# Performing differential co-expression analysis using dcanr

Dharmesh D Bhuva1,2

1Bioinformatics Division, Walter and Eliza Hall Institute of Medical Research, Parkville, VIC 3052, Australia
2School of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia

#### 2021-10-26

#### Package

dcanr 1.10.0

# 1 Introduction

This package provides methods to perform differential co-expression analysis and to evaluate differential co-expression methods using simulated data. Differential co-expression analysis attempts to identify gene-gene associations that change across conditions. Currently, 10 methods that identify changes between binary conditions are included: 8 are novel Bioconductor implementations of previously published methods, and; 2 are accessed through interfaces to existing packages.

This vignette focuses on the application of differential co-expression inference methods to real data. Available methods, putative pipelines, and visualisations provided by the method are introduced.

# 2 Installation

Download the package from Bioconductor

    if (!requireNamespace("BiocManager", quietly = TRUE))
      install.packages("BiocManager")
    BiocManager::install("dcanr")

Or install the development version of the package from Github.

    BiocManager::install("DavisLaboratory/dcanr")

Load the installed package into an R session.

    library(dcanr)

# 3 Available inference methods

The package implements 10 methods to infer differential co-expression networks across binary conditions. The list of available methods can be accessed by the `dcMethods()` function.

    library(dcanr)
    dcMethods()

    ##  [1] "dicer"       "diffcoex"    "ebcoexpress" "ecf"         "entropy"
    ##  [6] "ftgi"        "ggm-based"   "ldgm"        "magic"       "mindy"
    ## [11] "zscore"

# 4 A generic differential co-expression analysis pipeline

A differential co-expression pipeline generally consists of 4 steps:

1. Generating scores/statistics for each pair of genes
2. Assessing scores using statistical tests
3. Correcting for multiple hypothesis testing
4. Selecting differential associations

Not all methods follow this pipeline. EBcoexpress computes posterior probabilities therefore no statistical test needs to be performed and steps 2-3 can be skipped. Like-wise DiffCoEx does not perform any statistical tests and instead performs a soft-thresholding on the scores. FTGI performs a statistical test and \(p\)-values from this test are used as scores, therefore step 2 is skipped. A standard analysis with the z-score method using all 4 steps is shown here.

# 5 Load an example dataset (simulated)

We first load an example simulated dataset (included in the package) to extract the expression matrix and condition vector. Please note that multiple knock-down experiments are performed per simulation and we use one such knock-down as a condition here. The list of all knock-downs can be retrieved using `getConditionNames()`.

    #load data
    data(sim102)
    #get available conditions
    getConditionNames(sim102)

    ## [1] "ADR1" "UME6"

    #get expression data and conditions for 'UME6' knock-down
    simdata <- getSimData(sim102, cond.name = 'UME6', full = FALSE)
    emat <- simdata$emat
    ume6_kd <- simdata$condition
    print(emat[1:5, 1:5]) #149 genes and 406 samples

    ##       sample_1  sample_2  sample_3  sample_4   sample_5
    ## ADR1 0.4997864 0.4692072 0.3937255 0.1390989 0.05291159
    ## FLO8 0.3340156 0.2845828 0.3682575 0.2263656 0.19292056
    ## GIS1 0.3955383 0.4922471 0.5006614 0.2672858 0.48041978
    ## IME4 0.4658504 0.3529325 0.4188025 0.3824827 0.33371681
    ## KAR4 0.3705384 0.5812146 0.5282095 0.4945329 0.46677489

    head(ume6_kd) #NOTE: binary conditions encoded with 1's and 2's

    ## sample_1 sample_2 sample_3 sample_4 sample_5 sample_6
    ##        2        2        1        1        1        1

# 6 Step 1: Compute scores

All inference methods can be accessed using the same call therefore making it easier to change between methods. Method specific parameters can be passed to this function and will be managed accordingly. The default inference method is z-score therefore it does not need to be specified via `dc.method`. We recommend using the Spearman correlation as a measure of correlation as it is robust to outliers which may be present in RNA-seq data.

    #apply the z-score method with Spearman correlations
    z_scores <- dcScore(emat, ume6_kd, dc.method = 'zscore', cor.method = 'spearman')
    print(z_scores[1:5, 1:5])

    ##             ADR1        FLO8       GIS1       IME4       KAR4
    ## ADR1          NA -0.05890109  1.0645602 -0.6869672 -0.2843683
    ## FLO8 -0.05890109          NA  0.1855110  0.9256449  0.6803593
    ## GIS1  1.06456016  0.18551097         NA  0.6336496 -1.2508845
    ## IME4 -0.68696722  0.92564487  0.6336496         NA  0.4433642
    ## KAR4 -0.28436825  0.68035927 -1.2508845  0.4433642         NA

# 7 Step 2: Perform a statistical test

Appropriate statistical tests are automatically selected for the method applied. Tests are applied on the result of the `dcScore()` function (z-test for the z-score method and permutation tests for other methods). The testing function returns the score matrix (unmodified) if the method is either EBcoexpress, FTGI or DiffCoEx.

NOTE: Do NOT modify the result of the scoring method as this will result in failure of the testing function. This is intended as tests should be performed for all computed scores to prevent bias in the subsequent correction for multiple hypothesis testing. The same applies for the next step.

