metaAnalysis: Meta-analysis of binary and continuous variables

In WGCNA: Weighted Correlation Network Analysis

Meta-analysis of binary and continuous variables

Description

This is a meta-analysis complement to functions standardScreeningBinaryTrait and standardScreeningNumericTrait. Given expression (or other) data from multiple independent data sets, and the corresponding clinical traits or outcomes, the function calculates multiple screening statistics in each data set, then calculates meta-analysis Z scores, p-values, and optionally q-values (False Discovery Rates). Three different ways of calculating the meta-analysis Z scores are provided: the Stouffer method, weighted Stouffer method, and using user-specified weights.

Usage

metaAnalysis(multiExpr, multiTrait, 
             binary = NULL, 
             metaAnalysisWeights = NULL, 
             corFnc = cor, corOptions = list(use = "p"), 
             getQvalues = FALSE, 
             getAreaUnderROC = FALSE,
             useRankPvalue = TRUE,
             rankPvalueOptions = list(),
             setNames = NULL, 
             kruskalTest = FALSE, var.equal = FALSE, 
             metaKruskal = kruskalTest, na.action = "na.exclude")

Arguments

multiExpr	Expression data (or other data) in multi-set format (see checkSets). A vector of lists; in each list there must be a component named data whose content is a matrix or dataframe or array of dimension 2.
multiTrait	Trait or ourcome data in multi-set format. Only one trait is allowed; consequesntly, the data component of each component list can be either a vector or a data frame (matrix, array of dimension 2).
binary	Logical: is the trait binary (TRUE) or continuous (FALSE)? If not given, the decision will be made based on the content of multiTrait.
metaAnalysisWeights	Optional specification of set weights for meta-analysis. If given, must be a vector of non-negative weights, one entry for each set contained in multiExpr.
corFnc	Correlation function to be used for screening. Should be either the default cor or its robust alternative, bicor.
corOptions	A named list giving extra arguments to be passed to the correlation function.
getQvalues	Logical: should q-values (FDRs) be calculated?
getAreaUnderROC	Logical: should area under the ROC be calculated? Caution, enabling the calculation will slow the function down considerably for large data sets.
useRankPvalue	Logical: should the rankPvalue function be used to obtain alternative meta-analysis statistics?
rankPvalueOptions	Additional options for function rankPvalue. These include na.last (default "keep"), ties.method (default "average"), calculateQvalue (default copied from input getQvalues), and pValueMethod (default "all"). See the help file for rankPvalue for full details.
setNames	Optional specification of set names (labels). These are used to label the corresponding components of the output. If not given, will be taken from the names attribute of multiExpr. If names(multiExpr) is NULL, generic names of the form Set_1, Set2, ... will be used.
kruskalTest	Logical: should the Kruskal test be performed in addition to t-test? Only applies to binary traits.
var.equal	Logical: should the t-test assume equal variance in both groups? If TRUE, the function will warn the user that the returned test statistics will be different from the results of the standard t.test function.
metaKruskal	Logical: should the meta-analysis be based on the results of Kruskal test (TRUE) or Student t-test (FALSE)?
na.action	Specification of what should happen to missing values in t.test.

Details

The Stouffer method of combines Z statistics by simply taking a mean of input Z statistics and multiplying it by sqrt(n), where n is the number of input data sets. We refer to this method as Stouffer.equalWeights. In general, a better (i.e., more powerful) method of combining Z statistics is to weigh them by the number of degrees of freedom (which approximately equals n). We refer to this method as weightedStouffer. Finally, the user can also specify custom weights, for example if a data set needs to be downweighted due to technical concerns; however, specifying own weights by hand should be done carefully to avoid possible selection biases.

Value

Data frame with the following components:

ID	Identifier of the input genes (or other variables)
Z.equalWeights	Meta-analysis Z statistics obtained using Stouffer's method with equal weights
p.equalWeights	p-values corresponding to Z.Stouffer.equalWeights
q.equalWeights	q-values corresponding to p.Stouffer.equalWeights, only present if getQvalues is TRUE.
Z.RootDoFWeights	Meta-analysis Z statistics obtained using Stouffer's method with weights given by the square root of the number of (non-missing) samples in each data set
p.RootDoFWeights	p-values corresponding to Z.DoFWeights
q.RootDoFWeights	q-values corresponding to p.DoFWeights, only present if getQvalues is TRUE.
Z.DoFWeights	Meta-analysis Z statistics obtained using Stouffer's method with weights given by the number of (non-missing) samples in each data set
p.DoFWeights	p-values corresponding to Z.DoFWeights
q.DoFWeights	q-values corresponding to p.DoFWeights, only present if getQvalues is TRUE.
Z.userWeights	Meta-analysis Z statistics obtained using Stouffer's method with user-defined weights. Only present if input metaAnalysisWeights are present.
p.userWeights	p-values corresponding to Z.userWeights
q.userWeights	q-values corresponding to p.userWeights, only present if getQvalues is TRUE.

