# Downstream Analyses

The goal of mpactr is to correct for errors that occur during the pre-processing of raw tandem MS/MS data. This data needs to be filtered prior to downstream analyses because of limitations in mass spectrometry detection capabilities. Once filtering is complete, you should have a feature table containing high quality MS1 features. This table can be used for a variety of analyses that can be conducted in R to better understand if and how samples differ from one another.

In this article, we will highlight just a few analyses. This is not an exhaustive list, and there are certainly other ways to conduct the analyses shown below - the beauty of R! We will walk you through how to do the following:

- creating an interactive plot of input features and the filters they failed, if any, using `ggplot` and `plotly`
- correlating sample profiles at multiple levels (sample, technical replicates, and biological replicates) using `Hmisc` and `corrplot`
- visualizing sample clustering as a dendrogram with `ggdendro`
- differential abundance analysis:
  - calculating fold change between two biological groups
  - visualizing fold change, m/z, and retention time as a 3D scatter plot
  - conducting t-tests for fold change differences, calculating p-values, and calculating q-values for false discovery rate (FDR) correction
  - visualizing significant fold change differences in a volcano plot

# Load required libraries

We will be using multiple libraries for data analysis and visualization, which can be loaded below. If you do not have some or all of the packages listed, you can install them with `install.packages("packagename")`.

    library(mpactr)
    library(viridis)
    library(plotly)
    library(data.table)
    library(tidyverse)
    library(Hmisc)
    library(corrplot)
    library(ggdendro)
    library(ggtext)

# Filter MS1 feature table with `mpactr`

    data <- import_data(example_path("cultures_peak_table.csv"),
      example_path("cultures_metadata.csv"),
      format = "Progenesis"
    )

We will be using example data in the `mpactr` package, which has 24 samples and 8 biological groups. Biological groups are: JC1, Media, JC28, ANGDT, ANG18, Coculture, Mixed_Monoculture, Solvent_Blank.

We will check our feature table for mispicked ions, remove solvent blank and media blanks features with a relative ion abundance > 0.01, relative to other groups, and check ions for replicability.

    data_filtered <- data |>
      filter_mispicked_ions(merge_peaks = TRUE, merge_method = "sum") |>
      filter_group(group_to_remove = "Solvent_Blank") |>
      filter_group(group_to_remove = "Media") |>
      filter_cv(cv_threshold = 0.2)
    #> ℹ Checking 1334 peaks for mispicked peaks.
    #> ℹ Argument merge_peaks is: TRUE. Merging mispicked peaks with method sum.
    #> ✔ 73 ions failed the mispicked filter, 1261 ions remain.
    #> ℹ Parsing 1261 peaks based on the sample group: Solvent_Blank.
    #> ℹ Argument remove_ions is: TRUE.Removing peaks from Solvent_Blank.
    #> ✔ 25 ions failed the Solvent_Blank filter, 1236 ions remain.
    #> ℹ Parsing 1236 peaks based on the sample group: Media.
    #> ℹ Argument remove_ions is: TRUE.Removing peaks from Media.
    #> ✔ 751 ions failed the Media filter, 485 ions remain.
    #> ℹ Parsing 485 peaks for replicability across technical replicates.
    #> ✔ 22 ions failed the cv_filter filter, 463 ions remain.

Overall, 463 ions remain in the feature table. A summary of the filtering, as a tree map is below:

    plot_qc_tree(data_filtered)

# Interactive scatter plot of all input ions and their fate during filtering

Visualizing each compound by m/z and retention time, and their fate during filtering may be useful to see if filters are removing features at certain retention time or m/z ranges. To create this plot, we first need to extract the raw data table, which has all pre-filtered ions (including m/z and retention time). We can do this with the mpactr function `get_raw_data()`, and then select the Compound, mz, and rt columns.

    get_raw_data(data_filtered) %>%
      select(Compound, mz, rt) %>%
      head()
    #>    Compound       mz        rt
    #>       <int>    <num>     <num>
    #> 1:        1 256.0883 0.7748333
    #> 2:        2 484.2921 0.7756667
    #> 3:        3 445.2276 0.7786667
    #> 4:        4 354.1842 0.7786667
    #> 5:        5 353.1995 0.7816667
    #> 6:        6 448.2945 0.7846667

Next, we need to extract the ion status with `mpactr` function `qc_summary()`. This function returns a `data.table` reporting the ion status for each input ion. This includes which filter each ion failed or passed, or if the ion passed all applied filters.

    qc_summary(data_filtered) %>%
      head()
    #>    status compounds
    #>    <char>    <char>
    #> 1: Passed      1000
    #> 2: Passed      1001
    #> 3: Passed      1002
    #> 4: Passed      1003
    #> 5: Passed      1004
    #> 6: Passed      1005

