Contents
1 Brief Introduction
PLSDA-batch is a new batch effect correction method based on Projection to Latent Structures Discriminant Analysis to correct data prior to any downstream analysis. It estimates latent components related to treatment and batch effects to remove batch variation. PLSDA-batch is highly suitable for microbiome data as it is non-parametric, multivariate and allows for ordination and data visualisation. Combined with centered log ratio transformation for addressing uneven library sizes and compositional structure, PLSDA-batch addresses all characteristics of microbiome data that existing correction methods have ignored so far.
Apart from the main method, the R package also includes two variants called 1/ weighted PLSDA-batch for unbalanced batch x treatment designs that are commonly encountered in studies with small sample size, and 2/ sparse PLSDA-batch for selection of discriminative variables to avoid overfitting in classification problems. These two variants have widened the scope of applicability of PLSDA-batch to different data settings (???).
This vignette includes microbiome data pre-processing, batch effect detection and visualisation, the usage of PLSDA-batch series methods, assessment of batch effect removal and variable selection after batch effect correction. See “Batch Effects Management in Case Studies” for different choices of methods for batch effect management according to experimental purposes and designs.
2 Packages installation and loading
First, we load the packages necessary for analysis, and check the version of each package.
# CRAN
library(pheatmap)
library(vegan)
library(gridExtra)
# Bioconductor
library(mixOmics)
library(Biobase)
library(TreeSummarizedExperiment)
library(PLSDAbatch)
# print package versions
package.version('pheatmap')## [1] "1.0.12"package.version('vegan')## [1] "2.6-8"package.version('gridExtra')## [1] "2.3"package.version('mixOmics')## [1] "6.30.0"package.version('Biobase')## [1] "2.66.0"package.version('PLSDAbatch')## [1] "1.2.0"3 Case study description
We considered a case study to illustrate the application of PLSDA-batch. This study is described as follows:
\(\color{blue}{\bf{\text{Anaerobic digestion.}}}\) This study explored the microbial indicators that could improve the efficacy of anaerobic digestion (AD) bioprocess and prevent its failure (???). This data include 75 samples and 567 microbial variables. The samples were treated with two different ranges of phenol concentration (effect of interest) and processed at five different dates (batch effect). This study includes a clear and strong batch effect with an approx. balanced batch x treatment design.
4 Data pre-processing
4.1 Pre-filtering
We load the \(\color{blue}{\text{AD data}}\) stored internally with function
data(), and then extract the batch and treatment information out.
# AD data
data('AD_data')
ad.count <- assays(AD_data$FullData)$Count
dim(ad.count)## [1] 75 567ad.metadata <- rowData(AD_data$FullData)
ad.batch = factor(ad.metadata$sequencing_run_date,
levels = unique(ad.metadata$sequencing_run_date))
ad.trt = as.factor(ad.metadata$initial_phenol_concentration.regroup)
names(ad.batch) <- names(ad.trt) <- rownames(ad.metadata)The raw \(\color{blue}{\text{AD data}}\) include 567 OTUs and 75 samples.
We then use the function PreFL() from our \(\color{orange}{\text{PLSDAbatch}}\)
R package to filter the data.
ad.filter.res <- PreFL(data = ad.count)
ad.filter <- ad.filter.res$data.filter
dim(ad.filter)## [1] 75 231# zero proportion before filtering
ad.filter.res$zero.prob## [1] 0.6328042# zero proportion after filtering
sum(ad.filter == 0)/(nrow(ad.filter) * ncol(ad.filter))## [1] 0.3806638After filtering, 231 OTUs remained, and the proportion of zeroes decreased from 63% to 38%.
Note: The PreFL() function is only dedicated to raw counts, rather than
relative abundance data. We also recommend to start the pre-filtering on raw
counts, rather than relative abundance data to mitigate the compositionality
issue.
