waddR-package: waddR: Statistical Test for Detecting Differential...

In waddR: Statistical tests for detecting differential distributions based on the 2-Wasserstein distance

Description

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.

Details

The Wasserstein package offers utilities for three distinct use cases:

• Computation of the 2-Wasserstein distance

• Two-sample test to check for differences between two distributions

• Detect differential gene expression distributions in scRNAseq data

Wasserstein Distance functions

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. It 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. wasserstein_metric is a Cpp reimplementation of the wasserstein1d method 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 suared_wass_decomp also returning the decomosition terms for location, size, and shape. See ?wasserstein_metric, ?squared_wass_aprox, and ?squared_wass_decomp as well as the accompanying paper Schefzik and Goncalves 2019.

Two-Sample Testing

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 the documentation of the function ?wasserstein.test for more details.

Single Cell Test

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 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 testing function ?wasserstein.sc and the test for zero expression levels ?testZeroes for more details.

Author(s)

Maintainer: Julian Flesch [e-mail]

Authors:

• Roman Schefzik [e-mail]

See Also

Useful links:

• https://github.com/goncalves-lab/waddR.git

• Report bugs at https://github.com/goncalves-lab/waddR/issues

waddR documentation built on Nov. 8, 2020, 8:32 p.m.