populationMeansInAdmixture: Estimate the population-specific mean values in an admixed population.

Description

Uses the expression values from an admixed population and estimates of the proportions of sub-populations to estimate the population specific mean values. For example, this function can be used to estimate the cell type specific mean gene expression values based on expression values from a mixture of cells. The method is described in Shen-Orr et al (2010) where it was used to estimate cell type specific gene expression levels based on a mixture sample.

Usage

populationMeansInAdmixture(
    datProportions, datE.Admixture, 
    scaleProportionsTo1 = TRUE,
    scaleProportionsInCelltype = TRUE, 
    setMissingProportionsToZero = FALSE)

Arguments

datProportions

a matrix of non-negative numbers (ideally proportions) where the rows correspond to the samples (rows of datE.Admixture) and the columns correspond to the sub-populations of the mixture. The function calculates a mean expression value for each column of datProportions. Negative entries in datProportions lead to an error message. But the rows of datProportions do not have to sum to 1, see the argument scaleProportionsTo1.

datE.Admixture

a matrix of numbers. The rows correspond to samples (mixtures of populations). The columns contain the variables (e.g. genes) for which the means should be estimated.

scaleProportionsTo1

logical. If set to TRUE (default) then the proportions in each row of datProportions are scaled so that they sum to 1, i.e. datProportions[i,]=datProportions[i,]/max(datProportions[i,]). In general, we recommend to set it to TRUE.

scaleProportionsInCelltype

logical. If set to TRUE (default) then the proportions in each cell types are recaled and make the mean to 0.

setMissingProportionsToZero

logical. Default is FALSE. If set to TRUE then it sets missing values in datProportions to zero.

Value

a numeric matrix whose rows correspond to the columns of datE.Admixture (e.g. to genes) and whose columns correspond to the columns of datProportions (e.g. sub populations or cell types).

Details

The function outputs a matrix of coefficients resulting from fitting a regression model. If the proportions sum to 1, then i-th row of the output matrix reports the coefficients of the following model lm(datE.Admixture[,i]~.-1,data=datProportions). Aside, the minus 1 in the formula indicates that no intercept term will be fit. Under certain assumptions, the coefficients can be interpreted as the mean expression values in the sub-populations (Shen-Orr 2010).

References

Shen-Orr SS, Tibshirani R, Khatri P, Bodian DL, Staedtler F, Perry NM, Hastie T, Sarwal MM, Davis MM, Butte AJ (2010) Cell type-specific gene expression differences in complex tissues. Nature Methods, vol 7 no.4

Examples

Run this code

# NOT RUN {
set.seed(1)
# this is the number of complex (mixed) tissue samples, e.g. arrays
m=10
# true count data (e.g. pure cells in the mixed sample)
datTrueCounts=as.matrix(data.frame(TrueCount1=rpois(m,lambda=16),
TrueCount2=rpois(m,lambda=8),TrueCount3=rpois(m,lambda=4),
TrueCount4=rpois(m,lambda=2)))
no.pure=dim(datTrueCounts)[[2]]

# now we transform the counts into proportions
divideBySum=function(x) t(x)/sum(x)
datProportions= t(apply(datTrueCounts,1,divideBySum))
dimnames(datProportions)[[2]]=paste("TrueProp",1:dim(datTrueCounts)[[2]],sep=".")

# number of genes that are highly expressed in each pure population
no.genesPerPure=rep(5, no.pure)
no.genes= sum(no.genesPerPure)
GeneIndicator=rep(1:no.pure, no.genesPerPure)
# true mean values of the genes in the pure populations
# in the end we hope to estimate them from the mixed samples
datTrueMeans0=matrix( rnorm(no.genes*no.pure,sd=.3), nrow= no.genes,ncol=no.pure)
for (i in 1:no.pure ){
datTrueMeans0[GeneIndicator==i,i]= datTrueMeans0[GeneIndicator==i,i]+1
}
dimnames(datTrueMeans0)[[1]]=paste("Gene",1:dim(datTrueMeans0)[[1]],sep="." )
dimnames(datTrueMeans0)[[2]]=paste("MeanPureCellType",1:dim(datTrueMeans0)[[2]],
                                   sep=".")
# plot.mat(datTrueMeans0)
# simulate the (expression) values of the admixed population samples

noise=matrix(rnorm(m*no.genes,sd=.1),nrow=m,ncol= no.genes)
datE.Admixture= as.matrix(datProportions) %*% t(datTrueMeans0) + noise
dimnames(datE.Admixture)[[1]]=paste("MixedTissue",1:m,sep=".")

datPredictedMeans=populationMeansInAdmixture(datProportions,datE.Admixture)

par(mfrow=c(2,2))
for (i in 1:4 ){
verboseScatterplot(datPredictedMeans[,i],datTrueMeans0[,i],
xlab="predicted mean",ylab="true mean",main="all populations")
abline(0,1)
}

#assume we only study 2 populations (ie we ignore the others)
selectPopulations=c(1,2)
datPredictedMeansTooFew=populationMeansInAdmixture(datProportions[,selectPopulations],
                                                   datE.Admixture)

par(mfrow=c(2,2))
for (i in 1:length(selectPopulations) ){
verboseScatterplot(datPredictedMeansTooFew[,i],datTrueMeans0[,i],
xlab="predicted mean",ylab="true mean",main="too few populations")
abline(0,1)
}

#assume we erroneously add a population
datProportionsTooMany=data.frame(datProportions,WrongProp=sample(datProportions[,1]))
datPredictedMeansTooMany=populationMeansInAdmixture(datProportionsTooMany,
                                 datE.Admixture)

par(mfrow=c(2,2))
for (i in 1:4 ){
  verboseScatterplot(datPredictedMeansTooMany[,i],datTrueMeans0[,i],
  xlab="predicted mean",ylab="true mean",main="too many populations")
  abline(0,1)
}

# }

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