4.2 Transformation
Prior to CLR transformation, we recommend adding 1 as the offset for the data
(e.g., \(\color{blue}{\text{AD data}}\)) that are raw count data, and 0.01 as
the offset for the data that are relative abundance data. We use
logratio.transfo() function in \(\color{orange}{\text{mixOmics}}\) package to
CLR transform the data.
ad.clr <- logratio.transfo(X = ad.filter, logratio = 'CLR', offset = 1)
class(ad.clr) = 'matrix'5 Batch effect detection
5.1 PCA
We apply pca() function from \(\color{orange}{\text{mixOmics}}\) package to
the \(\color{blue}{\text{AD data}}\) and Scatter_Density() function from
\(\color{orange}{\text{PLSDAbatch}}\) to represent the PCA sample plot with
densities.
# AD data
ad.pca.before <- pca(ad.clr, ncomp = 3, scale = TRUE)
Scatter_Density(object = ad.pca.before, batch = ad.batch, trt = ad.trt,
title = 'AD data', trt.legend.title = 'Phenol conc.')
Figure 1: The PCA sample plot with densities in the AD data
In the above figure, we observed 1) the distinction between samples treated with different phenol concentrations and 2) the differences between samples sequenced at “14/04/2016”, “21/09/2017” and the other dates. Therefore, the batch effect related to dates needs to be removed.
5.2 Boxplots and density plots
We first identify the top OTU driving the major variance in PCA using
selectVar() in \(\color{orange}{\text{mixOmics}}\) package. Each identified
OTU can then be plotted as boxplots and density plots using box_plot() and
density_plot() in \(\color{orange}{\text{PLSDAbatch}}\).
ad.OTU.name <- selectVar(ad.pca.before, comp = 1)$name[1]
ad.OTU_batch <- data.frame(value = ad.clr[,ad.OTU.name], batch = ad.batch)
box_plot(df = ad.OTU_batch, title = paste(ad.OTU.name, '(AD data)'),
x.angle = 30)
Figure 2: Boxplots of sample values in “OTU28” before batch effect correction in the AD data
density_plot(df = ad.OTU_batch, title = paste(ad.OTU.name, '(AD data)'))
Figure 3: Density plots of sample values in “OTU28” before batch effect correction in the AD data
The boxplot and density plot indicated a strong date batch effect because of the differences between “14/04/2016”, “21/09/2017” and the other dates in the “OTU28”.
We also apply a linear regression model to the “OTU28” using linear_regres()
from \(\color{orange}{\text{PLSDAbatch}}\) with batch and treatment effects as
covariates. We set “14/04/2016” and “21/09/2017” as the reference batch
respectively with relevel() from \(\color{orange}{\text{stats}}\).
# reference batch: 14/04/2016
ad.batch <- relevel(x = ad.batch, ref = '14/04/2016')
ad.OTU.lm <- linear_regres(data = ad.clr[,ad.OTU.name],
trt = ad.trt, batch.fix = ad.batch,
type = 'linear model')
summary(ad.OTU.lm$model$data)##
## Call:
## lm(formula = data[, i] ~ trt + batch.fix)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9384 -0.3279 0.1635 0.3849 0.9887
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8501 0.2196 3.871 0.000243 ***
## trt1-2 -1.6871 0.1754 -9.617 2.27e-14 ***
## batch.fix09/04/2015 1.5963 0.2950 5.410 8.55e-07 ***
## batch.fix01/07/2016 2.0839 0.2345 8.886 4.82e-13 ***
## batch.fix14/11/2016 1.7405 0.2480 7.018 1.24e-09 ***
## batch.fix21/09/2017 1.2646 0.2690 4.701 1.28e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7033 on 69 degrees of freedom
## Multiple R-squared: 0.7546, Adjusted R-squared: 0.7368
## F-statistic: 42.44 on 5 and 69 DF, p-value: < 2.2e-16# reference batch: 21/09/2017
ad.batch <- relevel(x = ad.batch, ref = '21/09/2017')
ad.OTU.lm <- linear_regres(data = ad.clr[,ad.OTU.name],
trt = ad.trt, batch.fix = ad.batch,
type = 'linear model')
summary(ad.OTU.lm$model$data)##
## Call:
## lm(formula = data[, i] ~ trt + batch.fix)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9384 -0.3279 0.1635 0.3849 0.9887
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.1147 0.2502 8.453 2.97e-12 ***
## trt1-2 -1.6871 0.1754 -9.617 2.27e-14 ***
## batch.fix14/04/2016 -1.2646 0.2690 -4.701 1.28e-05 ***
## batch.fix09/04/2015 0.3317 0.3139 1.056 0.29446
## batch.fix01/07/2016 0.8193 0.2573 3.185 0.00218 **
## batch.fix14/11/2016 0.4759 0.2705 1.760 0.08292 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7033 on 69 degrees of freedom
## Multiple R-squared: 0.7546, Adjusted R-squared: 0.7368
## F-statistic: 42.44 on 5 and 69 DF, p-value: < 2.2e-16From the results of linear regression, we observed P < 0.001 for the regression coefficients associated with all the other batches when the reference batch was “14/04/2016”, which confirmed the difference between the samples from batch “14/04/2016” and the other samples as observed from previous plots. When the reference batch was “21/09/2017”, we also observed significant differences between batch “21/09/2017” and “14/04/2016”, between “21/09/2017” and “01/07/2016”. Therefore, the batch effect because of “21/09/2017” also exists.
