`waddR`

packageThe `waddR`

package offers statistical tests based on the 2-Wasserstein distance for detecting and characterizing differences between two distributions given in the form of samples. Functions for calculating the 2-Wasserstein distance and testing for differential distributions are provided, as well as a specifically tailored test for differential expression in single-cell RNA sequencing data.

`waddR`

provides tools to address the following tasks, each described in a separate vignette:

Two-sample tests to check for differences between two distributions,

Detection of differential gene expression distributions in single-cell RNA sequencing (scRNAseq) data.

These are bundled into one package, because they are internally dependent: The procedure for detecting differential distributions in scRNAseq data is an adaptation of the general two-sample test, which itself uses the 2-Wasserstein distance to compare two distributions.

The 2-Wasserstein distance is a metric to describe the distance between two distributions, representing e.g. two diferent conditions \(A\) and \(B\). The `waddR`

package specifically considers the squared 2-Wasserstein distance which can be decomposed into location, size, and shape terms, thus providing a characterization of potential differences.

The `waddR`

package offers three functions to calculate the (squared) 2-Wasserstein distance, which are implemented in C++ and exported to R with Rcpp for faster computation. The function `wasserstein_metric`

is a Cpp reimplementation of the `wasserstein1d`

function from the R package `transport`

. The functions `squared_wass_approx`

and `squared_wass_decomp`

compute approximations of the squared 2-Wasserstein distance, with `squared_wass_decomp`

also returning the decomposition terms for location, size, and shape.

See `?wasserstein_metric`

, `?squared_wass_aprox`

, and `?squared_wass_decomp`

for more details.

The `waddR`

package provides two testing procedures using the 2-Wasserstein distance to test whether two distributions \(F_A\) and \(F_B\) given in the form of samples are different by testing the null hypothesis \(H_0: F_A = F_B\) against the alternative hypothesis \(H_1: F_A != F_B\).

The first, semi-parametric (SP), procedure uses a permutation-based test combined with a generalized Pareto distribution approximation to estimate small p-values accurately.

The second procedure uses a test based on asymptotic theory (ASY) which is valid only if the samples can be assumed to come from continuous distributions.

See `?wasserstein.test`

for more details.

The `waddR`

package provides an adaptation of the semi-parametric testing procedure based on the 2-Wasserstein distance which is specifically tailored to identify differential distributions in scRNAseq data. In particular, a two-stage (TS) approach is implemented that takes account of the specific nature of scRNAseq data by separately testing for differential proportions of zero gene expression (using a logistic regression model) and differences in non-zero gene expression (using the semiparametric 2-Wasserstein distance-based test) between two conditions.

See `?wasserstein.sc`

and `?testZeroes`

for more details.

To install `waddR`

from Bioconductor, use `BiocManager`

with the following commands:

```
if (!requireNamespace("BiocManager"))
install.packages("BiocManager")
BiocManager::install("MyPackage")
```

Using `BiocManager`

, the package can also be installed from GitHub directly:

The package `waddR`

can then be used in R:

```
sessionInfo()
#> R version 4.2.1 (2022-06-23)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 20.04.5 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.16-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.16-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] waddR_1.12.0
#>
#> loaded via a namespace (and not attached):
#> [1] Rcpp_1.0.9 lattice_0.20-45
#> [3] assertthat_0.2.1 digest_0.6.30
#> [5] SingleCellExperiment_1.20.0 utf8_1.2.2
#> [7] BiocFileCache_2.6.0 R6_2.5.1
#> [9] GenomeInfoDb_1.34.0 stats4_4.2.1
#> [11] RSQLite_2.2.18 evaluate_0.17
#> [13] coda_0.19-4 httr_1.4.4
#> [15] pillar_1.8.1 zlibbioc_1.44.0
#> [17] rlang_1.0.6 curl_4.3.3
#> [19] minqa_1.2.5 nloptr_2.0.3
#> [21] jquerylib_0.1.4 blob_1.2.3
#> [23] S4Vectors_0.36.0 Matrix_1.5-1
#> [25] rmarkdown_2.17 splines_4.2.1
#> [27] lme4_1.1-31 BiocParallel_1.32.0
#> [29] stringr_1.4.1 RCurl_1.98-1.9
#> [31] bit_4.0.4 DelayedArray_0.24.0
#> [33] compiler_4.2.1 xfun_0.34
#> [35] pkgconfig_2.0.3 BiocGenerics_0.44.0
#> [37] eva_0.2.6 htmltools_0.5.3
#> [39] tidyselect_1.2.0 SummarizedExperiment_1.28.0
#> [41] tibble_3.1.8 GenomeInfoDbData_1.2.9
#> [43] IRanges_2.32.0 codetools_0.2-18
#> [45] matrixStats_0.62.0 fansi_1.0.3
#> [47] withr_2.5.0 dplyr_1.0.10
#> [49] dbplyr_2.2.1 MASS_7.3-58.1
#> [51] bitops_1.0-7 rappdirs_0.3.3
#> [53] grid_4.2.1 nlme_3.1-160
#> [55] jsonlite_1.8.3 arm_1.13-1
#> [57] lifecycle_1.0.3 DBI_1.1.3
#> [59] magrittr_2.0.3 cli_3.4.1
#> [61] stringi_1.7.8 cachem_1.0.6
#> [63] XVector_0.38.0 bslib_0.4.0
#> [65] filelock_1.0.2 generics_0.1.3
#> [67] vctrs_0.5.0 boot_1.3-28
#> [69] tools_4.2.1 bit64_4.0.5
#> [71] Biobase_2.58.0 glue_1.6.2
#> [73] purrr_0.3.5 MatrixGenerics_1.10.0
#> [75] abind_1.4-5 parallel_4.2.1
#> [77] fastmap_1.1.0 yaml_2.3.6
#> [79] GenomicRanges_1.50.0 memoise_2.0.1
#> [81] knitr_1.40 sass_0.4.2
```