---
title: "MatrixQCvis: shiny-based interactive data quality exploration of omics data"
author:
 - name: Thomas Naake and Wolfgang Huber
   mail: thomas.naake@embl.de, thomasnaake@googlemail.com, wolfgang.huber@embl.de
   affiliation: European Molecular Biology Laboratory, Meyerhofstrasse 1, 69117 Heidelberg
package: MatrixQCvis
      
output:  
    BiocStyle::html_document:
        toc_float: true
bibliography: MatrixQCvis-citations.bib
vignette: >
    %\VignetteIndexEntry{Shiny-based interactive data quality exploration of omics data}
    %\VignetteEngine{knitr::rmarkdown}
    %\VignetteKeywords{Mass Spectrometry, MS, Metabolomics, Proteomics, Transcriptomics, Visualization, QC}
    %\VignettePackage{MatrixQCvis-vignette}
    %\VignetteEncoding{UTF-8}
---

```{r style, echo = FALSE, results = 'asis'}
BiocStyle::markdown()
```

```{r env, include=FALSE, echo=FALSE, cache=FALSE}
library("knitr")
opts_chunk$set(stop_on_error = 1L)
suppressPackageStartupMessages(library("MatrixQCvis"))
```

# Introduction {#sec-intro}

Data quality assessment is an integral part of preparatory data analysis 
to ensure sound biological information retrieval. 
We present here the `MatrixQCvis` package, which provides shiny-based 
interactive visualization of data quality metrics at the per-sample and 
per-feature level. It is broadly applicable to quantitative omics data types 
that come in matrix-like format (features x samples). It enables the detection 
of low-quality samples, drifts, outliers and batch effects in data sets.
Visualizations include amongst others bar- and violin plots of the 
(count/intensity) values, mean vs standard deviation plots, MA plots, 
empirical cumulative distribution function (ECDF) plots, visualizations 
of the distances between samples, and multiple types of dimension reduction
plots. 
`MatrixQCvis` builds upon the Bioconductor `SummarizedExperiment` S4 
class and enables thus the facile integration into existing workflows.

`MatrixQCvis` is especially addressed to analyze the quality of proteomics and 
metabolomics data sets that are characterized by missing values as it 
allows the user for imputation of missing values and differential expression analysis 
using the `proDA` package [@Ahlmann2019]. Besides this, `MatrixQCvis` is 
extensible to other type of data(e.g. transcriptomics count data) that can be 
represented as a `SummarizedExperiment` object. 
Furthermore, the `shiny` application facilitates simple differential 
expression analysis using either moderated t-tests (from the `limma` package,
@Ritchie2015) or Wald tests (from the `proDA` package, @Ahlmann2019).

Within this vignette, the term feature will refer to a probed molecular entity,
e.g. gene, transcript, protein, peptide, or metabolite. 

In the following, we will describe the major setup of `MatrixQCvis` and the 
navigation through the shiny application, `shinyQC`.

# Questions and bugs {-}

`MatrixQCvis` is currently under active development. If you
discover any bugs, typos or develop ideas of improving
`MatrixQCvis` feel free to raise an issue via
[GitHub](https://github.com/tnaake/MatrixQCvis) or
send a mail to the developer.

# Prepare the environment and load the data {#sec-prepare}
To install `MatrixQCvis` enter the following to the `R` console

```{r install, eval=FALSE}
if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("MatrixQCvis")
```

Before starting with the analysis, load the `MatrixQCvis` package. This 
will also load the required packages `Biobase`, `BiocGenerics`, `GenomeInfoDb`,
`GenomicRanges`, `ggplot2`, `IRanges`, `MatrixGenerics`,
`parallel`, `matrixStats`, `plotly`, `shiny`, `SummarizedExperiment`, and 
`stats4`.

```{r load_MatrixQCvis, eval=TRUE}
library(MatrixQCvis)
``` 

The most important function to assess the data quality is the `shinyQC` function
and its most important argument is `se`. `shinyQC` expects a `SummarizedExperiment` 
object. 

The `shinyQC` function sets the following requirements to the 
`SummarizedExperiment` object `se`:
 - `rownames(se)` are not allowed to be `NULL` and have to be set to the 
   feature names,
 - `colnames(se)` are not allowed to be `NULL` and have to be set to the 
   sample names,
 - `colnames(se)`, `colnames(assay(se))` and `rownames(colData(se))` all have 
    to be identical.
 
 If these requirements are not met, `shinyQC` will stop and throw an error.