5.3 Heatmap
We produce a heatmap using \(\color{orange}{\text{pheatmap}}\) package. The data first need to be scaled on both OTUs and samples.
# scale the clr data on both OTUs and samples
ad.clr.s <- scale(ad.clr, center = TRUE, scale = TRUE)
ad.clr.ss <- scale(t(ad.clr.s), center = TRUE, scale = TRUE)
ad.anno_col <- data.frame(Batch = ad.batch, Treatment = ad.trt)
ad.anno_colors <- list(Batch = color.mixo(seq_len(5)),
Treatment = pb_color(seq_len(2)))
names(ad.anno_colors$Batch) = levels(ad.batch)
names(ad.anno_colors$Treatment) = levels(ad.trt)
pheatmap(ad.clr.ss,
cluster_rows = FALSE,
fontsize_row = 4,
fontsize_col = 6,
fontsize = 8,
clustering_distance_rows = 'euclidean',
clustering_method = 'ward.D',
treeheight_row = 30,
annotation_col = ad.anno_col,
annotation_colors = ad.anno_colors,
border_color = 'NA',
main = 'AD data - Scaled')
Figure 4: Hierarchical clustering for samples in the AD data
In the heatmap, samples in the \(\color{blue}{\text{AD data}}\) from batch dated “14/04/2016” were clustered and distinct from other samples, indicating a batch effect.
5.4 pRDA
We apply pRDA with varpart() function from \(\color{orange}{\text{vegan}}\)
R package.
# AD data
ad.factors.df <- data.frame(trt = ad.trt, batch = ad.batch)
class(ad.clr) <- 'matrix'
ad.rda.before <- varpart(ad.clr, ~ trt, ~ batch,
data = ad.factors.df, scale = TRUE)
ad.rda.before$part$indfract## Df R.squared Adj.R.squared Testable
## [a] = X1|X2 1 NA 0.08943682 TRUE
## [b] = X2|X1 4 NA 0.26604420 TRUE
## [c] 0 NA 0.01296248 FALSE
## [d] = Residuals NA NA 0.63155651 FALSEIn the result, X1 and X2 represent the first and second covariates fitted
in the model. [a], [b] represent the independent proportion of variance
explained by X1 and X2 respectively, and [c] represents the intersection
variance shared between X1 and X2. In the \(\color{blue}{\text{AD data}}\),
batch variance (X2) was larger than treatment variance (X1) with some
interaction proportion (indicated in line [c], Adj.R.squared = 0.013). The
greater the intersection variance, the more unbalanced batch x treatment design
is. In this study, we considered the design as approx. balanced.
6 Batch effect correction
6.1 PLSDA-batch
The PLSDA_batch() function is implemented in
\(\color{orange}{\text{PLSDAbatch}}\) package. To use this function, we need to
specify the optimal number of components related to treatment (ncomp.trt) or
batch effects (ncomp.bat).
Here in the \(\color{blue}{\text{AD data}}\), we use plsda() from
\(\color{orange}{\text{mixOmics}}\) with only treatment grouping information to
estimate the optimal number of treatment components to preserve.