We can join these two `data.table`s for plotting data set:

    get_raw_data(data_filtered) %>%
      mutate(Compound = as.character(Compound)) %>%
      select(Compound, mz, rt) %>%
      left_join(qc_summary(data_filtered),
        by = join_by("Compound" == "compounds")
      ) %>%
      head()
    #>    Compound       mz        rt      status
    #>      <char>    <num>     <num>      <char>
    #> 1:        1 256.0883 0.7748333 group-Media
    #> 2:        2 484.2921 0.7756667 group-Media
    #> 3:        3 445.2276 0.7786667 group-Media
    #> 4:        4 354.1842 0.7786667 group-Media
    #> 5:        5 353.1995 0.7816667 group-Media
    #> 6:        6 448.2945 0.7846667 group-Media

Now we can create a scatter plot to show the input features (m/z ~ retention time) and their fate (status) using `ggolot` and `geom_point`.

    get_raw_data(data_filtered) %>%
      mutate(Compound = as.character(Compound)) %>%
      select(Compound, mz, rt) %>%
      left_join(qc_summary(data_filtered),
        by = join_by("Compound" == "compounds")
      ) %>%
      ggplot() +
      aes(x = rt, y = mz, color = status) +
      geom_point() +
      viridis::scale_color_viridis(discrete = TRUE) +
      labs(
        x = "Retention time (min)",
        y = "m/z",
        color = "Ion Status"
      ) +
      theme_bw() +
      theme(legend.position = "top")

We can also make the plot interactive with the `plotly` package function `ggplotly`.

    feature_plot <- get_raw_data(data_filtered) %>%
      mutate(Compound = as.character(Compound)) %>%
      select(Compound, mz, rt) %>%
      left_join(qc_summary(data_filtered),
        by = join_by("Compound" == "compounds")
      ) %>%
      ggplot() +
      aes(
        x = rt, y = mz, color = status,
        text = paste0("Compound: ", Compound)
      ) +
      geom_point() +
      viridis::scale_color_viridis(discrete = TRUE) +
      labs(
        x = "Retention time (min)",
        y = "m/z",
        color = "Ion Status"
      ) +
      theme_bw() +
      theme(legend.position = "top")

    ggplotly(feature_plot)

# Correlation between samples at different levels

We may be interested in how individual samples, or biological groups correlate to each other. For this analysis, we will need to extract the filtered feature table with `mpactr` function `get_peak_table()`. This function will return the filtered `data.table` where rows are features and columns are either compound metadata or intensity values for samples.

    ft <- get_peak_table(data_filtered)

    ft[1:5, 1:7]
    #> Key: <Compound, mz, kmd, rt>
    #>    Compound       mz     kmd       rt 102423_Blank_77_1_5095
    #>      <char>    <num>   <num>    <num>                  <num>
    #> 1:     1000 278.0638 0.06382 5.522833                      0
    #> 2:     1001 296.0736 0.07365 5.524667                      0
    #> 3:     1002 222.0751 0.07512 5.523333                      0
    #> 4:     1003 210.0771 0.07706 5.521500                      0
    #> 5:     1004 614.1282 0.12818 5.526167                      0
    #>    102423_Blank_77_2_5096 102423_Blank_77_3_5097
    #>                     <num>                  <num>
    #> 1:                      0                      0
    #> 2:                      0                      0
    #> 3:                      0                      0
    #> 4:                      0                      0
    #> 5:                      0                      0

### Correlation between each individual sample

First, we can look at the correlation between each individual sample, regardless of technical replicates and biological groups. This will show how well technical and biological replicates correlate, where we are expecting to see near perfect correlation replicates.

We will use `Hmisc::rcorr()` to perform spearman correlations. This function is expecting a `matrix` where columns are samples to correlate and rows are features. Since the feature table has columns for both feature metadata and samples, we need to remove feature metadata for `rcorr()`. We can do this by extracting sample names from the metadata `Injection` column, which match sample column names in the feature table. We also need to remove any samples that no longer have any features post-filtering (likely solvent blanks).

    counts <- ft %>%
      select(Compound, all_of(get_meta_data(data_filtered)$Injection)) %>%
      column_to_rownames(var = "Compound") %>%
      select(where(~ sum(.x) != 0))

    counts[1:5, 1:2]
    #>      102623_UM1848B_JC1_69_1_5004 102623_UM1847B_JC28_68_1_5006
    #> 1000                            0                     183612.30
    #> 1001                            0                      67698.17
    #> 1002                            0                      26108.09
    #> 1003                            0                      10467.85
    #> 1004                            0                      22165.75

Next we can run the correlation:

    counts_cor <- rcorr(as.matrix(counts), type = "spearman")

The `counts_cor` object is a list of data for the correlations. The correlation coefficients are stored in the `r` slot, and p-values in the `p` slot. We can see the correlations for first sample below