Alternatively, a `SummarizedExperiment` object can also be loaded from within 
`shinyQC` (when no `se` object is supplied to `shinyQC`).

Objects belonging to the `SummarizedExperiment` class are containers for one 
or more assays, 
which are (numerical) matrices containing the quantitative, measured information
of the experiment. The rows represent features of interest (e.g. 
transcripts, peptides, proteins, or metabolites) and the columns represent the 
samples. The 
`SummarizedExperiment` object stores also information on the features of 
interest (accessible by `rowData`) and information on the samples
(accessible by `colData`). The name of samples and features will be accessed
from `colnames(se)` and `rownames(se)`, respectively.

If there is more than one experimental data set (`assay`)
stored in the `SummarizedExperiment` object, a select option will appear in the 
sidebar allowing the user to select the `assay`. 

Here, we will generate a `SummarizedExperiment` object with synthetic 
quantitative information on proteins and use this object, `se`, to showcase the 
functionality of `shinyQC`. The object will contain information from 40 
samples. The samples consist of four different types (`1`, `2`, `3`, and `4`) 
and each type has two treatments, `A` and `B`. In total there are 1000 features. 

```{r, prepare_se, eval=TRUE, echo=TRUE}
## create synthetic assay using the generate_synthetic_data function from the
## proDA package
library(proDA)
n_samples <- 40
n_feat <- 1000
data <- generate_synthetic_data(n_feat, n_conditions = n_samples / 10, 
    n_replicates = n_samples / 4, frac_changed = 0.1)
a <- data$Y
colnames(a) <- gsub(colnames(a), pattern = "Condition", replacement = "Sample")

## add some treatment-specific effects
set.seed(1)
a[, 1:5] <- a[, 1:5] + rnorm(5000, mean = 1.0, sd = 0.5)
a[, 11:15] <- a[, 11:15] + rnorm(5000, mean = 0.8, sd = 0.5)
a[, 21:25] <- a[, 21:25] + rnorm(5000, mean = 1.2, sd = 0.5)
a[, 31:35] <- a[, 31:35] + rnorm(5000, mean = 0.7, sd = 0.5)

## create information on the samples
type_sample <- gsub(data$groups, pattern = "Condition", replacement = "Type")
trmt_sample <- paste(
   c(rep("1", 10), rep("2", 10), rep("3", 10), rep("4", 10)),
   c(rep("A", 5), rep("B", 5)), sep = "_")
cD <- data.frame(name = colnames(a), type = type_sample, 
                     treatment = trmt_sample)

## create information on the proteins
rD <- data.frame(spectra = rownames(a))

## create se
se <- SummarizedExperiment(assay = a, rowData = rD, colData = cD)

## remove the features that have only NA values
se <- se[!apply(assay(se), 1, function(row_i) all(is.na(row_i))), ]
se
```

The actual shiny application can then be started by entering the following 
to the `R` console:

```{r, eval=FALSE}
qc <- shinyQC(se)
```

The assignment to `qc` or any other object is not mandatory. Upon exiting the
shiny application, `shinyQC` will return a 
`SummarizedExperiment` object containing the imputed dataset
that can be in the following further analyzed. The object will only be 
returned if the function call was assigned to an object, e.g. 
`qc <- shinyQC(se)`.

Now, we will have a closer look on the user interface of the Shiny 
application. 

# Appearance of user interface depends on the data input
Please note: Depending on the supplied `SummarizedExperiment` object the user
interface of `shinyQC` will differ:

- for a `SummarizedExperiment` object containing missing values
    - the tabs `Samples`, `Measured Values`, `Missing Values`, `Values`,
    `Dimension Reduction` and `DE` will be displayed,
    - within the tabs `Values` and `Dimension Reduction` the 
    `imputed` data set **will be** visualized,
    - the sidebar panel **includes** a drop-down menu for the imputation method.
- for a `SummarizedExperiment` object containing no missing values (i.e.
 with complete observations)
    - the tabs `Samples`, `Values`, `Dimension Reduction` and `DE` 
    will be displayed,
    - within the tabs `Values` and `DE` the `imputed` data set 
    **will not** be visualized,
    - the sidebar panel **does not includes** a drop-down menu for the 
    imputation method.

In the following, the vignette will be (mainly) described from the point of view
of a `SummarizedExperiment` containing missing values. 