# estimate the number of treatment components
ad.trt.tune <- plsda(X = ad.clr, Y = ad.trt, ncomp = 5)
ad.trt.tune$prop_expl_var #1## $X
## comp1 comp2 comp3 comp4 comp5
## 0.18619506 0.07873817 0.08257396 0.09263497 0.06594757
##
## $Y
## comp1 comp2 comp3 comp4 comp5
## 1.00000000 0.33857374 0.17315267 0.10551296 0.08185822We choose the number that explains 100% variance in the outcome matrix Y,
thus from the result, 1 component was enough to preserve the treatment
information.
We then use PLSDA_batch() function with both treatment and batch grouping
information to estimate the optimal number of batch components to remove.
# estimate the number of batch components
ad.batch.tune <- PLSDA_batch(X = ad.clr,
Y.trt = ad.trt, Y.bat = ad.batch,
ncomp.trt = 1, ncomp.bat = 10)
ad.batch.tune$explained_variance.bat #4## $X
## comp1 comp2 comp3 comp4 comp5 comp6 comp7
## 0.17470922 0.11481264 0.10122717 0.07507395 0.03955458 0.03549997 0.03009383
## comp8 comp9 comp10
## 0.03411377 0.01873017 0.01151062
##
## $Y
## comp1 comp2 comp3 comp4 comp5 comp6 comp7 comp8
## 0.2474654 0.2615741 0.2301382 0.2608223 0.2300984 0.2524412 0.2438371 0.1098029
## comp9 comp10
## 0.1638204 0.2300389sum(ad.batch.tune$explained_variance.bat$Y[seq_len(4)])## [1] 1Using the same criterion as choosing treatment components, we choose the number of batch components that explains 100% variance in the outcome matrix of batch. According to the result, 4 components were required to remove batch effects.
We then can correct for batch effects applying PLSDA_batch() with treatment,
batch grouping information and corresponding optimal number of related
components.
ad.PLSDA_batch.res <- PLSDA_batch(X = ad.clr,
Y.trt = ad.trt, Y.bat = ad.batch,
ncomp.trt = 1, ncomp.bat = 4)
ad.PLSDA_batch <- ad.PLSDA_batch.res$X.nobatch6.2 sPLSDA-batch
We apply sPLSDA-batch using the same function PLSDA_batch(), but we specify
the number of variables to select on each component (usually only
treatment-related components keepX.trt). To determine the optimal number of
variables to select, we use tune.splsda() function from
\(\color{orange}{\text{mixOmics}}\) package (???) with all
possible numbers of variables to select for each component (test.keepX).
# estimate the number of variables to select per treatment component
set.seed(777)
ad.test.keepX = c(seq(1, 10, 1), seq(20, 100, 10),
seq(150, 231, 50), 231)
ad.trt.tune.v <- tune.splsda(X = ad.clr, Y = ad.trt,
ncomp = 1, test.keepX = ad.test.keepX,
validation = 'Mfold', folds = 4,
nrepeat = 50)
ad.trt.tune.v$choice.keepX #100Here the optimal number of variables to select for the treatment component was 100. Since we have adjusted the amount of treatment variation to preserve, we need to re-choose the optimal number of components related to batch effects using the same criterion mentioned in section PLSDA-batch.
# estimate the number of batch components
ad.batch.tune <- PLSDA_batch(X = ad.clr,
Y.trt = ad.trt, Y.bat = ad.batch,
ncomp.trt = 1, keepX.trt = 100,
ncomp.bat = 10)
ad.batch.tune$explained_variance.bat #4## $X
## comp1 comp2 comp3 comp4 comp5 comp6 comp7
## 0.17420018 0.11477097 0.09813477 0.07894965 0.03278495 0.03540224 0.04168413
## comp8 comp9 comp10
## 0.02200350 0.02524104 0.01347680
##
## $Y
## comp1 comp2 comp3 comp4 comp5 comp6
## 0.247477492 0.260671553 0.230108093 0.261742862 0.248318269 0.252676585
## comp7 comp8 comp9 comp10
## 0.253146090 0.240732821 0.005126235 0.259210314sum(ad.batch.tune$explained_variance.bat$Y[seq_len(4)])## [1] 1According to the result, we needed 4 batch related components to remove batch
variance from the data with function PLSDA_batch().
ad.sPLSDA_batch.res <- PLSDA_batch(X = ad.clr,
Y.trt = ad.trt, Y.bat = ad.batch,
ncomp.trt = 1, keepX.trt = 100,
ncomp.bat = 4)
ad.sPLSDA_batch <- ad.sPLSDA_batch.res$X.nobatchNote: for unbalanced batch x treatment design (with the exception of the
nested design), we can specify balance = FALSE in PLSDA_batch() function
to apply weighted PLSDA-batch.
