`waddR`

package`waddR`

is an R package that provides a 2-Wasserstein distance based statistical test for detecting and describing differential distributions in one-dimensional data. Functions for wasserstein distance calculation, differential distribution testing, and a specialized test for differential expression in scRNA data are provided.

The package `waddR`

provides three sets of utilities to cover distinct use cases, each described in a separate vignette:

Fast and accurate calculation of the 2-Wasserstein distance

Two-sample test to check for differences between two distributions

Detect differential gene expression distributions in scRNAseq data

These are bundled into the same package, because they are internally dependent: The procedure for detecting differential distributions in single-cell data is a refinement 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 two diferent conditions A and B. This package specifically considers the squared 2-Wasserstein distance d := W^2 which offers a decomposition into location, size, and shape terms.

The package `waddR`

offers three functions to calculate the 2-Wasserstein distance, all of which are implemented in Cpp and exported to R with Rcpp for better performance. The function `wasserstein_metric`

is a Cpp reimplementation of the function `wasserstein1d`

from the package `transport`

and offers the most exact results. The functions `squared_wass_approx`

and `squared_wass_decomp`

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

also returning the decomosition terms for location, size, and shape. See `?wasserstein_metric`

, `?squared_wass_aprox`

, and `?squared_wass_decomp`

.

This 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 ba specifically testing the null hypothesis H0: F_A = F_B against the alternative hypothesis H1: F_A != F_B.

The first, semi-parametric (SP), procedure uses a test based on permutations combined with a generalized pareto distribution approximation to estimate small pvalues accurately.

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

See `?wasserstein.test`

for more details.

semi-parametric testing procedure based on the 2-Wasserstein distance which is specifically tailored to identify differential distributions in single-cell RNA-seqencing (scRNA-seq) data. In particular, a two-stage (TS) approach has been implemented that takes account of the specific nature of scRNA-seq 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 semi-parametric 2-Wasserstein distance-based test) between two conditions.

See the documentation of the single cell procedure `?wasserstein.sc`

and the test for zero expression levels `?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 3.6.3 (2020-02-29)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 18.04.4 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.10-bioc/R/lib/libRlapack.so
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 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_1.0.1
#>
#> loaded via a namespace (and not attached):
#> [1] SummarizedExperiment_1.16.1 tidyselect_1.0.0
#> [3] xfun_0.12 purrr_0.3.3
#> [5] splines_3.6.3 lattice_0.20-40
#> [7] vctrs_0.2.4 htmltools_0.4.0
#> [9] stats4_3.6.3 BiocFileCache_1.10.2
#> [11] yaml_2.2.1 blob_1.2.1
#> [13] rlang_0.4.5 nloptr_1.2.2.1
#> [15] pillar_1.4.3 glue_1.3.2
#> [17] DBI_1.1.0 BiocParallel_1.20.1
#> [19] rappdirs_0.3.1 SingleCellExperiment_1.8.0
#> [21] BiocGenerics_0.32.0 bit64_0.9-7
#> [23] dbplyr_1.4.2 matrixStats_0.56.0
#> [25] GenomeInfoDbData_1.2.2 stringr_1.4.0
#> [27] zlibbioc_1.32.0 coda_0.19-3
#> [29] memoise_1.1.0 evaluate_0.14
#> [31] Biobase_2.46.0 knitr_1.28
#> [33] IRanges_2.20.2 GenomeInfoDb_1.22.0
#> [35] parallel_3.6.3 curl_4.3
#> [37] Rcpp_1.0.4 arm_1.10-1
#> [39] DelayedArray_0.12.2 S4Vectors_0.24.3
#> [41] XVector_0.26.0 abind_1.4-5
#> [43] bit_1.1-15.2 lme4_1.1-21
#> [45] digest_0.6.25 stringi_1.4.6
#> [47] dplyr_0.8.5 GenomicRanges_1.38.0
#> [49] grid_3.6.3 tools_3.6.3
#> [51] bitops_1.0-6 magrittr_1.5
#> [53] RCurl_1.98-1.1 tibble_2.1.3
#> [55] RSQLite_2.2.0 crayon_1.3.4
#> [57] pkgconfig_2.0.3 MASS_7.3-51.5
#> [59] Matrix_1.2-18 minqa_1.2.4
#> [61] assertthat_0.2.1 rmarkdown_2.1
#> [63] httr_1.4.1 boot_1.3-24
#> [65] R6_2.4.1 nlme_3.1-145
#> [67] compiler_3.6.3
```