    counts_cor$r[, 1]
    #>       102623_UM1848B_JC1_69_1_5004      102623_UM1847B_JC28_68_1_5006
    #>                         1.00000000                        -0.38680057
    #>     102623_UM1850B_ANGDT_71_1_5007     102623_UM1849B_ANG18_70_1_5008
    #>                        -0.44327083                        -0.06901314
    #> 102623_UM1852B_Coculture_72_1_5009  102623_MixedMonoculture_84_1_5015
    #>                        -0.63515074                         0.20015123
    #>       102623_UM1848B_JC1_69_1_5017      102623_UM1847B_JC28_68_1_5019
    #>                         0.99850314                        -0.38586432
    #>     102623_UM1850B_ANGDT_71_1_5020     102623_UM1849B_ANG18_70_1_5021
    #>                        -0.44449167                        -0.06919162
    #> 102623_UM1852B_Coculture_72_1_5022  102623_MixedMonoculture_84_1_5028
    #>                        -0.63669267                         0.19887627
    #>       102623_UM1848B_JC1_69_1_5030      102623_UM1847B_JC28_68_1_5032
    #>                         0.99832601                        -0.38552256
    #>     102623_UM1850B_ANGDT_71_1_5033     102623_UM1849B_ANG18_70_1_5034
    #>                        -0.44384366                        -0.06919162
    #> 102623_UM1852B_Coculture_72_1_5035  102623_MixedMonoculture_84_1_5041
    #>                        -0.63785492                         0.19125997

Finally, we can plot the correlations map with `corrplot`. Style options can be customized to your liking (see corrplot).

    corrplot(counts_cor$r,
      type = "lower",
      method = "square",
      order = "hclust",
      col = COL2("BrBG", 10),
      tl.col = "black",
      tl.cex = .5
    )

### Correlation between technical replicates

Next, we can look at the correlation between technical replicates to see how they compare across the dataset. For this, we will calculate the average intensity for each compound across technical replicates and run a correlation in the same manner shown above.

In the original `counts` table, we set the row names from the column `Compound`, which holds the compound id. Here we need to reset our `Compound` column and pivot the data table for calculating averages.

    meta <- get_meta_data(data_filtered)

    counts %>%
      rownames_to_column(var = "Compound") %>%
      pivot_longer(
        cols = starts_with("102623"),
        names_to = "Injection",
        values_to = "Intensity"
      ) %>%
      head()
    #> # A tibble: 6 × 3
    #>   Compound Injection                          Intensity
    #>   <chr>    <chr>                                  <dbl>
    #> 1 1000     102623_UM1848B_JC1_69_1_5004              0
    #> 2 1000     102623_UM1847B_JC28_68_1_5006        183612.
    #> 3 1000     102623_UM1850B_ANGDT_71_1_5007         3680.
    #> 4 1000     102623_UM1849B_ANG18_70_1_5008            0
    #> 5 1000     102623_UM1852B_Coculture_72_1_5009        0
    #> 6 1000     102623_MixedMonoculture_84_1_5015     15295.

Next, we will join with sample meta data so we can calculate averages by `Sample_Code`.

    counts %>%
      rownames_to_column(var = "Compound") %>%
      pivot_longer(
        cols = starts_with("102623"),
        names_to = "Injection",
        values_to = "Intensity"
      ) %>%
      left_join(meta, by = "Injection") %>%
      head()
    #> # A tibble: 6 × 6
    #>   Compound Injection             Intensity Sample_Code Biological_Group dilution
    #>   <chr>    <chr>                     <dbl> <chr>       <chr>               <int>
    #> 1 1000     102623_UM1848B_JC1_6…        0  UM1848B     JC1                     1
    #> 2 1000     102623_UM1847B_JC28_…   183612. UM1847B     JC28                    1
    #> 3 1000     102623_UM1850B_ANGDT…     3680. UM1850B     ANGDT                   1
    #> 4 1000     102623_UM1849B_ANG18…        0  UM1849B     ANG18                   1
    #> 5 1000     102623_UM1852B_Cocul…        0  UM1852B     Coculture               1
    #> 6 1000     102623_MixedMonocult…    15295. MixedMonoc… Mixed_Monocultu…        1

Now we can calculate mean intensity for each `Compound` and `Sample_Code`.

    counts %>%
      rownames_to_column(var = "Compound") %>%
      pivot_longer(
        cols = starts_with("102623"),
        names_to = "Injection",
        values_to = "Intensity"
      ) %>%
      left_join(meta, by = "Injection") %>%
      summarise(
        mean_intensity = mean(Intensity),
        .by = c(Compound, Sample_Code)
      ) %>%
      head()
    #> # A tibble: 6 × 3
    #>   Compound Sample_Code      mean_intensity
    #>   <chr>    <chr>                     <dbl>
    #> 1 1000     UM1848B                      0
    #> 2 1000     UM1847B                 182682.
    #> 3 1000     UM1850B                   3762.
    #> 4 1000     UM1849B                      0
    #> 5 1000     UM1852B                      0
    #> 6 1000     MixedMonoculture         14130.