7 Assessing batch effect correction
We apply different visualisation and quantitative methods to assessing batch effect correction.
7.1 Methods that detect batch effects
PCA
In the \(\color{blue}{\text{AD data}}\), we compared the PCA sample plots before and after batch effect correction.
ad.pca.before <- pca(ad.clr, ncomp = 3, scale = TRUE)
ad.pca.PLSDA_batch <- pca(ad.PLSDA_batch, ncomp = 3, scale = TRUE)
ad.pca.sPLSDA_batch <- pca(ad.sPLSDA_batch, ncomp = 3, scale = TRUE)# order batches
ad.batch = factor(ad.metadata$sequencing_run_date,
levels = unique(ad.metadata$sequencing_run_date))
ad.pca.before.plot <- Scatter_Density(object = ad.pca.before,
batch = ad.batch,
trt = ad.trt,
title = 'Before correction')ad.pca.PLSDA_batch.plot <- Scatter_Density(object = ad.pca.PLSDA_batch,
batch = ad.batch,
trt = ad.trt,
title = 'PLSDA-batch')ad.pca.sPLSDA_batch.plot <- Scatter_Density(object = ad.pca.sPLSDA_batch,
batch = ad.batch,
trt = ad.trt,
title = 'sPLSDA-batch')
Figure 5: The PCA sample plots with densities before and after batch effect correction in the AD data
As shown in the PCA sample plots, the differences between the samples sequenced at “14/04/2016”, “21/09/2017” and the other dates were removed after batch effect correction. The data corrected with PLSDA-batch included slightly more treatment variation mostly on the first PC than sPLSDA-batch, as indicated on the x-axis label (26%). We can also compare the boxplots and density plots for key variables identified in PCA driving the major variance or heatmaps showing obvious patterns before and after batch effect correction (results not shown).
pRDA
We calculate the global explained variance across all microbial variables
using pRDA. To achieve this, we create a loop for each variable from the
original (uncorrected) and batch effect-corrected data. The final results are
then displayed with partVar_plot() from
\(\color{orange}{\text{PLSDAbatch}}\) package.
# AD data
ad.corrected.list <- list(`Before correction` = ad.clr,
`PLSDA-batch` = ad.PLSDA_batch,
`sPLSDA-batch` = ad.sPLSDA_batch)
ad.prop.df <- data.frame(Treatment = NA, Batch = NA,
Intersection = NA,
Residuals = NA)
for(i in seq_len(length(ad.corrected.list))){
rda.res = varpart(ad.corrected.list[[i]], ~ trt, ~ batch,
data = ad.factors.df, scale = TRUE)
ad.prop.df[i, ] <- rda.res$part$indfract$Adj.R.squared}
rownames(ad.prop.df) = names(ad.corrected.list)
ad.prop.df <- ad.prop.df[, c(1,3,2,4)]
ad.prop.df[ad.prop.df < 0] = 0
ad.prop.df <- as.data.frame(t(apply(ad.prop.df, 1,
function(x){x/sum(x)})))
partVar_plot(prop.df = ad.prop.df)
Figure 6: Global explained variance before and after batch effect correction for the AD data
As shown in the above figure, the intersection between batch and treatment variance was small (1.3%) for the \(\color{blue}{\text{AD data}}\), which implies that the batch x treatment design is not highly unbalanced. Thus the unweighted PLSDA-batch and sPLSDA-batch were still applicable, and thus the weighted versions were not used. sPLSDA-batch corrected data led to a better performance with undetectable batch and intersection variance compared to PLSDA-batch.
