gsMMD2.default {GeneSelectMMD} | R Documentation |
Gene selection based on the marginal distributions of gene profiles that characterized by a mixture of three-component multivariate distributions. Input is a data matrix. The user needs to provide initial gene cluster membership.
gsMMD2.default(X, memSubjects, memIni, maxFlag = TRUE, thrshPostProb = 0.5, geneNames = NULL, alpha = 0.05, transformFlag = FALSE, transformMethod = "boxcox", scaleFlag = FALSE, if.center = TRUE, if.scale = TRUE, criterion = c("cor", "skewness", "kurtosis"), minL = -10, maxL = 10, stepL = 0.1, eps = 0.001, ITMAX = 100, plotFlag = FALSE, quiet=TRUE)
X |
a data matrix. The rows of the matrix are genes. The columns of the matrix are subjects. |
memSubjects |
a vector of membership of subjects. memSubjects[i]=1 means the i-th subject belongs to diseased group, 0 otherwise.
|
memIni |
a vector of user-provided gene cluster membership. |
maxFlag |
logical. Indicate how to assign gene class membership. maxFlag =TRUE means that a gene will be assigned
to a class in which the posterior probability of the gene belongs to this class is maximum. maxFlag =FALSE means that a gene will be assigned to class 1 if the posterior probability of the gene belongs to class 1 is
greater than thrshPostProb . Similarly, a gene will be assigned to class 1 if the posterior probability of the gene belongs to class 1 is
greater than thrshPostProb . If the posterior probability is less than thrshPostProb , the gene
will be assigned to class 2 (non-differentially expressed gene group). |
thrshPostProb |
threshold for posterior probabilities. For example, if the posterior probability that a gene belongs to cluster 1 given its gene expression levels is larger than thrshPostProb , then this gene will be assigned to cluster 1. |
geneNames |
an optional character vector of gene names |
alpha |
significant level which is equal to 1-conf.level ,
conf.level is the argument for the function t.test .
|
transformFlag |
logical. Indicate if data transformation is needed |
transformMethod |
method for transforming data. Available methods include "boxcox", "log2", "log10", "log", "none". |
scaleFlag |
logical. Indicate if gene profiles are to be scaled. If transformFlag=TRUE and scaleFlag=TRUE , then scaling is performed after transformation. |
if.center |
logical. If scaleFlag=TRUE and if.center=TRUE , then each gene profile will be centered to have mean zero. |
if.scale |
logical. If scaleFlag=TRUE and if.scale=TRUE , then each gene profile will be scaled to have variance one. |
criterion |
if transformFlag=TRUE , criterion indicates what criterion to determine if data looks like normal. “cor” means using Pearson's correlation. The idea is that the observed quantiles after transformation should be close to theoretical normal quantiles. So we can use Pearson's correlation to check if the scatter plot of theoretical normal quantiles versus observed quantiles is a straightline. “skewness” means using skewness measure to check if the distribution of the transformed data are close to normal distribution; “kurtosis” means using kurtosis measure to check normality. |
minL |
lower limit for the lambda parameter used in Box-Cox transformation |
maxL |
upper limit for the lambda parameter used in Box-Cox transformation |
stepL |
step increase when searching the optimal lambda parameter used in Box-Cox transformation |
eps |
a small positive value. If the absolute value of a value is smaller than eps , this value is regarded as zero. |
ITMAX |
maximum iteration allowed for iterations in the EM algorithm |
plotFlag |
logical. Indicate if the Box-Cox normality plot should be output. |
quiet |
logical. Indicate if intermediate results should be printed out. |
We assume that the distribution of gene expression profiles is a mixture of 3-component multivariate normal distributions sum_{k=1}^{3} π_k f_k(x|theta). Each component distribution f_k corresponds to a gene cluster. The 3 components correspond to 3 gene clusters: (1) up-regulated gene cluster, (2) non-differentially expressed gene cluster, and (3) down-regulated gene cluster. The model parameter vector is theta=(π_1, π_2, π_3, μ_{c1}, σ^2_{c1}, rho_{c1}, μ_{n1}, σ^2_{n1}, rho_{n1}, μ_2, σ^2_2, rho_2, μ_{c3}, σ^2_{c3}, rho_{c3}, μ_{n3}, σ^2_{n3}, rho_{n3}. where π_1, π_2, and π_3 are the mixing proportions; μ_{c1}, σ^2_{c1}, and rho_{c1} are the marginal mean, variance, and correlation of gene expression levels of cluster 1 (up-regulated genes) for diseased subjects; μ_{n1}, σ^2_{n1}, and rho_{n1} are the marginal mean, variance, and correlation of gene expression levels of cluster 1 (up-regulated genes) for non-diseased subjects; μ_2, σ^2_2, and rho_2 are the marginal mean, variance, and correlation of gene expression levels of cluster 2 (non-differentially expressed genes); μ_{c3}, σ^2_{c3}, and rho_{c3} are the marginal mean, variance, and correlation of gene expression levels of cluster 3 (up-regulated genes) for diseased subjects; μ_{n3}, σ^2_{n3}, and rho_{n3} are the marginal mean, variance, and correlation of gene expression levels of cluster 3 (up-regulated genes) for non-diseased subjects.