## Sidebar
The sidebar enables the user to exclude (e.g. in the case of identified outliers)
and select samples (e.g. in the case if there is interest for a specific 
sample type). Samples are excluded/selected by entering the sample name 
in the input field and pressing `Enter` on the keyboard or by clicking 
on the name of the samples in the drop-down menu and activating the 
relevant option (`"all"` for all samples; `"exclude"`, `"select"`). If the 
option is set to `"select"` at least three samples have to be selected for 
the selection to take place. 

In addition, in the tabs `Values`, 
`Dimension Reduction`, and `DE`, the sidebars allows the user for 

 - normalization: currently the methods `sum`, `quantile divion`, `quantile`
   and `none`, i.e. no normalization, are supported;
 - batch correction: currently the methods `removeBatchEffect` from the `limma`
   package [@Ritchie2015] and `none`, i.e. no batch correction, are supported.
   It is highly advised to consult the dimension reduction plots before 
   performing any batch correction. Batch correction should not be done based 
   solely on (count/intensity) value distributions (boxplots/violin plots);
 - transformation: currently the methods `log`, `log2`, `vsn` 
   (variance stabilizing normalization/transformation, @Huber2002), and `none`, i.e.
   no transformation, are supported;
 - imputation (only for `SummarizedExperiment` containing missing values): 
   currently the methods `BPCA`, `KNN`, `MLE`, `Min`, `MinDet`, 
   and `MinProb` are supported (see also @Lazar2016 for a review on 
   imputation methods for label-free quantitative proteomics data sets).
   
By clicking on `Generate report` a markdown report will be created 
(the progress of rendering is displayed in the bottom right corner). After 
rendering there is the possibility to open or to save the report. The 
report will take all values as set in the `shinyQC` application - if the 
plot was not called yet, default values will be taken for the rendering. 
   
By exiting the shiny application, a `SummarizedExperiment` object 
is returned to the `qc` object.
If the supplied `SummarizedExperiment` contains missing values, the 
`SummarizedExperiment` with imputed values is returned, otherwise the
`SummarizedExperiment` with batch corrected values is returned.

The `metadata` slot contains information about the method of 
 - the normalization,
 - the batch correction,
 - the transformation, and
 - the imputation of (count/intensity) values (if the supplied 
   `SummarizedExperiment` contains missing values).

The sidebar in the last tab (`DE`) is different from the other tabs and will
be explained in the section `Tab: DE`. 
  

# Tab: Samples
The tab `Samples` gives general information on the number of samples in the 
`se` object. 

## Histogram
The first panel shows a barplot and displays the number of 
samples per sample type, treatment, etc. As an example, if we want to display
how many samples are in `se` for the different `type`s (`type` is a 
column name in `colData(se)` and any column in `colData(se)` can be selected), 
this panel will show the following output:
```{r hist_sample, eval=TRUE, echo=FALSE, crop=NULL}
tbl <- hist_sample_num(se = se, category = "type")
partial_bundle(hist_sample(tbl, category = "type"))
```

## Mosaic
The figure in this panel displays the relative proportions of the numbers, 
e.g. how many samples (in %) are there for `type` against `treatment`. Again,
`type` and `treatment` are columns in `colData(se)` and any column in 
`colData(se)` can be selected. 
The figure will tell us that `se` contains the different types/treatments in a
balanced manner:
```{r mosaic, eval=TRUE, echo=FALSE, crop=NULL}
mosaic(se = se, f1 = "type", f2 = "treatment")
```

   
# Tab: Measured Values and Missing Values

The tabs `Measured Values` and `Missing Values` are only displayed if the 
`SummarizedExperiment` object contains missing values. 

The layout in the tabs `Measured Values` and `Missing Values` is similar. 
Therefore, the two tabs are described here simultaneously and the differences
are pointed out where necessary. 

## Barplot for samples
The plot shows the number of measured or missing values per sample 
in the data set (depending on the selected tab). For example for the tab
`Measured Values`, the plot will look like

```{r samplesMeasuredMissing, eval=TRUE, echo=FALSE, crop=NULL}
tbl <- samplesMeasuredMissing(se) 
partial_bundle(barplotSamplesMeasuredMissing(tbl, measured = TRUE))
```

In this case, the samples show approximately the same number of measured features,
i.e. there is no indication to remove any sample based on this measure. 

## Histogram Features

The plot shows different data depending on which tab 
(`Measured Values` or `Missing Values`) is selected. The binwidth will be 
determined by the slider input (`Binwidth (Measured Values)` or 
`Binwidth (Missing Values)`).