7.2 Other methods
\(\mathbf{R^2}\)
The \(R^2\) values for each variable are calculated with lm() from
\(\color{orange}{\text{stats}}\) package. To compare the \(R^2\) values among
variables, we scale the corrected data before \(R^2\) calculation. The results
are displayed with ggplot() from \(\color{orange}{\text{ggplot2}}\) R package.
# AD data
# scale
ad.corr_scale.list <- lapply(ad.corrected.list,
function(x){apply(x, 2, scale)})
ad.r_values.list <- list()
for(i in seq_len(length(ad.corr_scale.list))){
ad.r_values <- data.frame(trt = NA, batch = NA)
for(c in seq_len(ncol(ad.corr_scale.list[[i]]))){
ad.fit.res.trt <- lm(ad.corr_scale.list[[i]][,c] ~ ad.trt)
ad.r_values[c,1] <- summary(ad.fit.res.trt)$r.squared
ad.fit.res.batch <- lm(ad.corr_scale.list[[i]][,c] ~ ad.batch)
ad.r_values[c,2] <- summary(ad.fit.res.batch)$r.squared
}
ad.r_values.list[[i]] <- ad.r_values
}
names(ad.r_values.list) <- names(ad.corr_scale.list)
ad.boxp.list <- list()
for(i in seq_len(length(ad.r_values.list))){
ad.boxp.list[[i]] <-
data.frame(r2 = c(ad.r_values.list[[i]][ ,'trt'],
ad.r_values.list[[i]][ ,'batch']),
Effects = as.factor(rep(c('Treatment','Batch'),
each = 231)))
}
names(ad.boxp.list) <- names(ad.r_values.list)
ad.r2.boxp <- rbind(ad.boxp.list$`Before correction`,
ad.boxp.list$removeBatchEffect,
ad.boxp.list$ComBat,
ad.boxp.list$`PLSDA-batch`,
ad.boxp.list$`sPLSDA-batch`,
ad.boxp.list$`Percentile Normalisation`,
ad.boxp.list$RUVIII)
ad.r2.boxp$methods <- rep(c('Before correction', 'PLSDA-batch', 'sPLSDA-batch'),
each = 462)
ad.r2.boxp$methods <- factor(ad.r2.boxp$methods,
levels = unique(ad.r2.boxp$methods))
ggplot(ad.r2.boxp, aes(x = Effects, y = r2, fill = Effects)) +
geom_boxplot(alpha = 0.80) +
theme_bw() +
theme(text = element_text(size = 18),
axis.title.x = element_blank(),
axis.title.y = element_blank(),
axis.text.x = element_text(angle = 60, hjust = 1, size = 18),
axis.text.y = element_text(size = 18),
panel.grid.minor.x = element_blank(),
panel.grid.major.x = element_blank(),
legend.position = "right") + facet_grid( ~ methods) +
scale_fill_manual(values=pb_color(c(12,14))) 
Figure 7: AD study: \(R^2\) values for each microbial variable before and after batch effect correction
The batch effects related variance was reduced after both PLSDA-batch and sPLSDA-batch correction, but the former maintained a bit more treatment related variance.
##################################
ad.barp.list <- list()
for(i in seq_len(length(ad.r_values.list))){
ad.barp.list[[i]] <- data.frame(r2 = c(sum(ad.r_values.list[[i]][ ,'trt']),
sum(ad.r_values.list[[i]][ ,'batch'])),
Effects = c('Treatment','Batch'))
}
names(ad.barp.list) <- names(ad.r_values.list)
ad.r2.barp <- rbind(ad.barp.list$`Before correction`,
ad.barp.list$removeBatchEffect,
ad.barp.list$ComBat,
ad.barp.list$`PLSDA-batch`,
ad.barp.list$`sPLSDA-batch`,
ad.barp.list$`Percentile Normalisation`,
ad.barp.list$RUVIII)
ad.r2.barp$methods <- rep(c('Before correction', 'PLSDA-batch', 'sPLSDA-batch'),
each = 2)
ad.r2.barp$methods <- factor(ad.r2.barp$methods,
levels = unique(ad.r2.barp$methods))
ggplot(ad.r2.barp, aes(x = Effects, y = r2, fill = Effects)) +
geom_bar(stat="identity") +
theme_bw() +
theme(text = element_text(size = 18),
axis.title.x = element_blank(),
axis.title.y = element_blank(),
axis.text.x = element_text(angle = 60, hjust = 1, size = 18),
axis.text.y = element_text(size = 18),
panel.grid.minor.x = element_blank(),
panel.grid.major.x = element_blank(),
legend.position = "right") + facet_grid( ~ methods) +
scale_fill_manual(values=pb_color(c(12,14)))
Figure 8: AD study: the sum of \(R^2\) values for each microbial variable before and after batch effect correction
The overall sum of \(R^2\) values indicated that sPLSDA-batch removed slightly more batch variance (PLSDA-batch: 12.40, sPLSDA-batch: 9.25) but preserved less treatment variance (PLSDA-batch: 40.00, sPLSDA-batch: 36.22) than PLSDA-batch.
