calculate_cvm: Cramer von Mises for differential analysis of genomics data
In EMDomics: Earth Mover's Distance for Differential Analysis of Genomics Data

Description Usage Arguments Value See Also Examples

This is a main user interface to the EMDomics package, and will usually the only function needed when conducting an analysis using the CVM algorithm. Analyses can also be conducted with the Komolgorov-Smirnov Test using calculate_ks or the Earth Mover's Distance algorithm using calculate_emd.

The algorithm is used to compare genomics data between any number of groups. Usually the data will be gene expression values from array-based or sequence-based experiments, but data from other types of experiments can also be analyzed (e.g. copy number variation).

Traditional methods like Significance Analysis of Microarrays (SAM) and Linear Models for Microarray Data (LIMMA) use significance tests based on summary statistics (mean and standard deviation) of the two distributions. This approach tends to give non-significant results if the two distributions are highly heterogeneous, which can be the case in many biological circumstances (e.g sensitive vs. resistant tumor samples).

The Cramer von Mises (CVM) algorithm generates a test statistic that is the sum of the squared values of the differences between two cumulative distribution functions (CDFs). As a result, the test statistic tends to overestimate the similarity between two distributions and cannot effectively handle partial matching like EMD does. However, it is one of the most commonly referenced nonparametric two-class distribution comparison tests in non-genomic contexts.

The CVM-based algorithm implemented in EMDomics has two main steps. First, a matrix (e.g. of expression data) is divided into data for each of the groups. Every possible pairwise CVM score is then computed and stored in a table. The CVM score for a single gene is calculated by averaging all of the pairwise CVM scores. Next, the labels for each of the groups are randomly permuted a specified number of times, and an CVM score for each permutation is calculated. The median of the permuted scores for each gene is used as the null distribution, and the False Discovery Rate (FDR) is computed for a range of permissive to restrictive significance thresholds. The threshold that minimizes the FDR is defined as the q-value, and is used to interpret the significance of the CVM score analogously to a p-value (e.g. q-value < 0.05 is significant.)

1 2	calculate_cvm(data, outcomes, nperm = 100, pairwise.p = FALSE, seq = FALSE, quantile.norm = FALSE, verbose = TRUE, parallel = TRUE)

`data`	A matrix containing genomics data (e.g. gene expression levels). The rownames should contain gene identifiers, while the column names should contain sample identifiers.
`outcomes`	A vector containing group labels for each of the samples provided in the `data` matrix. The names should be the sample identifiers provided in `data`.
`nperm`	An integer specifying the number of randomly permuted CVM scores to be computed. Defaults to 100.
`pairwise.p`	Boolean specifying whether the permutation-based q-values should be computed for each pairwise comparison. Defaults to `FALSE`.
`seq`	Boolean specifying if the given data is RNA Sequencing data and ought to be normalized. Set to `TRUE`, if passing transcripts per million (TPM) data or raw data that is not scaled. If `TRUE`, data will be normalized by first multiplying by 1E6, then adding 1, then taking the log base 2. If `FALSE`, the data will be handled as is (unless `quantile.norm` is `TRUE`). Note that as a distribution comparison function, K-S will compute faster with scaled data. Defaults to `FALSE`.
`quantile.norm`	Boolean specifying is data should be normalized by quantiles. If `TRUE`, then the `normalize.quantiles` function is used. Defaults to `FALSE`.
`verbose`	Boolean specifying whether to display progress messages.
`parallel`	Boolean specifying whether to use parallel processing via the BiocParallel package. Defaults to `TRUE`.

The function returns an CVMomics object.

CVMomics CramerVonMisesTwoSamples

# 100 genes, 100 samples
dat <- matrix(rnorm(10000), nrow=100, ncol=100)
rownames(dat) <- paste("gene", 1:100, sep="")
colnames(dat) <- paste("sample", 1:100, sep="")

# "A": first 50 samples; "B": next 30 samples; "C": final 20 samples
outcomes <- c(rep("A",50), rep("B",30), rep("C",20))
names(outcomes) <- colnames(dat)

results <- calculate_cvm(dat, outcomes, nperm=10, parallel=FALSE)
head(results$cvm)

sh: 1: wc: Permission denied
Calculating pairwise cvm scores...done.
Calculating cvm...done.
Calculating for overall q-values...
Calculating permuted cvm #1 of 10...done.
Calculating permuted cvm #2 of 10...done.
Calculating permuted cvm #3 of 10...done.
Calculating permuted cvm #4 of 10...done.
Calculating permuted cvm #5 of 10...done.
Calculating permuted cvm #6 of 10...done.
Calculating permuted cvm #7 of 10...done.
Calculating permuted cvm #8 of 10...done.
Calculating permuted cvm #9 of 10...done.
Calculating permuted cvm #10 of 10...done.
Calculating q-values...done.
            cvm   q-value
gene1 0.0740000 1.0000000
gene2 0.7366667 0.0000000
gene3 0.2630833 0.5641026
gene4 0.2251429 0.8333333
gene5 0.6262500 0.0000000
gene6 0.1327500 1.0000000