### Measured Variables
The plot shows how often a feature was measured in a certain number of 
samples.

Examples:

1. in the case of one sample (x-axis), the y-axis will denote the number of 
features for which only one feature was measured.

2. in the case of the number of total samples (x-axis), the y-axis will 
denote the number of features with complete observations (i.e. the number 
of features for which the feature was quantified in all samples).

```{r histFeature_measured, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE, crop=NULL}
partial_bundle(histFeature(assay(se), measured = TRUE))
```

### Missing Variables
The plot shows how often a feature was missing in a certain number of samples.

Examples:

1. in the case of one sample (x-axis), the y-axis will denote the number of 
features for which only one feature was missing.

2. in the case of the number of total samples (x-axis), the y-axis will 
denote the number of features with completely missing observations 
(i.e. the number of features for which no feature was quantified in all 
samples).

```{r histFeature_missing, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE, crop=NULL}
partial_bundle(histFeature(assay(se), measured = FALSE))
```

## Histogram Features along variable

The plot in this panel can be read accordingly to the one in the panel 
`Histogram Features`, but, it is segregated for the specified variable 
(e.g. it shows the distribution of measured/missing values among the sample 
types).

```{r histFeatureCategory, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE, crop=NULL}
partial_bundle(histFeatureCategory(se, measured = TRUE, category = "type"))
```

## UpSet
The plot shows the interaction of sets between different variables 
depending on their presence or absence. The dots in the UpSet plot specify 
if the criteria for presence/absence are fulfilled (see below for the 
definition). In each column the intersections are displayed together with 
the number of features regarding the type of intersection. The boxplots in 
the rows display the number of present/absent features per set.

All sets present in the data set are displayed. Depending on the data set, 
however, not all intersections sets are displayed (see the help page for 
the `upset` function from the `UpSetR` package).

### Measured Values
Presence is defined by a feature being measured in at least one sample of a 
set.

```{r upsetmeasured, eval=TRUE, echo=FALSE, crop=NULL}
upsetCategory(se, category = "type", measured = TRUE) 
```

### Missing Values
Absence is defined by a feature with only missing values (i.e. no measured 
values) of a set.

```{r upsetmissing, eval=TRUE, echo=FALSE, crop=NULL}
upsetCategory(se, category = "type", measured = FALSE)
```

## Sets

This panel will retrieve the features specified by intersection of sets. 

This panel builds upon the `Upset` panel. By selecting the check boxes, 
the names of the features (taken from the `rownames` of the features) are 
printed as text that fulfill the defined intersection of sets.

Example: Four sets (`Type_1`, `Type_2`, `Type_3`, and `Type_4`) are found for 
a specified variable (here: `type`). When selecting the boxes for `Type_1` and 
`Type_2` (while not selecting the boxes for `Type_3` and `Type_4`) the 
features that are present/absent for `Type_1` and `Type_2` 
(but not in the sets `Type_3` and `Type_4`) are returned.

For the tab `Measured Values`, presence is defined by a feature being 
measured in at least one sample of a set.

For the tab `Missing Values`, absence is defined by a feature with only 
missing values (i.e. no measured values) of a set.

# Tab: Values
The tab `Values` will take a closer look on the `assay` slot of the 
`SummarizedExperiment`. 

## Boxplot/Violin plot

This panel shows the (count/intensity) values for raw (`raw`), 
batch corrected (`normalized`), normalized+batch corrected (`batch corrected`), 
normalized+batch corrected+transformed (`transformed`), and
normalized+batch corrected+transformed+imputed (`imputed`) (count/intensity) 
values (imputation of missing values, `imputed` will only be shown if there are 
missing values in the `SummarizedExperiment`). As already mentioned, the 
different methods for normalization, batch correction, transformation (and 
imputation) are specified in the side panel.

For visualization purposes only, the (count/intensity) values for the raw,
normalized and batch corrected data sets can be `log2` transformed (see the 
radio buttons in
`Display log2 values? (only for 'raw', 'normalized' and 'batch corrected')`).

The type of visualization (boxplot or violin plot) can be specified by 
selecting `boxplot` or `violin` in the radio button panel (`Type of display`).

