calculate_ks: Calculate the Komolgorov-Smirnov test statistic and q-values...
In EMDomics: Earth Mover's Distance for Differential Analysis of Genomics Data

Description Usage Arguments Value See Also Examples

This is only function needed when conducting an analysis using the Komolgorov-Smirnov algorithm. Analyses can also be conducted with the EMD algorithm using calculate_emd or the Cramer Von Mises (CVM) algorithm using calculate_cvm.

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).

Komolgorov-Smirnov instead calculates a test statistic that is the maximum distance between two cumulative distribution functions (CDFs). Unlike the EMD score, the KS test statistic summarizes only the maximum difference (while EMD considers quantity and distance between all differences).

The KS 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 KS score is then computed and stored in a table. The KS score for a single gene is calculated by averaging all of the pairwise KS scores. If the user sets pairwise.p to true, then the p-values from the KS test are adjusted using the Benjamini-Hochberg method and stored in a table. Next, the labels for each of the groups are randomly permuted a specified number of times, and an EMD 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 EMD score analogously to a p-value (e.g. q-value < 0.05 = significant). The q-values returned by the KS test (and adjusted for multiple significance testing) can be compared to the permuted q-values.

1 2	calculate_ks(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 EMD scores to be computed. Defaults to 100.
`pairwise.p`	Boolean specifying whether the user wants the pairwise p-values. Pairwise p-values returned by `ks.test` are adjusted within pairwise comparison using the Benjamini-Hochberg (BH) method. 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 KSomics object.

EMDomics ks.test

# 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_ks(dat, outcomes, nperm=10, parallel=FALSE)
head(results$ks)

Calculating pairwise KS scores...done.
Calculating KS...done.
Calculating permuted KS #1 of 10...done.
Calculating permuted KS #2 of 10...done.
Calculating permuted KS #3 of 10...done.
Calculating permuted KS #4 of 10...done.
Calculating permuted KS #5 of 10...done.
Calculating permuted KS #6 of 10...done.
Calculating permuted KS #7 of 10...done.
Calculating permuted KS #8 of 10...done.
Calculating permuted KS #9 of 10...done.
Calculating permuted KS #10 of 10...done.
Calculating q-values...done.
        ks permutation q-value
gene1 0.42                0.00
gene2 0.20                1.00
gene3 0.20                1.00
gene4 0.29                0.44
gene5 0.33                0.00
gene6 0.35                0.00