wmwTest: Wilcoxon-Mann-Whitney rank sum test for high-throughput...
In Accio/BioQC: Detect tissue heterogeneity in expression profiles with gene sets

Description Usage Arguments Details Value Methods (by class) Note Author(s) References See Also Examples

wmwTest is a highly efficient Wilcoxon-Mann-Whitney rank sum test for high-dimensional data, such as gene expression profiling. For datasets with more than 100 features (genes), the function can be more than 1,000 times faster than its R implementations (wilcox.test in stats, or rankSumTestWithCorrelation in limma).

wmwTest(
  x,
  indexList,
  col = "GeneSymbol",
  valType = c("p.greater", "p.less", "p.two.sided", "U", "abs.log10p.greater",
    "log10p.less", "abs.log10p.two.sided", "Q", "r", "f", "U1", "U2"),
  simplify = TRUE
)

## S4 method for signature 'matrix,IndexList'
wmwTest(x, indexList, valType = "p.greater", simplify = TRUE)

## S4 method for signature 'numeric,IndexList'
wmwTest(x, indexList, valType = "p.greater", simplify = TRUE)

## S4 method for signature 'matrix,GmtList'
wmwTest(x, indexList, valType = "p.greater", simplify = TRUE)

## S4 method for signature 'eSet,GmtList'
wmwTest(
  x,
  indexList,
  col = "GeneSymbol",
  valType = "p.greater",
  simplify = TRUE
)

## S4 method for signature 'eSet,numeric'
wmwTest(
  x,
  indexList,
  col = "GeneSymbol",
  valType = "p.greater",
  simplify = TRUE
)

## S4 method for signature 'eSet,logical'
wmwTest(
  x,
  indexList,
  col = "GeneSymbol",
  valType = "p.greater",
  simplify = TRUE
)

## S4 method for signature 'eSet,list'
wmwTest(
  x,
  indexList,
  col = "GeneSymbol",
  valType = "p.greater",
  simplify = TRUE
)

## S4 method for signature 'ANY,numeric'
wmwTest(x, indexList, valType = "p.greater", simplify = TRUE)

## S4 method for signature 'ANY,logical'
wmwTest(x, indexList, valType = "p.greater", simplify = TRUE)

## S4 method for signature 'ANY,list'
wmwTest(x, indexList, valType = "p.greater", simplify = TRUE)

## S4 method for signature 'matrix,SignedIndexList'
wmwTest(x, indexList, valType, simplify = TRUE)

## S4 method for signature 'matrix,SignedGenesets'
wmwTest(x, indexList, valType, simplify = TRUE)

## S4 method for signature 'numeric,SignedIndexList'
wmwTest(x, indexList, valType, simplify = TRUE)

## S4 method for signature 'eSet,SignedIndexList'
wmwTest(x, indexList, valType, simplify = TRUE)

## S4 method for signature 'eSet,SignedGenesets'
wmwTest(
  x,
  indexList,
  col = "GeneSymbol",
  valType = c("p.greater", "p.less", "p.two.sided", "U", "abs.log10p.greater",
    "log10p.less", "abs.log10p.two.sided", "Q", "r", "f", "U1", "U2"),
  simplify = TRUE
)

`x`	A numeric matrix. All other data types (e.g. numeric vectors or `ExpressionSet` objects) are coerced into matrix.
`indexList`	A list of integer indices (starting from 1) indicating signature genes. Can be of length zero. Other data types (e.g. a list of numeric or logical vectors, or a numeric or logical vector) are coerced into such a list. See `details` below for a special case using GMT files.
`col`	a string sometimes used with a `eSet`
`valType`	The value type to be returned, allowed values include `p.greater`, `p.less`, `abs.log10p.greater` and `abs.log10p.less` (one-sided tests),`p.two.sided`, and `U` statistic (or more specifically, either `U1` or `U2`), and a few other variants. See details below.
`simplify`	Logical. If not, the returning value is in matrix format; if set to `TRUE`, the results are simplified into vectors when possible (default).

The basic application of the function is to test the enrichment of gene sets in expression profiling data or differentially expressed data (the matrix with feature/gene in rows and samples in columns).

A special case is when x is an eSet object (e.g. ExpressionSet), and indexList is a list returned from readGmt function. In this case, the only requirement is that one column named GeneSymbol in the featureData contain gene symbols used in the GMT file. The same applies to signed Gmt files. See the example below.

Besides the conventional value types such as ‘p.greater’, ‘p.less’, ‘p.two.sided’ , and ‘U’ (the U-statistic), wmwTest (from version 0.99-1) provides further value types: abs.log10p.greater and log10p.less perform log10 transformation on respective p-values and give the transformed value a proper sign (positive for greater than, and negative for less than); abs.log10p.two.sided transforms two-sided p-values to non-negative values; and Q score reports absolute log10-transformation of p-value of the two-side variant, and gives a proper sign to it, depending on whether it is rather greater than (positive) or less than (negative).

From version 1.19.1, the rank-biserial correlation coefficient (‘r’) and the common language effect size (‘f’) are supported value types.

Before version 1.19.3, the ‘U’ statistic returned is in fact ‘U2’. From version 1.19.3, ‘U1’ is returned when ‘U’ is used, and users can specify additional parameter values ‘U1’ and ‘U2’. The sum of ‘U1’ and ‘U2’ is the product of the sizes of two vectors to be compared.

