`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 Under development (unstable) (2021-10-19 r81077)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 20.04.3 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.15-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.15-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_1.9.0
#>
#> loaded via a namespace (and not attached):
#> [1] MatrixGenerics_1.7.0 Biobase_2.55.0
#> [3] httr_1.4.2 sass_0.4.0
#> [5] bit64_4.0.5 jsonlite_1.7.2
#> [7] splines_4.2.0 bslib_0.3.1
#> [9] assertthat_0.2.1 stats4_4.2.0
#> [11] BiocFileCache_2.3.0 blob_1.2.2
#> [13] GenomeInfoDbData_1.2.7 yaml_2.2.1
#> [15] pillar_1.6.4 RSQLite_2.2.8
#> [17] lattice_0.20-45 glue_1.4.2
#> [19] digest_0.6.28 GenomicRanges_1.47.1
#> [21] XVector_0.35.0 minqa_1.2.4
#> [23] htmltools_0.5.2 Matrix_1.3-4
#> [25] pkgconfig_2.0.3 zlibbioc_1.41.0
#> [27] purrr_0.3.4 BiocParallel_1.29.0
#> [29] lme4_1.1-27.1 arm_1.12-2
#> [31] tibble_3.1.5 generics_0.1.1
#> [33] IRanges_2.29.0 ellipsis_0.3.2
#> [35] withr_2.4.2 cachem_1.0.6
#> [37] SummarizedExperiment_1.25.0 BiocGenerics_0.41.0
#> [39] magrittr_2.0.1 crayon_1.4.1
#> [41] memoise_2.0.0 evaluate_0.14
#> [43] fansi_0.5.0 nlme_3.1-153
#> [45] MASS_7.3-54 tools_4.2.0
#> [47] lifecycle_1.0.1 matrixStats_0.61.0
#> [49] stringr_1.4.0 S4Vectors_0.33.0
#> [51] DelayedArray_0.21.0 eva_0.2.6
#> [53] compiler_4.2.0 jquerylib_0.1.4
#> [55] GenomeInfoDb_1.31.0 rlang_0.4.12
#> [57] grid_4.2.0 RCurl_1.98-1.5
#> [59] nloptr_1.2.2.2 rappdirs_0.3.3
#> [61] SingleCellExperiment_1.17.0 bitops_1.0-7
#> [63] rmarkdown_2.11 boot_1.3-28
#> [65] abind_1.4-5 DBI_1.1.1
#> [67] curl_4.3.2 R6_2.5.1
#> [69] knitr_1.36 dplyr_1.0.7
#> [71] fastmap_1.1.0 bit_4.0.4
#> [73] utf8_1.2.2 filelock_1.0.2
#> [75] stringi_1.7.5 parallel_4.2.0
#> [77] Rcpp_1.0.7 vctrs_0.3.8
#> [79] dbplyr_2.1.1 tidyselect_1.1.1
#> [81] xfun_0.27 coda_0.19-4
```