`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")
::install("MyPackage") BiocManager
```

Using `BiocManager`

, the package can also be installed from GitHub directly:

`::install("goncalves-lab/waddR") BiocManager`

The package `waddR`

can then be used in R:

`library("waddR")`

```
sessionInfo()
#> R Under development (unstable) (2022-10-25 r83175)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 22.04.1 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.17-bioc/R/lib/libRblas.so
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
#>
#> 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_1.13.0
#>
#> loaded via a namespace (and not attached):
#> [1] SummarizedExperiment_1.29.0 xfun_0.34
#> [3] bslib_0.4.0 Biobase_2.59.0
#> [5] lattice_0.20-45 vctrs_0.5.0
#> [7] tools_4.3.0 bitops_1.0-7
#> [9] generics_0.1.3 stats4_4.3.0
#> [11] curl_4.3.3 parallel_4.3.0
#> [13] tibble_3.1.8 fansi_1.0.3
#> [15] RSQLite_2.2.18 blob_1.2.3
#> [17] pkgconfig_2.0.3 Matrix_1.5-1
#> [19] arm_1.13-1 dbplyr_2.2.1
#> [21] S4Vectors_0.37.0 assertthat_0.2.1
#> [23] lifecycle_1.0.3 GenomeInfoDbData_1.2.9
#> [25] compiler_4.3.0 stringr_1.4.1
#> [27] codetools_0.2-18 eva_0.2.6
#> [29] GenomeInfoDb_1.35.0 htmltools_0.5.3
#> [31] sass_0.4.2 RCurl_1.98-1.9
#> [33] yaml_2.3.6 nloptr_2.0.3
#> [35] pillar_1.8.1 jquerylib_0.1.4
#> [37] MASS_7.3-58.1 BiocParallel_1.33.0
#> [39] SingleCellExperiment_1.21.0 DelayedArray_0.25.0
#> [41] cachem_1.0.6 abind_1.4-5
#> [43] boot_1.3-28 nlme_3.1-160
#> [45] tidyselect_1.2.0 digest_0.6.30
#> [47] stringi_1.7.8 purrr_0.3.5
#> [49] dplyr_1.0.10 splines_4.3.0
#> [51] fastmap_1.1.0 grid_4.3.0
#> [53] cli_3.4.1 magrittr_2.0.3
#> [55] utf8_1.2.2 withr_2.5.0
#> [57] filelock_1.0.2 rappdirs_0.3.3
#> [59] bit64_4.0.5 rmarkdown_2.17
#> [61] XVector_0.39.0 httr_1.4.4
#> [63] matrixStats_0.62.0 lme4_1.1-31
#> [65] bit_4.0.4 coda_0.19-4
#> [67] memoise_2.0.1 evaluate_0.17
#> [69] knitr_1.40 GenomicRanges_1.51.0
#> [71] IRanges_2.33.0 BiocFileCache_2.7.0
#> [73] rlang_1.0.6 Rcpp_1.0.9
#> [75] glue_1.6.2 DBI_1.1.3
#> [77] BiocGenerics_0.45.0 minqa_1.2.5
#> [79] jsonlite_1.8.3 R6_2.5.1
#> [81] zlibbioc_1.45.0 MatrixGenerics_1.11.0
```