Finally, we need to reformat the table so columns are sample codes for the correlation.

    sample_counts <- counts %>%
      rownames_to_column(var = "Compound") %>%
      pivot_longer(
        cols = starts_with("102623"),
        names_to = "Injection",
        values_to = "Intensity"
      ) %>%
      left_join(meta, by = "Injection") %>%
      summarise(
        mean_intensity = mean(Intensity),
        .by = c(Compound, Sample_Code)
      ) %>%
      pivot_wider(
        names_from = Sample_Code,
        values_from = mean_intensity
      ) %>%
      column_to_rownames(var = "Compound")

    sample_counts[1:5, 1:5]
    #>      UM1848B   UM1847B  UM1850B UM1849B UM1852B
    #> 1000       0 182681.78 3762.133       0       0
    #> 1001       0  69643.45 6540.170       0       0
    #> 1002       0  25588.00 3730.070       0       0
    #> 1003       0  10424.57    0.000       0       0
    #> 1004       0  23216.59 1724.140       0       0

Run the correlation:

    sample_counts_cor <- rcorr(as.matrix(sample_counts), type = "spearman")

And finally visualize:

    corrplot(sample_counts_cor$r,
      type = "lower",
      method = "square",
      order = "alphabet",
      col = COL2("BrBG", 10),
      tl.col = "black"
    )

### Correlation between biological replicates

We can also look at the correlation between biological groups. In this dataset, technical replicates and biological groups are the same; however if you have multiple technical replicates you may also be interested in the correlation between biological groups. We will calculate mean intensity values for `Biological_Group` in the same manner as we did for `Sample_Code`.

    group_counts <- counts %>%
      rownames_to_column(var = "Compound") %>%
      pivot_longer(
        cols = starts_with("102623"),
        names_to = "Injection",
        values_to = "Intensity"
      ) %>%
      left_join(meta, by = "Injection") %>%
      summarise(
        mean_intensity = mean(Intensity),
        .by = c(Compound, Biological_Group)
      ) %>%
      pivot_wider(
        names_from = Biological_Group,
        values_from = mean_intensity
      ) %>%
      column_to_rownames(var = "Compound")

Run the correlation analysis with `rcorr()`:

    group_counts_cor <- rcorr(as.matrix(group_counts), type = "spearman")

Visualize correlation:

    corrplot(group_counts_cor$r,
      type = "lower",
      method = "square",
      order = "alphabet",
      col = COL2("BrBG", 10),
      tl.col = "black"
    )

As expected, the biological group correlation matrix matches the technical replicates correlation.

# Dendrogram

You may be interested in visualizing how similar samples are with a dendrogram. For this we will need to calculate the distance between samples with `stats::dist()`, cluster with `hclust()`, and visualize with `ggplot` and `ggdendro` packages.

First, calculate distance and cluster:

    dist <- stats::dist(t(counts), method = "euclidian")
    cluster <- stats::hclust(dist, method = "complete")

Calculate dendrogram components with `stats::as.dendrogram()`:

    dendro <- as.dendrogram(cluster)

Extract plotting elements with `ggdendrogram::dendro_data()`

    den_data <- dendro_data(dendro, type = "rectangle")

Use `ggplot` and `ggdendrogram` to plot the dendrogram. For more customizations, see ggdendro documentation.

    ggplot(segment(den_data)) +
      geom_segment(aes(x = x, y = y, xend = xend, yend = yend)) +
      geom_text(
        data = den_data$labels,
        aes(x = x, y = y, label = label),
        size = 3,
        hjust = "outward"
      ) +
      coord_cartesian(ylim = c((min(segment(den_data)$y) + 10),
                               (max(segment(den_data)$y)))) +
      coord_flip() +
      scale_y_reverse(expand = c(.5, 0)) +
      theme_dendro()
    #> Coordinate system already present. Adding new coordinate system, which will
    #> replace the existing one.

# Fold change analysis

Say we wanted to compare metabolite profiles between our Coculture and ANG18 groups. We can extract group means from the filtered compounds using the mpactr function `get_group_averages()`, isolate the groups of interest, here Coculture and ANG18 monocoluture, and calculate compound fold change.

### Calculate fold change

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      mutate(fc = Coculture / ANG18) %>%
      head()
    #> # A tibble: 6 × 4
    #>   Compound ANG18 Coculture    fc
    #>   <chr>    <dbl>     <dbl> <dbl>
    #> 1 1000         0         0   NaN
    #> 2 1001         0         0   NaN
    #> 3 1002         0         0   NaN
    #> 4 1003         0         0   NaN
    #> 5 1004         0         0   NaN
    #> 6 1005         0         0   NaN

Inherently, tandem MS/MS datasets can be filled with many zeros. In some instances a compound is found in the experimental group but not in the control group, or vice versa. In these cases, the fold change calculation yields an infinite number as there is a zero either in the numerator or denominator (\(fold change = experimental / control\)). There is also the chance that the compound is not found in either group, yielding a fold change on NaN (0/0).

Compounds that are not in either group are of no interest in this comparison and can therefore be removed from the analysis.

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      mutate(nonzero_compound = if_else(Coculture == 0 & ANG18 == 0,
                                        FALSE,
                                        TRUE)) %>%
      filter(nonzero_compound == TRUE) %>%
      mutate(fc = Coculture / ANG18) %>%
      head()
    #> # A tibble: 6 × 5
    #>   Compound ANG18 Coculture nonzero_compound    fc
    #>   <chr>    <dbl>     <dbl> <lgl>            <dbl>
    #> 1 1007        0      8929. TRUE               Inf
    #> 2 1023        0      6117. TRUE               Inf
    #> 3 1024        0     11317. TRUE               Inf
    #> 4 103         0      5152. TRUE               Inf
    #> 5 1040      669.        0  TRUE                 0
    #> 6 105         0     16501. TRUE               Inf

There are multiple ways to handle compounds that are found in the one group but not the other. Here we will create pseudo-counts by adding a small number (0.001) to all counts prior to calculating fold change. This will alleviate division by 0.