The next set of columns is present only if input useRankPvalue is TRUE and contain the output of the function rankPvalue with the same column weights as the above meta-analysis. Depending on the input options calculateQvalue and pValueMethod in rankPvalueOptions, some columns may be missing. The following columns are calculated using equal weights for each data set.

pValueExtremeRank.equalWeights	This is the minimum between pValueLowRank and pValueHighRank, i.e. min(pValueLow, pValueHigh)
pValueLowRank.equalWeights	Asymptotic p-value for observing a consistently low value across the columns of datS based on the rank method.
pValueHighRank.equalWeights	Asymptotic p-value for observing a consistently low value across the columns of datS based on the rank method.
pValueExtremeScale.equalWeights	This is the minimum between pValueLowScale and pValueHighScale, i.e. min(pValueLow, pValueHigh)
pValueLowScale.equalWeights	Asymptotic p-value for observing a consistently low value across the columns of datS based on the Scale method.
pValueHighScale.equalWeights	Asymptotic p-value for observing a consistently low value across the columns of datS based on the Scale method.
qValueExtremeRank.equalWeights	local false discovery rate (q-value) corresponding to the p-value pValueExtremeRank
qValueLowRank.equalWeights	local false discovery rate (q-value) corresponding to the p-value pValueLowRank
qValueHighRank.equalWeights	local false discovery rate (q-value) corresponding to the p-value pValueHighRank
qValueExtremeScale.equalWeights	local false discovery rate (q-value) corresponding to the p-value pValueExtremeScale
qValueLowScale.equalWeights	local false discovery rate (q-value) corresponding to the p-value pValueLowScale
qValueHighScale.equalWeights	local false discovery rate (q-value) corresponding to the p-value pValueHighScale
...	Analogous columns calculated by weighting each input set using the square root of the number of samples, number of samples, and user weights (if given). The corresponding column names carry the suffixes RootDofWeights, DoFWeights, userWeights.

The following columns contain results returned by standardScreeningBinaryTrait or standardScreeningNumericTrait (depending on whether the input trait is binary or continuous).

For binary traits, the following information is returned for each set:

corPearson.Set_1, corPearson.Set_2, ...	Pearson correlation with a binary numeric version of the input variable. The numeric variable equals 1 for level 1 and 2 for level 2. The levels are given by levels(factor(y)).
t.Student.Set_1, t.Student.Set_2, ...	Student t-test statistic
pvalueStudent.Set_1, pvalueStudent.Set_2, ...	two-sided Student t-test p-value.
qvalueStudent.Set_1, qvalueStudent.Set_2, ...	(if input qValues==TRUE) q-value (local false discovery rate) based on the Student T-test p-value (Storey et al 2004).
foldChange.Set_1, foldChange.Set_2, ...	a (signed) ratio of mean values. If the mean in the first group (corresponding to level 1) is larger than that of the second group, it equals meanFirstGroup/meanSecondGroup. But if the mean of the second group is larger than that of the first group it equals -meanSecondGroup/meanFirstGroup (notice the minus sign).
meanFirstGroup.Set_1, meanSecondGroup.Set_2, ...	means of columns in input datExpr across samples in the second group.
SE.FirstGroup.Set_1, SE.FirstGroup.Set_2, ...	standard errors of columns in input datExpr across samples in the first group. Recall that SE(x)=sqrt(var(x)/n) where n is the number of non-missing values of x.
SE.SecondGroup.Set_1, SE.SecondGroup.Set_2, ...	standard errors of columns in input datExpr across samples in the second group.
areaUnderROC.Set_1, areaUnderROC.Set_2, ...	the area under the ROC, also known as the concordance index or C.index. This is a measure of discriminatory power. The measure lies between 0 and 1 where 0.5 indicates no discriminatory power. 0 indicates that the "opposite" predictor has perfect discriminatory power. To compute it we use the function rcorr.cens with outx=TRUE (from Frank Harrel's package Hmisc).
nPresentSamples.Set_1, nPresentSamples.Set_2, ...	number of samples with finite measurements for each gene.

If input kruskalTest is TRUE, the following columns further summarize results of Kruskal-Wallis test:

stat.Kruskal.Set_1, stat.Kruskal.Set_2, ...	Kruskal-Wallis test statistic.
stat.Kruskal.signed.Set_1, stat.Kruskal.signed.Set_2, ...	(Warning: experimental) Kruskal-Wallis test statistic including a sign that indicates whether the average rank is higher in second group (positive) or first group (negative).
pvaluekruskal.Set_1, pvaluekruskal.Set_2, ...	Kruskal-Wallis test p-value.
qkruskal.Set_1, qkruskal.Set_2, ...	q-values corresponding to the Kruskal-Wallis test p-value (if input qValues==TRUE).
Z.Set1, Z.Set2, ...	Z statistics obtained from pvalueStudent.Set1, pvalueStudent.Set2, ... or from pvaluekruskal.Set1, pvaluekruskal.Set2, ..., depending on input metaKruskal.

For numeric traits, the following columns are returned:

cor.Set_1, cor.Set_2, ...	correlations of all genes with the trait
Z.Set1, Z.Set2, ...	Fisher Z statistics corresponding to the correlations
pvalueStudent.Set_1, pvalueStudent.Set_2, ...	Student p-values of the correlations
qvalueStudent.Set_1, qvalueStudent.Set_1, ...	(if input qValues==TRUE) q-values of the correlations calculated from the p-values
AreaUnderROC.Set_1, AreaUnderROC.Set_2, ...	area under the ROC
nPresentSamples.Set_1, nPresentSamples.Set_2, ...	number of samples present for the calculation of each association.

Author(s)

Peter Langfelder

References

For Stouffer's method, see

Stouffer, S.A., Suchman, E.A., DeVinney, L.C., Star, S.A. & Williams, R.M. Jr. 1949. The American Soldier, Vol. 1: Adjustment during Army Life. Princeton University Press, Princeton.

A discussion of weighted Stouffer's method can be found in

Whitlock, M. C., Combining probability from independent tests: the weighted Z-method is superior to Fisher's approach, Journal of Evolutionary Biology 18:5 1368 (2005)

See Also

standardScreeningBinaryTrait, standardScreeningNumericTrait for screening functions for individual data sets

WGCNA documentation built on Sept. 18, 2024, 5:08 p.m.