kendallWmat: Use Kendall's W and graph theory to assign independent...

In bedapub/ribiosGSEA: Gene-Set Enrichment Analysis Tools in Ribios

Use Kendall's W and graph theory to assign independent measurements into sub-groups by correlation

Description

Kendall's W, also known as Kendall's coefficient of concordance, is a non-parametric statistic developed to assess agreement among raters used in psychological or similar experimental settings.

Usage

kendallWmat(
  mat,
  row.factor,
  summary = c("none", "mean", "median", "max.mean.sig", "max.var.sig"),
  na.rm = TRUE,
  alpha = 0.01
)

Arguments

mat	A numeric matrix. It must contain at least 2 rows and 2 columns.
row.factor	A factor indicating groups of rows. In expression analysis, for instance, this can be GeneIDs indicating which probesets in rows belong to the same gene.
summary	Character, action to take once the sub-groups have been determined. ‘none’ indicates no action should be taken, the original data is returned with the information of sub-grouping. The option ‘mean’ (or ‘median’) will take mean/median of features in each sub-group as result. On contrast, max.mean.sig or max.var.sig picks the feature of the largest mean signal or the largest variance in each sub-group as the representative. See details below.
na.rm	Logical, should those features whose row.factor are NA be left out? If set to TRUE (which is default), these unannotated features will be discarded from the results.
alpha	Nunmeric value, the significance level of the Kendall's W statistic. The larger the value, the more abbreviations from strong associations are allowed in sub-groups. Default is 0.01.

Details

In computational biology, the concept of associating features with similar patterns while keeping outliers can be useful in many cases. See the Details section for examples.

This function implements the Kendall's W recursively with graph theory. It split grouped measurements into strongly associated sub-groups. See the Details section.

We take a microarray experiment as an example to demonstrate how the function works. In microarrays, a gene is often represented by more than one probeset, and it is not rare that they do not all resemble the same expression pattern. Usually a one gene-one value relation is desired. Common practices including choosing the probeset with the highest average signal or the highest variance, as well as taking the mean/median value of all probesets mapped to one gene as the representative value.

Kendall's W takes a very different approach. First it tries to judge whether multiple probesets of one gene are concordant. The concordance is determined by a non-parametric statistic closely related to Spearman correlation coefficient as well as Friedman's test. If all probesets are concordant, it means that their expression patterns are closely associated with each other. Any one of them, or the mean value, can be then used to represent the expression level of the gene.

In cases where there is little concordance among probesets, we can take use of graph theory to iteratively search for sub-groups of probesets resemble each other's expression patterns. In the extreme case, each probeset can be different from the rest, and in this case the number of sub-groups will be equal to the number of probesets mapped to the gene. Such cases can appear, for instance, when each probeset was designed to target a different region of a transcript with splice variants. By using Kendall's W statistic with graph theory, the kendallWmat function can detect sub-groups with strongly correlated expression patterns, while keeping outliers on their own, therefore providing help for both conventional expression analysis and post-hoc analysis with the help of sequence analysis. See reference for examples on this application.

We believe this approach is only useful for microarray, but can be also interesting for other applications like next-generation sequencing (NGS) or pathway/network analysis. For instance, in NGS experiments, this method can help to determine which splice variants of a transcript have similar expression patterns, and how different are other variants. In pathway analysis, when rows indicate gene expression values and row.factor indicate pathway membership, the result reveals which sub-networks are regulated associatively.

Value

Currently a matrix with one attribute slot named info.

Author(s)

Jitao David Zhang <[e-mail]>

References

The concept of Kendall's W was introduced in the seminal paper The problem of m rankings by M.G. Kendall and B.B. Smith (The Annals of Mathematical Statistics, 1939). Schneider, Smith and Hansen developed the SCOREM algorithm combining this statistic with graph theory (SCOREM: statistical consolidation of redundant expression measures, Nucleic Acids Research, 2011). This implementation is very much based on the SCOREM algorithm. The main changes are (1) the current implementation is more generic, applicable to native R data structures, therefore able to be applied in other scenario than microarray analysis (2) it takes not-annotated features into account as well and (3) it is possible to directly calculate summary statistics from sub-groups.

Examples

## use a mock example
emat <- matrix(c(2,3,5,
                 8,9,2,
                 3,4,7,
                 0,2,1,
                 NA, 3, 1.2,
                 5, -3,4,
                 5,7,11), ncol=3, byrow=TRUE,
               dimnames=list(paste("row", 1:7, sep=""),NULL))
efac <- factor(c("a", "b", "c", NA, "b", "a", "a"),
               levels=letters[1:5])

print(emat)
kendallWmat(emat, efac, summary="none")
kendallWmat(emat, efac, summary="none", na.rm=FALSE)
kendallWmat(emat, efac, summary="mean")
kendallWmat(emat, efac, summary="mean", na.rm=FALSE)
kendallWmat(emat, efac, summary="median")
kendallWmat(emat, efac, summary="median", na.rm=FALSE)
kendallWmat(emat, efac, summary="max.mean.sig")
kendallWmat(emat, efac, summary="max.mean.sig", na.rm=FALSE)
kendallWmat(emat, efac, summary="max.var.sig")
kendallWmat(emat, efac, summary="max.var.sig", na.rm=TRUE)

## kendallW acts as an interface to matrix
kendallW(emat, efac, summary="none")

## kendallW acts as an interface to ExpressionSet
data(ribios.ExpressionSet, package="ribiosExpression")
kendallW(ribios.ExpressionSet, 
  Biobase::fData(ribios.ExpressionSet)$GeneID,
  summary="none")
kendallW(ribios.ExpressionSet, 
  Biobase::fData(ribios.ExpressionSet)$GeneID, 
  summary="mean")

bedapub/ribiosGSEA documentation built on March 30, 2023, 3:26 p.m.