First, extract group averages from the `mpactr` object and select the two groups of interest. Here we are interested in the columns Coculture and ANG18:

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      head()
    #>    Compound Biological_Group average
    #>      <char>           <char>   <num>
    #> 1:     1000            ANG18       0
    #> 2:     1000        Coculture       0
    #> 3:     1001            ANG18       0
    #> 4:     1001        Coculture       0
    #> 5:     1002            ANG18       0
    #> 6:     1002        Coculture       0

To calculate fold change, we need to have two columns: one for the control group, here ANG18, and one for the experimental group, Coculture:

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      head()
    #>    Compound Biological_Group average
    #>      <char>           <char>   <num>
    #> 1:     1000            ANG18       0
    #> 2:     1000        Coculture       0
    #> 3:     1001            ANG18       0
    #> 4:     1001        Coculture       0
    #> 5:     1002            ANG18       0
    #> 6:     1002        Coculture       0

Now we create pseudo-counts by adding 0.001 to the counts column:

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      mutate(average = average + 0.001) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      head()
    #> # A tibble: 6 × 3
    #>   Compound ANG18 Coculture
    #>   <chr>    <dbl>     <dbl>
    #> 1 1000     0.001     0.001
    #> 2 1001     0.001     0.001
    #> 3 1002     0.001     0.001
    #> 4 1003     0.001     0.001
    #> 5 1004     0.001     0.001
    #> 6 1005     0.001     0.001

Now we can remove compounds with an intensity of 0 in both groups. This equates to a pseudo-count of 0.001:

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      mutate(average = average + 0.001) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      mutate(nonzero_compound = if_else(Coculture == 0.001 & ANG18 == 0.001,
                                        FALSE,
                                        TRUE)) %>%
      filter(nonzero_compound == TRUE) %>%
      head()
    #> # A tibble: 6 × 4
    #>   Compound   ANG18 Coculture nonzero_compound
    #>   <chr>      <dbl>     <dbl> <lgl>
    #> 1 1007       0.001  8929.    TRUE
    #> 2 1023       0.001  6117.    TRUE
    #> 3 1024       0.001 11317.    TRUE
    #> 4 103        0.001  5152.    TRUE
    #> 5 1040     669.        0.001 TRUE
    #> 6 105        0.001 16501.    TRUE

Next, we calculate fold change for all remaining compounds:

    get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      mutate(average = average + 0.001) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      mutate(nonzero_compound = if_else(Coculture == 0.001 & ANG18 == 0.001,
                                        FALSE,
                                        TRUE)) %>%
      filter(nonzero_compound == TRUE) %>%
      mutate(fc = Coculture / ANG18) %>%
      head()
    #> # A tibble: 6 × 5
    #>   Compound   ANG18 Coculture nonzero_compound      fc
    #>   <chr>      <dbl>     <dbl> <lgl>              <dbl>
    #> 1 1007       0.001  8929.    TRUE             8.93e+6
    #> 2 1023       0.001  6117.    TRUE             6.12e+6
    #> 3 1024       0.001 11317.    TRUE             1.13e+7
    #> 4 103        0.001  5152.    TRUE             5.15e+6
    #> 5 1040     669.        0.001 TRUE             1.49e-6
    #> 6 105        0.001 16501.    TRUE             1.65e+7

Finally, transform fold change to log2:

    foldchanges <- get_group_averages(data_filtered) %>%
      filter(Biological_Group == "Coculture" |
               Biological_Group == "ANG18") %>%
      select(Compound, Biological_Group, average) %>%
      mutate(average = average + 0.001) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      mutate(nonzero_compound = if_else(Coculture == 0.001 & ANG18 == 0.001,
                                        FALSE,
                                        TRUE)) %>%
      filter(nonzero_compound == TRUE) %>%
      mutate(fc = Coculture / ANG18,
             logfc = log2(fc))

    head(foldchanges)
    #> # A tibble: 6 × 6
    #>   Compound   ANG18 Coculture nonzero_compound      fc logfc
    #>   <chr>      <dbl>     <dbl> <lgl>              <dbl> <dbl>
    #> 1 1007       0.001  8929.    TRUE             8.93e+6  23.1
    #> 2 1023       0.001  6117.    TRUE             6.12e+6  22.5
    #> 3 1024       0.001 11317.    TRUE             1.13e+7  23.4
    #> 4 103        0.001  5152.    TRUE             5.15e+6  22.3
    #> 5 1040     669.        0.001 TRUE             1.49e-6 -19.4
    #> 6 105        0.001 16501.    TRUE             1.65e+7  24.0