Alignment scores
To use the alignment_score() function from
\(\color{orange}{\text{PLSDAbatch}}\), we need to specify the proportion of data
variance to explain (var), the number of nearest neighbours (k) and the
number of principal components to estimate (ncomp). We then use ggplot()
function from \(\color{orange}{\text{ggplot2}}\) to visualise the results.
# AD data
ad.scores <- c()
names(ad.batch) <- rownames(ad.clr)
for(i in seq_len(length(ad.corrected.list))){
res <- alignment_score(data = ad.corrected.list[[i]],
batch = ad.batch,
var = 0.95,
k = 8,
ncomp = 50)
ad.scores <- c(ad.scores, res)
}
ad.scores.df <- data.frame(scores = ad.scores,
methods = names(ad.corrected.list))
ad.scores.df$methods <- factor(ad.scores.df$methods,
levels = rev(names(ad.corrected.list)))
ggplot() + geom_col(aes(x = ad.scores.df$methods,
y = ad.scores.df$scores)) +
geom_text(aes(x = ad.scores.df$methods,
y = ad.scores.df$scores/2,
label = round(ad.scores.df$scores, 3)),
size = 3, col = 'white') +
coord_flip() + theme_bw() + ylab('Alignment Scores') +
xlab('') + ylim(0,0.85)
Figure 9: Comparison of alignment scores before and after batch effect correction using different methods for the AD data
The alignment scores complement the PCA results, especially when batch effect removal is difficult to assess on PCA sample plots. For example in Figure 5, we observed that the samples across different batches were better mixed after batch effect correction with different methods than before, whereas the performance of difference methods was difficult to compare. Since a higher alignment score indicates that samples are better mixed, as shown in the above bar plot, sPLSDA-batch gave a superior performance compared to PLSDA-batch.
8 Variable selection
After batch effect correction, we can select discriminative variables against different treatments.
Here, we use splsda() from \(\color{orange}{\text{mixOmics}}\) to select the
top 50 microbial variables that, in combination, discriminate the different
treatment
groups in the \(\color{blue}{\text{AD data}}\).
For the details to apply sPLS-DA, see mixOmics.
splsda.plsda_batch <- splsda(X = ad.PLSDA_batch, Y = ad.trt,
ncomp = 3, keepX = rep(50,3))
select.plsda_batch <- selectVar(splsda.plsda_batch, comp = 1)
head(select.plsda_batch$value)## value.var
## OTU46 0.3084712
## OTU24 0.2833650
## OTU28 0.2807199
## OTU35 -0.2669300
## OTU68 0.2610368
## OTU61 0.2558267splsda.splsda_batch <- splsda(X = ad.sPLSDA_batch, Y = ad.trt,
ncomp = 3, keepX = rep(50,3))
select.splsda_batch <- selectVar(splsda.splsda_batch, comp = 1)
head(select.splsda_batch$value)## value.var
## OTU46 0.3016966
## OTU24 0.2783030
## OTU28 0.2727259
## OTU35 -0.2650401
## OTU61 0.2566640
## OTU68 0.2554550length(intersect(select.plsda_batch$name, select.splsda_batch$name))## [1] 43The discriminative variables were selected and listed according to their contributions against sample groups treated with different ranges of phenol concentration (0-0.5 vs. 1-2 g/L).