Note that genes in cluster 2 are non-differentially expressed across abnormal and normal tissue samples. Hence there are only 3 parameters for cluster 2.
We apply the EM algorithm to estimate the model parameters. We regard the cluster membership of genes as missing values.
A list contains 10 elements.
dat |
the (transformed) microarray data matrix. If tranformation
performed, then dat will be different from the input
microarray data matrix. |
memSubjects |
the same as the input memSubjects . |
memGenes |
a vector of cluster membership of genes. 1 means up-regulated gene; 2 means non-differentially expressed gene; 3 means down-regulated gene. |
memGenes2 |
an variant of the vector of cluster membership of genes. 1 means differentially expressed gene; 0 means non-differentially expressed gene. |
para |
parameter estimates (c.f. details). |
llkh |
value of the loglikelihood function. |
wiMat |
posterior probability that a gene belongs to a cluster given the expression levels of this gene. Column i is for cluster i. |
memIni |
the initial cluster membership of genes. |
paraIni |
the parameter estimates based on initial gene cluster membership. |
llkhIni |
the value of loglikelihood function. |
lambda |
the parameter used to do Box-Cox transformation |
The speed of the program is slow for large data sets.
Weiliang Qiu stwxq@channing.harvard.edu, Wenqing He whe@stats.uwo.ca, Xiaogang Wang stevenw@mathstat.yorku.ca, Ross Lazarus ross.lazarus@channing.harvard.edu
Qiu, W.-L., He, W., Wang, X.-G. and Lazarus, R. (2008). A Marginal Mixture Model for Selecting Differentially Expressed Genes across Two Types of Tissue Samples. The International Journal of Biostatistics. 4(1):Article 20. http://www.bepress.com/ijb/vol4/iss1/20
library(ALL) data(ALL) eSet1 <- ALL[1:100, ALL$BT == "B3" | ALL$BT == "T2"] mat <- exprs(eSet1) mem.str <- as.character(eSet1$BT) nSubjects <- length(mem.str) memSubjects <- rep(0, nSubjects) # B3 coded as 0, T2 coded as 1 memSubjects[mem.str == "T2"] <- 1 myWilcox <- function(x, memSubjects, alpha = 0.05) { xc <- x[memSubjects == 1] xn <- x[memSubjects == 0] m <- sum(memSubjects == 1) res <- wilcox.test(x = xc, y = xn, conf.level = 1 - alpha) res2 <- c(res$p.value, res$statistic - m * (m + 1) / 2) names(res2) <- c("p.value", "statistic") return(res2) } tmp <- t(apply(mat, 1, myWilcox, memSubjects = memSubjects)) colnames(tmp) <- c("p.value", "statistic") memIni <- rep(2, nrow(mat)) memIni[tmp[, 1] < 0.05 & tmp[, 2] > 0] <- 1 memIni[tmp[, 1] < 0.05 & tmp[,2] < 0] <- 3 cat("initial gene cluster size>>\n"); print(table(memIni)); cat("\n"); obj.gsMMD <- gsMMD2.default(mat, memSubjects, memIni = memIni, transformFlag = TRUE, transformMethod = "boxcox", scaleFlag = TRUE) round(obj.gsMMD$para, 3)