The figure (violin plot) using the raw values will look like
```{r boxplot, eval=TRUE, echo=FALSE, warning=FALSE, crop=NULL}
createBoxplot(se, orderCategory = "name", title = "raw", log = FALSE, 
               violin = TRUE)
```

## Trend/drift 
This panel shows a trend line for aggregated values to 
indicate drifts/trends in data acquisition. It
shows the sum- or median-aggregated values (specified in
`Select aggregation`). The plot displays trends in data
acquisition that originate e.g. from differences in instrument 
sensitivity. The panel displays aggregated values for 
raw (`raw`), batch corrected (`batch corrected`), batch corrected+normalized 
(`normalized`), batch corrected+normalized+transformed (`transformed`), and
batch corrected+normalized+transformed+imputed (`imputed`) (count/intensity) values 
(imputation of missing values, `imputed` will only be shown if there are missing
values in the `SummarizedExperiment`). 
The different methods for normalization, batch correction, transformation (and 
imputation) are specified in the sidebar panel. 

The smoothing is calculated from the 
selection of samples that are specified by the drop-down menus
`Select variable` and `Select level to highlight`. 
The menu `Select variable` corresponds to the `colnames` in 
`colData(se)`. Here, we can select for the higher-order variable, e.g.
the sample type (containing for example `Type_1`, `Type_2`, ..., `QC`). 
The drop-down menu `Select level to highlight` will specify the actual selection 
from which
the trend line will be calculated (e.g. `Type_1`, `Type_2`, ..., `QC`). Also,
the menu will always include the level `all`, which will use all points to 
calculate the trend line. If we want to calculate the trend line of 
aggregated values of all samples belonging to the type `QC`, we select
`QC` in the drop-down menu. 

The panel allows the users for further customization after expanding the collapsed box.
The data input is selected in the drop-down menu under `Select data input`.
The smoothing method (either LOESS or linear model) is selected in the drop-down
menu under `Select smoothing method`. The aggregation method is selected 
in the drop-down menu `Select smoothing method`.

With the drop-down menu `Select categorical variable to order samples`, 
the samples (x-axis) will be ordered alphanumerically according to the 
selected level (and the sample name). 


Here, we are interested in observing if there is a trend/drift for 
samples of `type` `Type_1`. We select `LOESS` as the method for the trend line 
and `median` as the aggregation method. The figure will then look as follows:
```{r drift, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE, crop=NULL}
partial_bundle(driftPlot(se, aggregation = "median", category = "type",
          orderCategory = "type", level = "Type_1", method = "loess"))
```


## Coefficient of variation

This panel shows the coefficient of variation values for raw (`raw`),
normalized (`normalized`), normalized+batch corrected (`batch corrected`), 
normalized+batch corrected+transformed (`transformed`), and 
normalized+batch corrected+transformed+imputed (`imputed`) 
(count/intensity) values (imputation of missing values, `imputed` will only be shown 
if there are missing values in the `SummarizedExperiment`) among the samples. 
The different methods for normalization, batch corrected, transformation,
(and imputation) are specified in the sidebar panel. 

The panel displays the coefficient of variation values from the samples of the
`SummarizedExperiment` object. The coefficients of variation are calculated 
according to the formula `sd(x) / mean(x) * 100` with `x` the sample values 
and `sd` the standard deviation. The plot might be useful when looking at the
coefficient of variation values of a specific sample type (e.g. QCs) and trying
to identify outliers. 
 
Here, we shows the plot of coefficient of variation values from the 
raw values (as obtained by `assay(se)`), normalized values (using `sum` 
normalization), transformed values (using `vsn`), batch corrected values
(using `none`) and imputed values (using the `MinDet` algorithm, @Lazar2016).
```{r cv, eval=TRUE, echo=FALSE, warning=FALSE, message=FALSE, crop=NULL}
a <- assay(se)
a_n <- normalizeAssay(a, "sum")
se_n <- MatrixQCvis:::updateSE(se = se, assay = a_n)
a_b <- batchCorrectionAssay(se_n, method = "none")
a_t <- transformAssay(a_b, "vsn")
se_t <- MatrixQCvis:::updateSE(se = se, assay = a_t)

a_i <- imputeAssay(a_t, "MinDet")

## calculate cv values
cv_r <- cv(a, "raw")
cv_n <- cv(a_n, "normalized")
cv_b <- cv(a_b, "batch corrected")
cv_t <- cv(a_t, "transformed")
cv_i <- cv(a_i, "imputed")
 
df <- data.frame(cv_r, cv_n, cv_b, cv_t, cv_i)
plotCV(df)
```

 
## Mean-sd plot

The panel shows the three mean-sd (standard deviation) plots for
normalized+batch corrected+transformed (`transformed`)
and normalized+batch corrected+transformed+imputed (`imputed`) values
(`imputed` will only be shown if there are missing
values in the `SummarizedExperiment`). 
The sd and mean are calculated feature-wise from the values of the respective 
data set. The plot allows the user to visualize if there is a dependence of the sd on 
the mean. The red line depicts the running median estimator (window-width 10%). 
In case of sd-mean independence, the running median should be approximately 
horizontal.