The overlap between selections from the data corrected with PLSDA-batch and sPLSDA-batch is high (43 out of 50), but there still exist different variables between different selections.
9 Session Information
sessionInfo()## R version 4.4.1 (2024-06-14)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.20-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] PLSDAbatch_1.2.0 TreeSummarizedExperiment_2.14.0
## [3] Biostrings_2.74.0 XVector_0.46.0
## [5] SingleCellExperiment_1.28.0 SummarizedExperiment_1.36.0
## [7] GenomicRanges_1.58.0 GenomeInfoDb_1.42.0
## [9] IRanges_2.40.0 S4Vectors_0.44.0
## [11] MatrixGenerics_1.18.0 matrixStats_1.4.1
## [13] Biobase_2.66.0 BiocGenerics_0.52.0
## [15] mixOmics_6.30.0 ggplot2_3.5.1
## [17] MASS_7.3-61 gridExtra_2.3
## [19] vegan_2.6-8 lattice_0.22-6
## [21] permute_0.9-7 pheatmap_1.0.12
## [23] BiocStyle_2.34.0
##
## loaded via a namespace (and not attached):
## [1] Rdpack_2.6.1 rlang_1.1.4 magrittr_2.0.3
## [4] compiler_4.4.1 mgcv_1.9-1 vctrs_0.6.5
## [7] reshape2_1.4.4 stringr_1.5.1 pkgconfig_2.0.3
## [10] crayon_1.5.3 fastmap_1.2.0 magick_2.8.5
## [13] backports_1.5.0 labeling_0.4.3 utf8_1.2.4
## [16] rmarkdown_2.28 nloptr_2.1.1 UCSC.utils_1.2.0
## [19] tinytex_0.53 purrr_1.0.2 xfun_0.48
## [22] zlibbioc_1.52.0 cachem_1.1.0 jsonlite_1.8.9
## [25] highr_0.11 DelayedArray_0.32.0 BiocParallel_1.40.0
## [28] broom_1.0.7 parallel_4.4.1 cluster_2.1.6
## [31] R6_2.5.1 bslib_0.8.0 stringi_1.8.4
## [34] RColorBrewer_1.1-3 boot_1.3-31 car_3.1-3
## [37] numDeriv_2016.8-1.1 jquerylib_0.1.4 Rcpp_1.0.13
## [40] bookdown_0.41 knitr_1.48 Matrix_1.7-1
## [43] splines_4.4.1 igraph_2.1.1 tidyselect_1.2.1
## [46] abind_1.4-8 yaml_2.3.10 codetools_0.2-20
## [49] lmerTest_3.1-3 tibble_3.2.1 plyr_1.8.9
## [52] treeio_1.30.0 withr_3.0.2 rARPACK_0.11-0
## [55] evaluate_1.0.1 pillar_1.9.0 BiocManager_1.30.25
## [58] ggpubr_0.6.0 carData_3.0-5 insight_0.20.5
## [61] ellipse_0.5.0 generics_0.1.3 munsell_0.5.1
## [64] scales_1.3.0 tidytree_0.4.6 minqa_1.2.8
## [67] glue_1.8.0 lazyeval_0.2.2 tools_4.4.1
## [70] lme4_1.1-35.5 RSpectra_0.16-2 ggsignif_0.6.4
## [73] fs_1.6.4 grid_4.4.1 tidyr_1.3.1
## [76] ape_5.8 rbibutils_2.3 colorspace_2.1-1
## [79] nlme_3.1-166 GenomeInfoDbData_1.2.13 performance_0.12.4
## [82] Formula_1.2-5 cli_3.6.3 fansi_1.0.6
## [85] S4Arrays_1.6.0 dplyr_1.1.4 corpcor_1.6.10
## [88] gtable_0.3.6 rstatix_0.7.2 yulab.utils_0.1.7
## [91] sass_0.4.9 digest_0.6.37 SparseArray_1.6.0
## [94] ggrepel_0.9.6 farver_2.1.2 htmltools_0.5.8.1
## [97] lifecycle_1.0.4 httr_1.4.7