### Visualize fold change for compounds in a 3D scatter plot

We can then probe compounds by plotting a 3D scatter plot of log2 fold changes as a function of m/z and retention time:

    fc_plotting <- foldchanges %>%
      left_join(select(ft, Compound, mz, rt), by = "Compound")

    plot_ly(fc_plotting,
      x = ~logfc, y = ~rt, z = ~mz,
      marker = list(color = ~logfc, showscale = TRUE)
    ) %>%
      add_markers() %>%
      layout(
        scene = list(
          xaxis = list(title = "log2 Fold Change"),
          yaxis = list(title = "Retention Time (min)"),
          zaxis = list(title = "m/z")
        ),
        annotations = list(
          x = 1.13,
          y = 1.05,
          text = "log2 Fold Change",
          xref = "paper",
          yref = "paper",
          showarrow = FALSE
        )
      )

### Test for compounds with significant fold changes

For the t-tests, we have already calculated variation for compounds within biological groups as well as within technical replicates in biological groups. We can calculate the t statistic and degrees of freedom and use the t distribution (`pt()`) to calculate the p-value.

combine biological and technical variation and calculate sample size

    # Satterwaite
    calc_samplesize_ws <- function(sd1, n1, sd2, n2) {
      s1 <- sd1 / (n1^0.5)
      s2 <- sd2 / (n2^0.5)

      n <- (s1^2 / n1 + s2^2 / n2)^2
      d1 <- s1^4 / ((n1^2) * (n1 - 1))
      d2 <- s2^4 / ((n2^2) * (n2 - 1))

      d1[which(!is.finite(d1))] <- 0
      d2[which(!is.finite(d2))] <- 0

      d <- d1 + d2

      return(n / d)
    }

    my_comp <- c("Coculture", "ANG18")

    stats <- get_group_averages(data_filtered) %>%
      mutate(
        combRSD = sqrt(techRSD^2 + BiolRSD^2),
        combASD = combRSD * average,
        combASD = if_else(is.na(combASD), 0, combASD),
        BiolRSD = if_else(is.na(BiolRSD), 0, BiolRSD),
        techRSD = if_else(is.na(techRSD), 0, techRSD),
        neff = calc_samplesize_ws(techRSD, techn, BiolRSD, Bioln) + 1
      ) %>%
      filter(Biological_Group %in% my_comp)

    head(stats)
    #>    Compound Biological_Group average BiolRSD Bioln techRSD techn combRSD
    #>      <char>           <char>   <num>   <num> <int>   <num> <num>   <num>
    #> 1:     1000            ANG18       0       0     3       0     3      NA
    #> 2:     1000        Coculture       0       0     3       0     3      NA
    #> 3:     1001            ANG18       0       0     3       0     3      NA
    #> 4:     1001        Coculture       0       0     3       0     3      NA
    #> 5:     1002            ANG18       0       0     3       0     3      NA
    #> 6:     1002        Coculture       0       0     3       0     3      NA
    #>    combASD  neff
    #>      <num> <num>
    #> 1:       0   NaN
    #> 2:       0   NaN
    #> 3:       0   NaN
    #> 4:       0   NaN
    #> 5:       0   NaN
    #> 6:       0   NaN

calculate the t statistic

    denom <- stats %>%
      summarise(den = combASD^2 / (neff),
                .by = c("Compound", "Biological_Group")) %>%
      mutate(den = if_else(!is.finite(den), 0, den)) %>%
      summarise(denom = sqrt(sum(den)), .by = c("Compound"))

    t_test <- stats %>%
      select(Compound, Biological_Group, average) %>%
      pivot_wider(names_from = Biological_Group, values_from = average) %>%
      mutate(numerator = (Coculture - ANG18)) %>% # experimental - control
      left_join(denom, by = "Compound") %>%
      mutate(t = abs(numerator / denom))

    head(t_test)
    #> # A tibble: 6 × 6
    #>   Compound ANG18 Coculture numerator denom     t
    #>   <chr>    <dbl>     <dbl>     <dbl> <dbl> <dbl>
    #> 1 1000         0         0         0     0   NaN
    #> 2 1001         0         0         0     0   NaN
    #> 3 1002         0         0         0     0   NaN
    #> 4 1003         0         0         0     0   NaN
    #> 5 1004         0         0         0     0   NaN
    #> 6 1005         0         0         0     0   NaN

calculate degrees of freedom

    df <- stats %>%
      select(Compound, Biological_Group, neff) %>%
      mutate(neff = if_else(!is.finite(neff), 0, neff)) %>%
      pivot_wider(names_from = Biological_Group, values_from = neff) %>%
      mutate(deg = Coculture + ANG18 - 2) %>%
      select(Compound, deg)

    head(df)
    #> # A tibble: 6 × 2
    #>   Compound   deg
    #>   <chr>    <dbl>
    #> 1 1000        -2
    #> 2 1001        -2
    #> 3 1002        -2
    #> 4 1003        -2
    #> 5 1004        -2
    #> 6 1005        -2

calculate p-value

    t <- t_test %>%
      left_join(df, by = "Compound") %>%
      mutate(
        p = (1 - pt(t, deg)) * 2,
        logp = log10(p),
        neg_logp = -logp
      ) %>%
      select(Compound, t, deg, p, logp, neg_logp)