For the transformed values, the mean-sd plot will look like
```{r meansdplot, eval=TRUE, echo=FALSE, warning=FALSE, crop=NULL}
vsn::meanSdPlot(assay(se_t))
```

## MA plot

The panel displays MA plots and Hoeffding's D statistic. 

In the first part of the panel the `A` vs. `M` plots per sample are depicted.

The values are defined as follows

 - $A = \frac{1}{2} \cdot (I_i + I_j)$ and 
 - $M =  I_i−I_j$ ,
 
where $I_i$ and $I_j$  are per definition `log2`-transformed values. 
In the case of `raw`, `normalized`, or `batch corrected` the values are
`log2`-transformed prior to calculating `A` and `M`. In case of `transformed`
or `imputed` the values are taken as they are 
(N.B. when the transformation method is set to `none` the values are not 
`log2`-transformed).
   
The values for $I_i$ are taken from the sample $i$. For $I_j$, the 
feature-wise means are calculated from the values of the `group` $j$ of 
samples specified by the drop-down menu `group`. The sample for calculating 
$I_i$ is excluded from the group $j$. The group can be set to 
`"all"` (i.e. all samples except sample $i$ are used to calculate $I_j$) or 
any other column in `colData(se)`. For any group except `"all"` the group is 
taken to which the sample $i$ belongs to and the sample $i$ is excluded from 
the feature-wise calculation.

The MA values for all samples are by default displayed facet-wise. The MA plot 
can be set to a specific sample by changing the selected value in the 
drop-down menu `plot`.

The underlying data set can be selected by the drop-down menu 
(`Data set for the MA plot`).

In the second part of the panel, the Hoeffding's D statistic values are 
visualized for the different data sets `raw`, `normalized`, `batch corrected`,
`transformed`, and `imputed` (`imputed` will only be shown if there are
missing values in the `SummarizedExperiment`).

`D` is a measure of the distance between `F(A, M)` and `G(A)H(M)`, where 
`F(A, M)` is the joint cumulative distribution function (CDF) of `A` and `M`, 
and `G` and `H` are marginal CDFs. The higher the value of `D`, the more 
dependent are `A` and `M`. The `D` values are connected for the same 
samples along the different data sets (when `lines` is selected), enabling the
user to track the influence of normalization, batch correction,
transformation (and imputation) methods on the `D` values. 

The MA plot using the raw values and `group = "all"` will look like the 
following (`plot` = "Sample_1-1"`):
```{r maplot, eval=TRUE, echo = FALSE, show=FALSE, crop=NULL}
tbl <- MAvalues(se, group = "all")
MAplot(tbl, group = "all", plot = "Sample_1-1")
```

## ECDF
The plot shows the ECDF of the values of the sample 
$i$ and the feature-wise mean values of a group $j$ of samples specified 
by the drop-down menu `Group`. The sample for calculating $I_i$ is
excluded from the group $j$. The group can be set to `"all"`
(i.e. all samples except sample $i$ are used to calculate
$I_j$) or any other column in `colData(se)`. For any group except `"all"` the
group is taken to which the sample $i$ belongs to and the sample $i$ is 
excluded from the feature-wise calculation.

The underlying data set can be selected by the drop-down menu 
`Data set for the MA plot`. The sample $i$ can be selected by
the drop-down menu `Sample`. The group can be selected by 
the drop-down menu `Group`.

The ECDF plot for the sample `"Sample_1-1"`, `group = "all"`, and the 
raw values (as obtained by `assay(se)`) will look like:
```{r ecdf, eval=TRUE, echo=FALSE, crop=NULL}
ECDF(se, "Sample_1-1", group = "all")
```


## Distance matrix
On the left, the panel depicts heatmaps of distances between samples for 
the data sets of
raw (`raw`), normalized (`normalized`),
normalized+batch corrected (`batch corrected`), 
normalized+batch corrected+transformed (`transformed`), and 
normalized+batch corrected+transformed+imputed (`imputed`, 
`imputed` will only be shown if there are missing values in the 
`SummarizedExperiment`). The annotation of the heatmaps can be adjusted by 
the drop-down menu `annotation`.

On the right panel the sum of distances to other samples is depicted.

