lapmix (version 1.38.0)

lapmix.Fit: Empirical Bayes Statistics for Differential Expression under Laplace Model

Description

Computes posterior odds of differential expression under the Laplace mixture model, with parameters estimated using an empirical Bayes approach.

Usage

lapmix.Fit(Y, asym=FALSE, fast=TRUE, two.step=TRUE,  w=0.1, V=10, beta=0, gamma=1, alpha=0.1)

Arguments

Y

data.frame or matrix containing the log relative expression levels, where each row represents a gene. Alternatively, a list of arrays of possibly different sizes, or an object of class eSet or ExpressionSet.

asym

indicates whether the asymmetric Laplace model is used rather than the symmetric one.

fast

indicates whether the 'fast' estimation method is used.

two.step

indicates whether the two-step estimation method is used; otherwise the marginal likelihood is maximised in one step.

w,V,beta,gamma,alpha

initial values given to the optimization algorithms for the estimation of the hyperparameters.

Value

lap.lods

numeric vector containing the posterior log-odds of differential expression

prob

numeric vector containing the posterior probabilities of differential expression

med.number

number of differentially expressed genes according to the median rule

M

numeric vector with average log fold changes within genes

s_sq

numeric vector with sample variances within genes

nb.rep

numeric vector with number of replicates within genes

estimates

list containing the empirical Bayes estimates of the hyperparameters

code

integer indicating why the likelihood optmization terminated, cf. nlm routine. There are two such indicators in the case of the two-step estimation.

Details

This method fits the results of a microarray experiment to a Laplace mixture model. These results are assumed to take the form of normalized base 2 logarithm of the expression ratios. An empirical Bayes approach is used to estimate the hyperparameters of the model. The lap.lodds is sometimes known as the L-statistic (if the symmetric model is used) or the AL-statistic (if the asymmetric model is used). These statistics can be used to rank the genes according to the posterior odds of differential expression, via the routine laptopTable. They can be visualized using the lap.volcanoplot function.

If there are different numbers of replicates between genes, one may wish to write the data in a list of arrays. If a matrix representation is desired, one can stick in NaN's where appropriate.

The `fast' estimation method ignores the integrals which cannot be computed with the t-distribution function. This method is suggested, since these problematic integrals are few and far between. The estimates are practically not affected, and we avoid the potential problems that arise when integrating numerically with the integrate function.

References

Bhowmick, D., Davison, A.C., and Goldstein, D.R. (2006). A Laplace mixture model for identification of differential expression in microarray experiments.

Examples

#  Simulate gene expression data under Laplace mixture model: 3000 genes with
#  4 duplicates each; one gene in ten is differentially expressed.

G <- 3000
Y <- NULL
sigma_sq <- 1/rgamma(G, shape=2.8, scale=0.04)
mu <- rexp(G, rate=1/(sigma_sq*1.2))-rexp(G, rate=1/(sigma_sq*1.2))
is.diff <- sample(c(0,1), replace=TRUE, prob=c(0.9,0.1), size=G)
mu <- mu*is.diff
for(g in 1:G)
	Y <- rbind(Y, rnorm(4,mu[g], sd=sqrt(sigma_sq[g])))

# with symmetric model
res <- lapmix.Fit(Y)
res$estimates
laptopTable(res, 20)
lap.volcanoplot(res, highlight=res$med.number)

# with asymmetric model
res2 <- lapmix.Fit(Y, asym=TRUE)
res2$estimates
laptopTable(res2, 20)
lap.volcanoplot(res2, highlight=res2$med.number)