    head(t)
    #> # A tibble: 6 × 6
    #>   Compound     t   deg     p  logp neg_logp
    #>   <chr>    <dbl> <dbl> <dbl> <dbl>    <dbl>
    #> 1 1000       NaN    -2   NaN   NaN      NaN
    #> 2 1001       NaN    -2   NaN   NaN      NaN
    #> 3 1002       NaN    -2   NaN   NaN      NaN
    #> 4 1003       NaN    -2   NaN   NaN      NaN
    #> 5 1004       NaN    -2   NaN   NaN      NaN
    #> 6 1005       NaN    -2   NaN   NaN      NaN

combine t-test results with fold changes we calculated

    num_ions <- t %>%
      filter(p <= 1) %>%
      count() %>%
      pull()

    fc <- foldchanges %>%
      left_join(t, by = "Compound") %>%
      arrange(p) %>%
      mutate(
        qval = seq_len(length(p)),
        qval = p * num_ions / qval
      ) %>%
      arrange(desc(p))

    min_qval <- 1

    for (i in seq_len(nrow(fc))) {
      if (!is.finite(fc$qval[i])) {
        next
      }

      if (fc$qval[i] < min_qval) {
        min_qval <- fc$qval[i]
      } else {
        fc$qval[i] <- min_qval
      }
    }

    fc2 <- fc %>%
      mutate(neg_logq = -log10(qval))

### Volcano plot

Now we can create a volcano plot to see the magnitude of metabolite abundance differences between the Cocoulture and ANG18 groups.

We can plot log2 fold change values against log10 p-values or log10 q-values, both of which we calculated in our t-tests above.

log2 fold change ~ log10 p-values

The base of a volcano plot is a scatter plot with log2 fold changes on the x axis and -log10 p-values on the y axis:

    fc2 %>%
      ggplot() +
      aes(x = logfc, y = neg_logp) +
      geom_point() +
      labs(x = "log2 Fold Change",
           y = "-Log~10~ *P*",
           color = "Differential Abundance") +
      theme_bw()

This is good, but we probably want to know which compounds are above the p-value threshold and outside the log2 fold change threshold. Fold change threshold commonly ranges from 1.5 - 2. For this plot, we will show a p-value threshold of 0.05 and fold change threshold of 1.5.

First add a horizontal line to denote the cutoff of -log10 0.05:

    fc2 %>%
      ggplot() +
      aes(x = logfc, y = neg_logp) +
      geom_point() +
      geom_hline(yintercept = -log10(0.05), linetype = "dashed") +
      labs(x = "log2 Fold Change",
           y = "-Log~10~ *P*",
           color = "Differential Abundance") +
      theme_bw()

Now we can add vertical lines showing the positive and negative cutoffs for log2 fold change:

    fc2 %>%
      ggplot() +
      aes(x = logfc, y = neg_logp) +
      geom_point() +
      geom_hline(yintercept = -log10(0.05), linetype = "dashed") +
      labs(x = "log2 Fold Change",
           y = "-Log~10~ *P*",
           color = "Differential Abundance") +
      geom_vline(xintercept = log2(1.5), linetype = "dashed") +
      geom_vline(xintercept = -log2(1.5), linetype = "dashed") +
      theme_bw()

So now we can see the thresholds, but it’s difficult to make out which compounds have significant fold change values. It would be nice to color the compounds by their significance. Specifically, compounds whose intensity are significantly higher in the experimental group, compounds whose intensity are significantly lower in the experimental group, compounds with significant p-values but the fold change is below the fold change threshold, and compounds whose fold change are not significant.

We can do this by adding a new variable to our dataset and using this variable to color our points.

First, add a new variable `sig` which has values `Increased` (fold change > 1.5 & pvalue < 0.05), `Decreased` (fold change < -1.5 & pvalue < 0.05), `Inconclusive` (fold change -1.5 - 1.5 & pvalue < 0.05), and `not_sig` (pvalue > 0.05).

    fc2 %>%
      mutate(
        sig = case_when(
          p > 0.05 ~ "not_sig",
          p <= 0.05 & logfc > log2(1.5) ~ "Increased",
          p <= 0.05 & logfc < -log2(1.5) ~ "Decreased",
          TRUE ~ "Inconclusive"
        ),
        sig = factor(sig,
          levels = c("Increased", "Decreased", "Inconclusive", "not_sig"),
          labels = c("Increased", "Decreased", "Inconclusive", "Not significant")
        )
      ) %>%
      select(Compound, ANG18, Coculture, fc, logfc, p, sig) %>%
      head()
    #> # A tibble: 6 × 7
    #>   Compound    ANG18 Coculture      fc   logfc       p sig
    #>   <chr>       <dbl>     <dbl>   <dbl>   <dbl>   <dbl> <fct>
    #> 1 637      2174.     2022.    9.30e-1  -0.105 0.458   Not significant
    #> 2 699         0.001 38505.    3.85e+7  25.2   0.00420 Increased
    #> 3 1094      988.        0.001 1.01e-6 -19.9   0.00388 Decreased
    #> 4 597         0.001  5907.    5.91e+6  22.5   0.00388 Increased
    #> 5 782         0.001  6250.    6.25e+6  22.6   0.00374 Increased
    #> 6 664         0.001  4263.    4.26e+6  22.0   0.00348 Increased