The distance matrix and sum of distances (for raw values, as obtained by
`assay(se)`) will look like:
```{r distSampe, eval=TRUE, echo=FALSE, crop=NULL}
a <- assay(se)
dist_mat <- distShiny(a)
distSample(dist_mat, se, "type")
partial_bundle(sumDistSample(dist_mat, title = "raw"))
```

## Features

The first plot shows the values for each samples along the data 
processing steps.
The feature to be displayed is selected via the drop-down menu 
**Select feature**. 

```{r featurePlot, eval=TRUE, echo=FALSE, crop=NULL}
l_assays <- list(raw = a, normalized = a_n, `batch.corrected` = a_b,
   transformed = a_t, imputed = a_i)
df_feature <- createDfFeature(l_assays, feature = rownames(se)[1])
featurePlot(df_feature)
```

The second plot shows the coefficient of variation of the values for all features
in the data set along the data processing steps. The features of same 
identity can be connected by lines by clicking on `lines`. 

```{r cvFeaturePlot, eval=TRUE, echo=FALSE, crop=NULL}
partial_bundle(cvFeaturePlot(l_assays, lines = FALSE))
```

The element in the bottom of the tab panel (`Select features`) will specify 
the selection of features in the data set (the selection will be propagated through 
all tabs):

- `all`: when selected, all features in the uploaded `SummarizedExperiment` 
object will used,
- `exclude`: when selected, the features specified in the text input field
will be excluded from the uploaded `SummarizedExperiment`,
- `select`: when selected, the features specified in the text input field 
will be selected from the uploaded `SummarizedExperiment` 
(note: a minimum of three features needs to be selected in order for the 
selection to take place).


# Tab: Dimension Reduction

Within this tab several dimension reduction plots are displayed to visualize
the level of similarity of samples of a data set: 
principal component analysis (PCA), principal coordinates analysis 
(PCoA, also known as multidimensional scaling, MDS), 
non-metric multidimensional scaling (NMDS), 
t-distributed stochastic neighbor embedding (tSNE, @vanderMaaten2008), and 
uniform manifold approximation and projection (UMAP, @McInnes2018). 
Data input for the dimension reduction plots is the `imputed` data set. 

## PCA
The panel depicts a plot of PCA. The data input can be `scale`d and 
`center`ed prior to calculating the principal components by adjusting the
respective tick marks. The different PCs can be displayed by changing the
values in the drop-down menus for the x-axis and y-axis. 

A scree plot, showing the explained variance per PC, is displayed in the 
right panel.

## PCoA
The panel depicts a plot of PCoA (= multidimensional scaling). Different distance 
measures can be used to calculate the distances between the samples 
(euclidean, maximum, manhattan, canberra, minkowski). 
The different axes of the transformed data can be displayed by changing the
values in the drop-down menus for the x-axis and y-axis. 

## NMDS
The panel depicts a plot of NMDS. Different distance 
measures can be used to calculate the distances between the samples 
(euclidean, maximum, manhattan, canberra, minkowski). 
The different axes of the transformed data can be displayed by changing the
values in the drop-down menus for the x-axis and y-axis. 

## tSNE
The panel depicts a plot of tSNE. The parameters `Perplexity`, 
`Number of iterations`, `Number of retained dimensions in initial PCA`,
and `Output dimensionality` required for the tSNE algorithm can be
set with the sliders. For the parameter
`Number of retained dimensions in initial PCA` the panel 
`Principal components` can be employed that shows on the left panel a 
Scree plot of the data set and permuted values and corresponding p-values
from the permutation (set the number of principal components where the 
explained variance is above the permuted data set/where p-values are below
0.05).

The different dimensions of the transformed data can be displayed by changing 
the values in the drop-down menus for the x-axis and y-axis (either two or 
three dimensions according to the `Output dimensionality`).  

## UMAP
The panel depicts a plot of UMAP. The parameters `Minimum distance`, 
`Number of neighbors`, and `Spread`, required for the UMAP algorithm can be
set with the sliders. 

The different dimensions of the transformed data can be displayed by changing 
the values in the drop-down menus for the x-axis and y-axis.  

# DE
This tab enables the user to test for differential expression between conditions. 

Currently, two methods/tests are implemented for calculating differential 
expression between conditions: moderated t-tests from `limma` and the
Wald test from `proDA`. The approach of `proDA` does not require imputed 
values and will take the normalized+transformed+batch corrected 
(`batch corrected`) data set as input.