    #perform a statistical test: the z-test is selected automatically
    raw_p <- dcTest(z_scores, emat, ume6_kd)
    print(raw_p[1:5, 1:5])

    ##           ADR1      FLO8      GIS1      IME4      KAR4
    ## ADR1        NA 0.9530309 0.2870750 0.4921034 0.7761282
    ## FLO8 0.9530309        NA 0.8528283 0.3546306 0.4962770
    ## GIS1 0.2870750 0.8528283        NA 0.5263095 0.2109766
    ## IME4 0.4921034 0.3546306 0.5263095        NA 0.6575023
    ## KAR4 0.7761282 0.4962770 0.2109766 0.6575023        NA

For methods such as MINDy that require a permutation test, the number of permutations can be specified by the `B` parameter. Permutation tests are computationally expensive therefore we also provide a parallelised implementation. See the help page of `dcTest` for examples.

# 8 Step 3: Correcting for multiple hypothesis testing

Since all pairwise combinations of genes are tested, \(p\)-values need to be adjusted. Given \(n\) genes, the total number of hypothesis is \(\frac{n(n-1)}{2}\) as the score matrices are symmetric. Adjustment is performed accordingly. The default adjustment function is `stats::p.adjust` with the ‘fdr’ method used, however, custom functions and their parameters can be specified instead. `dcAdjust` provides a wrapper to apply an adjustment method to the raw \(p\)-value matrix. Results from EBcoexpress and DiffCoEx remain unmodified.

    #adjust p-values (raw p-values from dcTest should NOT be modified)
    adj_p <- dcAdjust(raw_p, f = p.adjust, method = 'fdr')
    print(adj_p[1:5, 1:5])

    ##           ADR1      FLO8      GIS1      IME4      KAR4
    ## ADR1        NA 0.9933963 0.8879726 0.9289498 0.9655700
    ## FLO8 0.9933963        NA 0.9748335 0.9116214 0.9289498
    ## GIS1 0.8879726 0.9748335        NA 0.9328853 0.8494282
    ## IME4 0.9289498 0.9116214 0.9328853        NA 0.9512398
    ## KAR4 0.9655700 0.9289498 0.8494282 0.9512398        NA

# 9 Step 4: Generating the differential co-expression network

The last step is thresholding the score/adjusted \(p\)-value matrix to select differential associations. Default adjusted \(p\)-value thresholds of 0.1 are applied where statistical tests are performed (to control for FDR at 0.1). Results are presented as an `igraph` object shown below where edges are coloured based on the score (negative to positive scores are represented using the purple to green gradient of colours).

    library(igraph)

    #get the differential network
    dcnet <- dcNetwork(z_scores, adj_p)
    plot(dcnet, vertex.label = '')

    #convert to an adjacency matrix
    adjmat <- as_adj(dcnet, sparse = FALSE)
    print(adjmat[1:5, 1:5])

    ##      ADR1 FLO8 GIS1 IME4 KAR4
    ## ADR1    0    0    0    0    0
    ## FLO8    0    0    0    0    0
    ## GIS1    0    0    0    0    0
    ## IME4    0    0    0    0    0
    ## KAR4    0    0    0    0    0

    #convert to a data.frame
    edgedf <- as_data_frame(dcnet, what = 'edges')
    print(head(edgedf))

    ##    from   to     score     color
    ## 1  ADR1 ACS1 -3.648617 #671F73B3
    ## 2  ADR1 CTA1 -4.399843 #40004BB3
    ## 3  ADR1 FOX2 -4.712234 #40004BB3
    ## 4  ADR1 GUT1 -5.999899 #40004BB3
    ## 5 STE12 BAR1  4.426577 #00441BB3
    ## 6  SWI5 RME1 -3.780175 #5E186AB3

# Session info

    ## R version 4.1.1 (2021-08-10)
    ## Platform: x86_64-pc-linux-gnu (64-bit)
    ## Running under: Ubuntu 20.04.3 LTS
    ##
    ## Matrix products: default
    ## BLAS:   /home/biocbuild/bbs-3.14-bioc/R/lib/libRblas.so
    ## LAPACK: /home/biocbuild/bbs-3.14-bioc/R/lib/libRlapack.so
    ##
    ## 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
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] igraph_1.2.7     dcanr_1.10.0     BiocStyle_2.22.0
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] Rcpp_1.0.7          bslib_0.3.1         compiler_4.1.1
    ##  [4] BiocManager_1.30.16 RColorBrewer_1.1-2  jquerylib_0.1.4
    ##  [7] highr_0.9           iterators_1.0.13    tools_4.1.1
    ## [10] rngtools_1.5.2      digest_0.6.28       jsonlite_1.7.2
    ## [13] evaluate_0.14       lattice_0.20-45     pkgconfig_2.0.3
    ## [16] rlang_0.4.12        doRNG_1.8.2         Matrix_1.3-4
    ## [19] foreach_1.5.1       magick_2.7.3        yaml_2.2.1
    ## [22] parallel_4.1.1      xfun_0.27           fastmap_1.1.0
    ## [25] stringr_1.4.0       knitr_1.36          sass_0.4.0
    ## [28] GlobalOptions_0.1.2 grid_4.1.1          R6_2.5.1
    ## [31] rmarkdown_2.11      bookdown_0.24       magrittr_2.0.1
    ## [34] codetools_0.2-18    htmltools_0.5.2     shape_1.4.6
    ## [37] circlize_0.4.13     colorspace_2.0-2    stringi_1.7.5