Now we can set the color aesthetic to the variable `sig` and select custom colors with `scale_color_manual()`:

    fc2 %>%
      mutate(
        sig = case_when(
          p > 0.05 ~ "not_sig",
          p <= 0.05 & logfc > log2(1.5) ~ "Increased",
          p <= 0.05 & logfc < -log2(1.5) ~ "Decreased",
          TRUE ~ "Inconclusive"
        ),
        sig = factor(sig,
          levels = c("Increased", "Decreased", "Inconclusive", "not_sig"),
          labels = c("Increased", "Decreased", "Inconclusive", "Not significant")
        )
      ) %>%
      ggplot() +
      aes(x = logfc, y = neg_logp, color = sig) +
      geom_point() +
      geom_hline(yintercept = -log10(0.05), linetype = "dashed") +
      geom_vline(xintercept = log2(1.5), linetype = "dashed") +
      geom_vline(xintercept = -log2(1.5), linetype = "dashed") +
      scale_color_manual(values = c("red", "blue", "grey", "black")) +
      labs(
        x = "log2 Fold Change",
        y = "-Log~10~ *P*",
        color = "Differential Abundance"
      ) +
      theme_bw()

Finally, adjust axis text and titles to your liking:

    fc2 %>%
      mutate(
        sig = case_when(
          p > 0.05 ~ "not_sig",
          p <= 0.05 & logfc > log2(1.5) ~ "Increased",
          p <= 0.05 & logfc < -log2(1.5) ~ "Decreased",
          TRUE ~ "Inconclusive"
        ),
        sig = factor(sig,
          levels = c("Increased", "Decreased", "Inconclusive", "not_sig"),
          labels = c("Increased", "Decreased", "Inconclusive", "Not significant")
        )
      ) %>%
      ggplot() +
      aes(x = logfc, y = neg_logp, color = sig) +
      geom_point() +
      geom_hline(yintercept = -log10(0.05), linetype = "dashed") +
      geom_vline(xintercept = log2(1.5), linetype = "dashed") +
      geom_vline(xintercept = -log2(1.5), linetype = "dashed") +
      scale_color_manual(values = c("red", "blue", "grey", "black")) +
      labs(
        x = "log2 Fold Change",
        y = "-Log~10~ *P*",
        color = "Differential Abundance"
      ) +
      theme_bw() +
      theme(
        axis.title = element_markdown(size = 20),
        axis.text = element_text(size = 15)
      )

We can also make the plot interactive, showing the compound id for each point:

    volcano <- fc2 %>%
      mutate(
        sig = case_when(
          p > 0.05 ~ "not_sig",
          p <= 0.05 & logfc > log2(1.5) ~ "Increased",
          p <= 0.05 & logfc < -log2(1.5) ~ "Decreased",
          TRUE ~ "Inconclusive"
        ),
        sig = factor(sig,
          levels = c("Increased", "Decreased", "Inconclusive", "not_sig"),
          labels = c("Increased", "Decreased", "Inconclusive", "Not significant")
        )
      ) %>%
      ggplot() +
      aes(
        x = logfc, y = neg_logp, color = sig,
        text = paste0("Compound: ", Compound)
      ) +
      geom_point() +
      geom_hline(yintercept = -log10(0.05), linetype = "dashed") +
      geom_vline(xintercept = log2(1.5), linetype = "dashed") +
      geom_vline(xintercept = -log2(1.5), linetype = "dashed") +
      scale_color_manual(values = c("red", "blue", "grey", "black")) +
      labs(
        x = "log2 Fold Change",
        y = "-Log~10~ *P*",
        color = "Differential Abundance"
      ) +
      theme_bw() +
      theme(
        axis.title = element_markdown(size = 20),
        axis.text = element_text(size = 15)
      )

    ggplotly(volcano)

log2 fold change ~ log10 q-values

You can also look at the volcano plot with the q value to control for false discovery rate (FDR) using the same approach shown for p values:

    fc2 %>%
      mutate(
        sig = case_when(
          qval > 0.05 ~ "not_sig",
          qval <= 0.05 & logfc > log2(1.5) ~ "Increased",
          qval <= 0.05 & logfc < -log2(1.5) ~ "Decreased",
          TRUE ~ "Inconclusive"
        ),
        sig = factor(sig,
          levels = c("Increased", "Decreased", "Inconclusive", "not_sig"),
          labels = c("Increased", "Decreased", "Inconclusive", "Not significant")
        )
      ) %>%
      ggplot() +
      aes(x = logfc, y = neg_logq, color = sig) +
      geom_point() +
      geom_hline(yintercept = -log10(0.05), linetype = "dashed") +
      geom_vline(xintercept = log2(1.5), linetype = "dashed") +
      geom_vline(xintercept = -log2(1.5), linetype = "dashed") +
      scale_color_manual(values = c("red", "blue", "grey", "black")) +
      labs(
        x = "log2 Fold Change",
        y = "-Log~10~ q-value",
        color = "Differential Abundance"
      ) +
      theme_bw() +
      theme(
        axis.title = element_markdown(size = 20),
        axis.text = element_text(size = 15)
      )