The volcano3D package provides a tool for analysis of three-class high dimensional data. It enables exploration of genes differentially expressed between three groups. Its main purpose is for the visualisation of differentially expressed genes in a three-dimensional volcano plot or three-way polar plot. These plots can be converted to interactive visualisations using plotly. The 3-way polar plots and 3d volcano plots can be applied to any data in which multiple attributes have been measured and their relative levels are being compared across three classes.

This vignette covers the basic features of the package using a small example data set. To explore more extensive examples and view the interactive radial and volcano plots, see the extended vignette which explores a case study from the PEAC rheumatoid arthritis trial (Pathobiology of Early Arthritis Cohort). The methodology has been published in Lewis, Myles J., et al. Molecular portraits of early rheumatoid arthritis identify clinical and treatment response phenotypes. Cell reports 28.9 (2019): 2455-2470. (DOI: 10.1016/j.celrep.2019.07.091) with an interactive, searchable web tool available at https://peac.hpc.qmul.ac.uk. This was creating as an R Shiny app and deployed to the web using a server.

There are also supplementary vignettes with further information on:

Lifecycle: Stable License: GPL v2 CRAN status Downloads 2023-05-17 Build GitHub issues

Getting Started


Install from CRAN

CRAN status


Install from Github

GitHub tag


Load the package



This vignette uses a subset of the 500 genes from the PEAC dataset to explore the package functions. This can be loaded using:


Which contains:

  • syn_example_rld - the log transformed expression data

  • syn_example_meta which contains sample information and divides the samples into 3 classes.

Samples in this cohort fall into three histological ‘pathotype’ groups:

kable(table(syn_example_meta$Pathotype), col.names = c("Pathotype", "Count"))
Pathotype Count
Lymphoid 45
Myeloid 20
Fibroid 16

These will be used as the differential expression classes for the three-way analysis.

Creating Polar Coordinates

The function polar_coords() is used to map attributes to polar coordinates. If you have RNA-Seq count data this step can be skipped and you can use functions deseq_polar() or voom_polar() instead (see Gene Expression pipeline).

polar_coords accepts raw data and performs all the calculations needed to generate coordinates, colours etc for plotting either a 3d volcano plot or radial 3-way plot. In brief, the function calculates the mean of each attribute/ variable for each group and maps the mean level per group onto polar coordinates along 3 axes in the x-y plane. The z axis is plotted as -log10(p-value) of the group statistical test (e.g. likelihood ratio test, one-way ANOVA or Kruskal-Wallis test).

A table of p-values can be supplied by the user (see table below for formatting requirements). If a table of p-values is absent, p-values are automatically calculated by polar_coords(). By default one-way ANOVA is used for the group comparison and t-tests are used for pairwise tests.

polar_coords() has the following inputs:

Variable Details


Vector containing three-level factor indicating which of the three classes each sample belongs to.


A dataframe or matrix containing data to be compared between the three classes (e.g. gene expression data). Note that variables are in columns, so gene expression data will need to be transposed. This is used to calculate z-score and fold change, so for gene expression count data it should be normalised such as log transformed or variance stabilised count transformation.



the pvals matrix which contains the statistical significance of probes or attributes between classes. This contains:

  • the first column is a group test such as one-way ANOVA or Kruskal-Wallis test.

  • columns 2-4 contain p-values one for each comparison in the sequence A vs B, A vs C, B vs C, where A, B, C are the three levels in sequence in the outcome factor. For gene expression RNA-Seq count data, conduit functions using ‘limma voom’ or ‘DESeq’ pipelines to extract p-values for analysis are provided in functions deseq_polar() and voom_polar(). If p-values are not provided by the user, they can be calculated via the polar_coords() function.


Matrix containing the adjusted p-values matching the pvals matrix.
pcutoff Cut-off for p-value significance
scheme Vector of colours starting with non-significant attributes
labs Optional character vector for labelling classes. Default NULL leads to abbreviated labels based on levels in outcome using abbreviate(). A vector of length 3 with custom abbreviated names for the outcome levels can be supplied. Otherwise a vector length 7 is expected, of the form “ns”, “B+”, “B+C+”, “C+”, “A+C+”, “A+”, “A+B+”, where “ns” means non-significant and A, B, C refer to levels 1, 2, 3 in outcome, and must be in the correct order.

This can be applied to the example data as below:


syn_polar <- polar_coords(outcome = syn_example_meta$Pathotype,
                          data = t(syn_example_rld))

This creates a ‘volc3d’ class object for downstream plotting.

Gene expression pipeline

RNA-Sequencing gene expression count data can be compared for differentially expressed genes between 3 classes using 2 pipeline functions to allow statistical analysis by Bioconductor packages ‘DESeq2’ and ‘limma voom’ to quickly generate a polar plotting object of class ‘volc3d’ which can be plotted either as a 2d polar plot with 3 axes or as a 3d cylindrical plot with a 3d volcano plot.

Two functions deseq_polar() and voom_polar() are available. They both take RNA-Seq count data objects as input and extract correct statistical results and then internally call polar_coords() to create a ‘volc3d’ class object which can be plotted straightaway.

Method using DESeq2

This takes 2 DESeqDataSet objects and converts the results to a ‘volc3d’ class object for plotting. object is an object of class ‘DESeqDataSet’ with the full design formula. Note the function DESeq needs to have been previously run on this object. objectLRT is an object of class ‘DESeqDataSet’ with the reduced design formula. The function DESeq needs to have been run on this object with DESeq argument test="LRT".

Note that in the DESeq2 design formula, the 3-class variable of interest should be first.


# setup initial dataset from Tximport
dds <- DESeqDataSetFromTximport(txi = syn_txi, 
                               colData = syn_metadata, 
                               design = ~ Pathotype + Batch + Gender)
# initial analysis run
dds_DE <- DESeq(dds)
# likelihood ratio test on 'Pathotype'
dds_LRT <- DESeq(dds, test = "LRT", reduced = ~ Batch + Gender, parallel = TRUE) 

# create 'volc3d' class object for plotting
res <- deseq_polar(dds_DE, dds_LRT, "Pathotype")

# plot 3d volcano plot

Method using limma voom

The method for limma voom is faster and takes a design formula, metadata and raw count data. The Bioconductor packages ‘limma’ and ‘edgeR’ are used to analyse the data using the ‘voom’ method. The results are converted to a ‘volc3d’ object ready for plotting a 3d volcano plot or 3-way polar plot.

Note the design formula must be of the form ~ 0 + outcome + .... The 3-class outcome variable must be the first variable after the ‘0’, and this variable must be a factor with exactly 3 levels.


syn_tpm <- syn_txi$counts  # raw counts

resl <- voom_polar(~ 0 + Pathotype + Batch + Gender, syn_metadata, syn_tpm)


Radial Plots

The differential expression can now be visualised on an interactive radial plot using radial_plotly.


Unfortunately CRAN does not support interactive plotly in the vignette, but these can be viewed on the extended vignette. When interactive, it is possible to identify genes for future interrogation by hovering over certain markers.

radial_plotly produces an SVG based plotly object by default. With 10,000s of points SVG can be slow, so for large number of points we recommend switching to webGL by piping the plotly object to toWebGL().

radial_plotly(syn_polar) %>% toWebGL()

A very similar looking static ggplot image can be created using radial_ggplot:

              marker_size = 2.3,
              legend_size = 10) +
  theme(legend.position = "right")