component. The variables are ranked by
the absolute values of their loadings.
To evaluate the performance of the created sPLS-DA models for
classification, use PlotSPLSDA.Classification. The performance
of the sPLS-DA models are evaluated using cross validations (CV) with
increasing numbers of components created using the specified number of
the variables. Users can choose to use either 5-fold CVs or leave one
out cross-validation (LOOCV). Please note that the results from 5-fold
CV may change slightly due to random subsampling procedures.
# Perform sPLS-DA analysis
mSet<-SPLSR.Anal(mSet, 5, 10, "same", "Mfold", 5, T)
# Plot sPLS-DA overview
mSet<-PlotSPLSPairSummary(mSet, "spls_pair_0_", format = "png", dpi=72, width=NA, 5)
# Create 2D sPLS-DA Score Plot
mSet<-PlotSPLS2DScore(mSet, "spls_score2d_0_", format = "png", dpi=72, width=NA, 1, 2, 0.95, 1, 0)
# Create 3D sPLS-DA Score Plot
mSet<-PlotSPLS3DScoreImg(mSet, "spls_score3d_0_", format = "png", 72, width=NA, 1, 2, 3, 40)
# Create sPLS-DA loadings plot
mSet<-PlotSPLSLoading(mSet, "spls_loading_0_", format = "png", dpi=72, width=NA, 1,"overview")
# Perform cross-validation and plot sPLS-DA classification
mSet<-PlotSPLSDA.Classification(mSet, "spls_cv_0_", format = "png", dpi=72, width=NA)
# View the 3D interactive PLS-DA score plot
mSet$imgSet$splsda.3d
