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# Statistical tests for detecting differential distributions based on the 2-Wasserstein distance
> For more details on the methods and further information, please have a look at our paper:
> Schefzik, R., Flesch, J., and Goncalves, A. (2021). Fast identification of differential distributions in
single-cell RNA-sequencing data with waddR. *Bioinformatics*, 37, 3204-3211. DOI: https://doi.org/10.1093/bioinformatics/btab226
The `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 specifically tailored test for differential expression in single-cell RNA sequencing data.
The package provides tools to address the following tasks:
1. Computation of the 2-Wasserstein distance
2. Two-sample tests to check for differences between two distributions
3. Detection of differential gene expression distributions in single-cell RNA sequencing data
* R >= 3.6.0
### Via Package Repository
Available on [Bioconductor](https://bioconductor.org/packages/release/bioc/html/waddR.html):
if (!requireNamespace("BiocManager", quietly = TRUE))
### From Github
The latest package version can be installed from Github using `BiocManager`:
## Running Tests
Tests can be run by calling `test()` from the `devtools` package.
All tests are implemented using the `testthat` package and reside in `tests/testhat`
## Using `waddR`
### 2-Wasserstein distance functions
The 2-Wasserstein distance is a metric to quantify the distance between two
distributions, representing two different conditions A and B. The `waddR` package
specifically considers the squared 2-Wasserstein distance, which
offers a decomposition into location, size, and shape terms, thus providing a characterization of potential differences.
The `waddR` package offers three functions to calculate the 2-Wasserstein
distance, which are implemented in C++ and exported to R with Rcpp for
The function `wasserstein_metric` is a C++ reimplementation of the
function `wasserstein1d` 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`, as well as the accompanying paper Schefzik et al. (2021).
### Testing for differences between two distributions
The `waddR` package provides two testing procedures using the 2-Wasserstein distance
to test whether two distributions given in the form of samples are
different by specifically testing the null hypothesis of no difference against the
alternative hypothesis that the two distributions are different.
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
See `?wasserstein.test` for more details.
### Testing for differences between two distributions in the context of single-cell RNA sequencing data:
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
single-cell RNA-seqencing (scRNA-seq) data. In particular, a two-stage
(TS) approach is 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.
Note that as input for scRNA-seq analysis, `waddR` expects a table of pre-filtered and normalised count data. As filtering and normalisation are important steps that can have a profound impact in a scRNA-seq workflow (Cole et al., 2019), these should be tailored to the specific question of interest before applying `waddR`. `waddR` is applicable to data from any scRNA-seq platform (demonstrated in our paper for 10x Genomics and Fluidigm C1 Smart-Seq2) normalised using most common methods, such as those implemented in the `Seurat` (Butler et al., 2018) or `scran` (Lun et al., 2016) packages. Normalisation approaches that change the shape of the gene distributions (such as quantile normalisation) and gene-wise scaling or standardizing should be avoided when using `waddR`.
See `?wasserstein.sc` and `?testZeroes` for more details.
We have included detailed examples of how to use the functions provided with
`waddR` in our vignettes.
They are available online [here](https://github.com/goncalves-lab/waddR)
*(update this link once it is final)* or from an R session with the
Butler, A., Hoffman, P., Smibert, P., Papalexi, E., and Satija, R. (2018).
Integrating single-cell transcriptomic data across different conditions,
technologies, and species. *Nature Biotechnology*, 36, 411–420.
Cole, M. B., Risso, D., Wagner, A., De Tomaso, D., Ngai, J., Purdom, E.,
Dudoit, S., and Yosef, N. (2019). Performance assessment and selection
of normalization procedures for single-cell RNA-seq. *Cell Systems*, 8,
Lun, A. T. L., Bach, K., and Marioni, J. C. (2016). Pooling across cells
to normalize single-cell RNA sequencing data with many zero counts.
*Genome Biology*, 17, 75.
Schefzik, R., Flesch, J., and Goncalves, A. (2021). Fast identification of differential distributions in
single-cell RNA-sequencing data with waddR. To appear in *Bioinformatics*. DOI: https://doi.org/10.1093/bioinformatics/btab226