wasserstein.sc-method: wasserstein.sc

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

Description

Two-sample test for single-cell RNA-sequencing data to check for differences between two distributions (conditions) using the 2-Wasserstein distance: Semi-parametric implementation using a permutation test with a generalized Pareto distribution (GPD) approximation to estimate small p-values accurately

Usage

wasserstein.sc(x, y, method = c("TS", "OS"), permnum = 10000, seed = NULL)

## S4 method for signature 'matrix,vector'
wasserstein.sc(x, y, method = c("TS", "OS"), permnum = 10000, seed = NULL)

## S4 method for signature 'SingleCellExperiment,SingleCellExperiment'
wasserstein.sc(x, y, method = c("TS", "OS"), permnum = 10000, seed = NULL)

Arguments

x	matrix of single-cell RNA-sequencing expression data with genes in rows and samples (cells) in columns
y	vector of condition labels
method	method employed in the testing procedure: <e2><80><9c>OS<e2><80><9d> for the one-stage method (i.e. semi-parametric testing applied to all (zero and non-zero) expression values); <e2><80><9c>TS<e2><80><9d> for the two-stage method (i.e. semi-parametric testing applied to non-zero expression values only, combined with a separate testing for differential proportions of zero expression using logistic regression). If this argument is not given, a two-sided test is run by default.
permnum	number of permutations used in the permutation testing procedure. If this argument is not given, 10000 is used as default
seed	number to be used to generate a L'Ecuyer-CMRG seed, which itself seeds the generation of an nextRNGStream() for each gene to achieve reproducibility. By default, NULL is given and no seed is set.

Details

Details concerning the permutation testing procedures for single-cell RNA-sequencing data can be found in Schefzik and Goncalves (2019). Corresponds to the function .testWass when identifying the argument inclZero=TRUE in .testWass with the argument method=<e2><80><9d>OS<e2><80><9d> and the argument inclZero=FALSE in .testWass with the argument method=<e2><80><9d>TS<e2><80><9d>.

Value

See the corresponding values in the description of the function .testWass, where the argument inclZero=TRUE in .testWass has to be identified with the argument method=<e2><80><9d>OS<e2><80><9d>, and the argument inclZero=FALSE in .testWass with the argument method=<e2><80><9d>TS<e2><80><9d>. A vector concerning the testing results, precisely (see Schefzik and Goncalves (2019) for details) in case of inclZero=TRUE:

• d.wass: 2-Wasserstein distance between the two samples computed by quantile approximation

• d.wass^2: squared 2-Wasserstein distance between the two samples computed by quantile approximation

• d.comp^2: squared 2-Wasserstein distance between the two samples computed by decomposition approximation

• d.comp: 2-Wasserstein distance between the two samples computed by decomposition approximation

• location: location term in the decomposition of the squared 2-Wasserstein distance between the two samples

• size: size term in the decomposition of the squared 2-Wasserstein distance between the two samples

• shape: shape term in the decomposition of the squared 2-Wasserstein distance between the two samples

• rho: correlation coefficient in the quantile-quantile plot

• pval: p-value of the semi-parametric 2-Wasserstein distance-based test

• p.ad.gpd in case the GPD fitting is performed: p-value of the Anderson-Darling test to check whether the GPD actually fits the data well (otherwise NA)

• N.exc: in case the GPD fitting is performed: number of exceedances (starting with 250 and iteratively decreased by 10 if necessary) that are required to obtain a good GPD fit (i.e. p-value of Anderson-Darling test greater or eqaul to 0.05)(otherwise NA)

• perc.loc: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.size: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.shape: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• decomp.error: relative error between the squared 2-Wasserstein distance computed by the quantile approximation and the squared 2-Wasserstein distance computed by the decomposition approximation

• pval.adj: adjusted p-value of the semi-parametric 2-Wasserstein distance-based test according to the method of Benjamini-Hochberg

In case of inclZero=FALSE:

• d.wass: 2-Wasserstein distance between the two samples computed by quantile approximation

• d.wass^2: squared 2-Wasserstein distance between the two samples computed by quantile approximation

• d.comp^2: squared 2-Wasserstein distance between the two samples computed by decomposition approximation

• d.comp: 2-Wasserstein distance between the two samples computed by decomposition approximation

• location: location term in the decomposition of the squared 2-Wasserstein distance between the two samples

• size: size term in the decomposition of the squared 2-Wasserstein distance between the two samples

• shape: shape term in the decomposition of the squared 2-Wasserstein distance between the two samples

• rho: correlation coefficient in the quantile-quantile plot

• p.nonzero: p-value of the semi-parametric 2-Wasserstein distance-based test (based on non-zero expression only)

• p.ad.gpd: in case the GPD fitting is performed: p-value of the Anderson-Darling test to check whether the GPD actually fits the data well (otherwise NA)

• N.exc: in case the GPD fitting is performed: number of exceedances (starting with 250 and iteratively decreased by 10 if necessary) that are required to obtain a good GPD fit (i.e. p-value of Anderson-Darling test greater or eqaul to 0.05)(otherwise NA)

• perc.loc: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.size: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• perc.shape: fraction (in overall squared 2-Wasserstein distance obtained by the decomposition approximation

• decomp.error: relative error between the squared 2-Wasserstein distance computed by the quantile approximation and the squared 2-Wasserstein distance computed by the decomposition approximation

• p.zero: p-value of the test for differential proportions of zero expression (logistic regression model)

• p.combined: combined p-value of p.nonzero and p.zero obtained by Fisher<e2><80><99>s method

• p.adj.nonzero: adjusted p-value of the semi-parametric 2-Wasserstein distance-based test (based on non-zero expression only) according to the method of Benjamini-Hochberg

• p.adj.zero: adjusted p-value of the test for differential proportions of zero expression (logistic regression model) according to the method of Benjamini-Hochberg

• p.adj.combined: adjusted combined p-value of p.nonzero and p.zero obtained by Fisher<e2><80><99>s method according to the method of Benjamini-Hochberg

References

Schefzik and Goncalves (2019).

Examples

# some data in two conditions
cond1 <- matrix(rnorm(100, 42, 1), nrow=1)
cond2 <- matrix(rnorm(100, 45, 3), nrow=1)

# call wasserstein.sc with a matrix
# and a vector denoting conditions
dat <- cbind(cond1, cond2)
condition <- c(rep(1, 100), rep(2, 100))
wasserstein.sc(dat, condition, "TS", 100)

# call wasserstein.sc with two SingleCellExperiment objects
sce1 <- SingleCellExperiment::SingleCellExperiment(
           assays=list(counts=cond1, logcounts=log10(cond1)))
sce2 <- SingleCellExperiment::SingleCellExperiment(
           assays=list(counts=cond2, logcounts=log10(cond2)))
wasserstein.sc(sce1, sce2, "TS", 100)

# for reproducible p-values
wasserstein.sc(sce1, sce2, seed=123)

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