permanova: Permutational multivariate analysis of variance (PERMANOVA)

In Sun-lab/ideas: Individual level Differential Expression Analysis for Single cells (IDEAS)

Permutational multivariate analysis of variance (PERMANOVA)

Description

PERMANOVA for differential expression analysis of scRNA-seq data.

Usage

permanova(dist_array, meta_ind, var2test, var2adjust = NULL, 
var2test_type = c("binary", "continuous"), n_perm = 999, 
r.seed = 2020, residulize.x = FALSE, delta = 0.5)

Arguments

dist_array	A three dimensional array with first dimension for the number of genes and the next two dimensions for the the number of individuals. For example, if we study 1000 genes and 20 individuals, it is an array of dimension 1000 x 20 x 20. It can be calculated by function ideas_dist.
meta_ind	A data.frame of meta information of all the individuals. Each row of meta_ind corresponds to an individual. At least two columns are required: "individual" for individual labels, and a column specified by var2test for the variable against which to test DE. The rows of meta_ind should be one to one correspondence to the rows/columns of each distance matrix dist_array[k,,], where k is the index for the k-th gene.
var2test	A string specifying the name of the variable against which to test DE. This variable should be included in meta_ind.
var2adjust	A character vector specifying the name of the variables included as covariates in DE analysis. They should be included in meta_ind.
var2test_type	The type of the variable against which to test DE.
n_perm	The number of permutations.
r.seed	Random seed.
residulize.x	To permute var2test, we can simply permute it or simulate it based on its conditional distribution with respect to var2adjust. If residulize.x is TRUE, we simulate it from conditional distribution and permute it otherwise.
delta	When sample size is small, a variable simulated based on conditional distribution with respect to var2adjust may have very different variance than the observed one. We will discard the permuted variables if its standard deviation is smaller than (1-delta) or larger than (1+delta) times of the stand deviation of the un-permuted variable. Usually this only exclude less than one percent of the permutated variables.

Details

When there is no covariate and the var2test is a binary variable, we simply run the standard PERMANOVA by calculating the summation of the between and within group distance. Otherwise we use the more general formula of F = tr(HGH)/tr[(I - H) G (I-H)], where G is the centralized similarity matrix and H is the hat matrix for the space spanned by var2test and var2adjust. In other words, we calculated the F-statistics to assess the contribution of both var2test and var2adjust on the distance matrix.

Value

A vector of p-values for each gene.

Author(s)

Wei Sun, Mengqi Zhang

References

McArdle, BH and Anderson, MJ (2001). Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology 82(1), 290-297.

Tang, Z. Z., Chen, G., & Alekseyenko, A. V. (2016). PERMANOVA-S: association test for microbial community composition that accommodates confounders and multiple distances. Bioinformatics, 32(17), 2618-2625.

See Also

ideas_dist

Sun-lab/ideas documentation built on Jan. 12, 2023, 12:50 a.m.