A numeric matrix or vector containing the statistic.

x = matrix,indexList = IndexList: x is a matrix and indexList is a IndexList
x = numeric,indexList = IndexList: x is a numeric and indexList is a IndexList
x = matrix,indexList = GmtList: x is a matrix and indexList is a GmtList
x = eSet,indexList = GmtList: x is a eSet and indexList is a GmtList
x = eSet,indexList = numeric: x is a eSet and indexList is a numeric
x = eSet,indexList = logical: x is a eSet and indexList is a logical
x = eSet,indexList = list: x is a eSet and indexList is a list
x = ANY,indexList = numeric: x is ANY and indexList is a numeric
x = ANY,indexList = logical: x is ANY and indexList is a logical
x = ANY,indexList = list: x is ANY and indexList is a list
x = matrix,indexList = SignedIndexList: x is a matrix and indexList is a SignedIndexList
x = matrix,indexList = SignedGenesets: x is a eSet and indexList is a SignedIndexList
x = numeric,indexList = SignedIndexList: x is a numeric and indexList is a SignedIndexList
x = eSet,indexList = SignedIndexList: x is a eSet and indexList is a SignedIndexList
x = eSet,indexList = SignedGenesets: x is a eSet and indexList is a SignedIndexList

The function has been optimized for expression profiling data. It avoids repetitive ranking of data as done by native R implementations and uses efficient C code to increase the performance and control memory use. Simulation studies using expression profiles of 22000 genes in 2000 samples and 200 gene sets suggested that the C implementation can be >1000 times faster than the R implementation. And it is possible to further accelerate by parallel calling the function with mclapply in the multicore package.

Jitao David Zhang <jitao_david.zhang@roche.com>, with critical inputs from Jan Aettig and Iakov Davydov about U statistics.

Barry, W.T., Nobel, A.B., and Wright, F.A. (2008). A statistical framework for testing functional namespaces in microarray data. _Annals of Applied Statistics_ 2, 286-315.

Wu, D, and Smyth, GK (2012). Camera: a competitive gene set test accounting for inter-gene correlation. _Nucleic Acids Research_ 40(17):e133

Zar, JH (1999). _Biostatistical Analysis 4th Edition_. Prentice-Hall International, Upper Saddle River, New Jersey.

codewilcox.test in the stats package, and rankSumTestWithCorrelation in the limma package.

## R-native data structures
set.seed(1887)
rd <- rnorm(1000)
rl <- sample(c(TRUE, FALSE), 1000, replace=TRUE)
wmwTest(rd, rl, valType="p.two.sided")
wmwTest(rd, which(rl), valType="p.two.sided")
rd1 <- rd + ifelse(rl, 0.5, 0)
wmwTest(rd1, rl, valType="p.greater")
wmwTest(rd1, rl, valType="U")
rd2 <- rd - ifelse(rl, 0.2, 0)
wmwTest(rd2, rl, valType="p.greater")
wmwTest(rd2, rl, valType="p.two.sided")
wmwTest(rd2, rl, valType="p.less")
wmwTest(rd2, rl, valType="r")
wmwTest(rd2, rl, valType="f")

## matrix forms
rmat <- matrix(c(rd, rd1, rd2), ncol=3, byrow=FALSE)
wmwTest(rmat, rl, valType="p.two.sided")
wmwTest(rmat, rl, valType="p.greater")

wmwTest(rmat, which(rl), valType="p.two.sided")
wmwTest(rmat, which(rl), valType="p.greater")

## other valTypes
wmwTest(rmat, which(rl), valType="U")
wmwTest(rmat, which(rl), valType="abs.log10p.greater")
wmwTest(rmat, which(rl), valType="log10p.less")
wmwTest(rmat, which(rl), valType="abs.log10p.two.sided")
wmwTest(rmat, which(rl), valType="Q")
wmwTest(rmat, which(rl), valType="r")
wmwTest(rmat, which(rl), valType="f")

## using ExpressionSet
data(sample.ExpressionSet)
testSet <- sample.ExpressionSet
fData(testSet)$GeneSymbol <- paste("GENE_",1:nrow(testSet), sep="")
mySig1 <- sample(c(TRUE, FALSE), nrow(testSet), prob=c(0.25, 0.75), replace=TRUE)
wmwTest(testSet, which(mySig1), valType="p.greater")

## using integer
exprs(testSet)[,1L] <- exprs(testSet)[,1L] + ifelse(mySig1, 50, 0)
wmwTest(testSet, which(mySig1), valType="p.greater")

## using lists
mySig2 <- sample(c(TRUE, FALSE), nrow(testSet), prob=c(0.6, 0.4), replace=TRUE)
wmwTest(testSet, list(first=mySig1, second=mySig2))
## using GMT file
gmt_file <- system.file("extdata/exp.tissuemark.affy.roche.symbols.gmt", package="BioQC")
gmt_list <- readGmt(gmt_file)

gss <- sample(unlist(sapply(gmt_list, function(x) x$genes)), 1000)
eset<-new("ExpressionSet",
         exprs=matrix(rnorm(10000), nrow=1000L),
         phenoData=new("AnnotatedDataFrame", data.frame(Sample=LETTERS[1:10])),
         featureData=new("AnnotatedDataFrame",data.frame(GeneSymbol=gss)))
esetWmwRes <- wmwTest(eset ,gmt_list, valType="p.greater")
summary(esetWmwRes)

## using signed GMT file
signed_gmt_file <- system.file("extdata/test.gmt", package="BioQC")
signed_gmt <- readSignedGmt(signed_gmt_file)
esetSignedWmwRes <- wmwTest(eset, signed_gmt, valType="p.greater")

esetMat <- exprs(eset); rownames(esetMat) <- fData(eset)$GeneSymbol
esetSignedWmwRes2 <- wmwTest(esetMat, signed_gmt, valType="p.greater")