The moderated t-statistic is the ratio of the M-value to its standard error, 
where the M-value is the log2-fold change for the feature of interest. 
The moderated t-statistic has the same interpretation as
an ordinary t-statistic except that the standard errors have been moderated
across features, borrowing information from the ensemble of features to aid
with inference about each individual feature [@Kammers2015]. We use the 
`eBayes` function from `limma` to compute the moderated t-statistics
 (`trend` and `robust` are set by default to `TRUE`, see `?eBayes` for 
 further information).

`proDA` [@Ahlmann2019] was developed for the differential abundance analysis
in label-free proteomics data sets. `proDA` models missing values in an 
intensity-dependent probabilistic manner based on a dropout curve 
(for further details see @Ahlmann2019).

In the input field for levels, the formula for the levels is entered.
The formula has to start with a `~` (tilde) and the `R`-specific symbolic form:

- `+` to add terms,
- `:` to denote an interaction term, 
- `*` to denote factor crossing (`a*b` is interpreted as `a+b+a:b`), `a` and `b`
   are columns in `colData(se)`,
- `-` to remove the specified term, e.g. `~ a - 1` to specify no intercept, and
   `a` a column in `colData(se)`,
- `+ 0` to alternatively specify a model without intercept.

The `colnames` of `colData` can be added as terms.  

The `colnames` of the model matrix can be used to calculate contrasts, e.g. 
`a - b` to specify the contrast between `a` and `b`. The contrasts can be 
specified in the input field in the sidebar panel.

The panels `Model matrix` and `Contrast matrix` will show the model and contrast
matrix upon correct specification of the levels and contrasts. 
The panel `Top DE` will show the differential features in a tabular format, 
while the panel `Volcano plot` will display the information of 
log fold change (for `limma`) or difference (for `proDA`) against the 
p-values (displayed as `-log10(p-value)`. 

In the following, we will look at the different panels with the
`se` input as specified above.

## Sample meta-data
The panel `Sample meta-data` will show the column data of the `se` object. The 
output will help to specify the levels for the model matrix.

```{r colData, echo=FALSE, eval=TRUE}
colData(se)
```

## Model matrix
When entering `~ treatment + 0` into the input field 
`Select levels for Model Matrix`, the `Model matrix` panel will look like
(only the first few rows are shown here):

```{r modelMatrix, echo=FALSE, eval=TRUE}
mM <- model.matrix(formula("~ treatment + 0"), data = colData(se))
head(mM)
```

## Contrast matrix
As an example, we are interested in the differential expression between 
`1_A` and `1_B`, i.e. the differential expression between treatment `A` and
`B` of the type `Type_1`. We enter `treatment1_B-treatment1_A` in the input
field `Select contast(s)`. The contrast matrix (only the first few rows 
are shown here) will then look like:

```{r contrasts, echo=FALSE, eval=TRUE, warning=FALSE, message=FALSE}
library(limma)
cM <- makeContrasts(contrasts = "treatment1_B-treatment1_A", levels = mM)
head(cM)
```


## Top DE
Switching to the panel `Top DE`, we will obtain a table with the differentially
expressed features (normalization method is set to `none`, 
transformation method to `none` and imputation method to `MinDet`). 
Here, differential expression is tested via moderated 
t-tests (from the `limma` package): 

The output will be:
```{r topDE, echo=FALSE, eval=TRUE, warning=FALSE, message=FALSE}
a <- assay(se)
a_n <- a %>% normalizeAssay(., "none")
a_t <- a_n %>% transformAssay(., "none")
a_i <- a_t %>% imputeAssay(., "MinDet")

fit <- lmFit(a_i, design = mM)
fit <- contrasts.fit(fit, contrasts = cM)
fit <- eBayes(fit, trend = TRUE, robust = TRUE)
tT <- topTable(fit, number = Inf, adjust.method = "fdr", p.value = 0.05)
rmarkdown::paged_table(tT)
```


## Volcano plot
The last panel of the tab `DE` displays the information from the differential
expression analysis. In the case of moderated t-tests, the plot shows the
log fold changes between the specified contrasts against the p-values. 
Using the afore-mentioned specification for the model matrix and the 
contrast matrix, the plot will look like:
```{r volcano, eval=TRUE, echo=FALSE, crop=NULL}
partial_bundle(volcanoPlot(tT, type = "ttest"))
```


# Appendix {-}

## Session information {-}

All software and respective versions to build this vignette are listed here:

```{r session,eval=TRUE, echo=FALSE}
sessionInfo()
```

## References

