shrinkt.stat: The Shrinkage t Statistic
In st: Shrinkage t Statistic and Correlation-Adjusted t-Score

Description Usage Arguments Details Value Author(s) References See Also Examples

shrinkt.stat and shrinkt.fun compute the “shrinkage t” statistic of Opgen-Rhein and Strimmer (2007).

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shrinkt.stat(X, L, lambda.var, lambda.freqs, var.equal=TRUE, 
   paired=FALSE, verbose=TRUE)
shrinkt.fun(L, lambda.var, lambda.freqs, var.equal=TRUE, verbose=TRUE)

`X`	data matrix. Note that the columns correspond to variables (“genes”) and the rows to samples.
`L`	factor with class labels for the two groups. If only a single label is given then a one-sample t-score against 0 is computed.
`lambda.var`	Shrinkage intensity for the variances. If not specified it is estimated from the data. `lambda.var=0` implies no shrinkage and `lambda.var=1` complete shrinkage.
`lambda.freqs`	Shrinkage intensity for the frequencies. If not specified it is estimated from the data. `lambda.freqs=0` implies no shrinkage (i.e. empirical frequencies).
`var.equal`	assume equal (default) or unequal variances in each group.
`paired`	compute paired t-score (default is to use unpaired t-score).
`verbose`	print out some (more or less useful) information during computation.

The “shrinkage t” statistic is similar to the usual t statistic, with the replacement of the sample variances by corresponding shrinkage estimates. These are derived in a distribution-free fashion and with little a priori assumptions. Using the “shrinkage t” statistic procduces highly accurate rankings - see Opgen-Rhein and Strimmer (2007).

The“shrinkage t” statistic can be generalized to include gene-wise correlation, see shrinkcat.stat.

The scale factor in the ”shrinkage t” statistic is computed from the estimated frequencies (to use the standard empirical scale factor set lambda.freqs=0).

shrinkt.stat returns a vector containing the “shrinkage t” statistic for each variable/gene.

The corresponding shrinkt.fun functions return a function that produces the “shrinkage t” statistics when applied to a data matrix (this is very useful for simulations).

Rainer Opgen-Rhein, Verena Zuber, and Korbinian Strimmer (https://strimmerlab.github.io).

Opgen-Rhein, R., and K. Strimmer. 2007. Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach. Statist. Appl. Genet. Mol. Biol. 6:9. <DOI:10.2202/1544-6115.1252>

studentt.stat, diffmean.stat, shrinkcat.stat.

# load st library 
library("st")

# load Choe et al. (2005) data
data(choedata)
X <- choe2.mat
dim(X) # 6 11475  
L <- choe2.L
L

# L may also contain some real labels
L = c("group 1", "group 1", "group 1", "group 2", "group 2", "group 2")

# shrinkage t statistic (equal variances)
score = shrinkt.stat(X, L)
order(score^2, decreasing=TRUE)[1:10]

# [1] 10979 11068    50  1022   724  5762    43  4790 10936  9939
#  lambda.var (variances):  0.3882
#  lambda.freqs (frequencies):  1

# shrinkage t statistic (unequal variances)
score = shrinkt.stat(X, L, var.equal=FALSE)
order(score^2, decreasing=TRUE)[1:10]

# [1] 11068    50 10979   724    43  1022  5762 10936  9939  9769
#  lambda.var class #1 and class #2 (variances):  0.3673   0.3362
#  lambda.freqs (frequencies): 1

# compute q-values and local false discovery rates
library("fdrtool")
fdr.out = fdrtool(score) 
sum( fdr.out$qval < 0.05 )
sum( fdr.out$lfdr < 0.2 )
fdr.out$param


# computation of paired t-score

# paired shrinkage t statistic
score = shrinkt.stat(X, L, paired=TRUE)
order(score^2, decreasing=TRUE)[1:10]
# [1] 50  4790  5393 11068  5762 10238  9939   708   728    68


# if there is no shrinkage the paired shrinkage t score reduces
# to the conventional paired student t statistic
score = studentt.stat(X, L, paired=TRUE)
score2 = shrinkt.stat(X, L, lambda.var=0, lambda.freqs=0, paired=TRUE, verbose=FALSE)
sum((score-score2)^2)