Description Usage Arguments Details Value Note Author(s) References See Also Examples
Performs twosample nonparametric multivariate test of means based on the minimum spanning tree (MST). It calculates the mean deviation between the cumulative distribution functions (CDFs) of sample ranks in two conditions. It tests the null hypothesis that a set of features has the same mean in two conditions versus different means.
1 
object 
a numeric matrix with columns and rows respectively corresponding to samples and features. 
group 
a numeric vector indicating group associations for samples. Possible values are 1 and 2. 
nperm 
number of permutations used to estimate the null distribution of the test statistic. If not given, a default value 1000 is used. 
pvalue.only 
logical. If 
This function tests the null hypothesis that a set of features has
no difference in mean (shift) between two conditions. It performs a twosample
nonparametric multivariate test by ranking samples based on the minimum spanning
tree (MST) as proposed by Friedman and Rafsky (1979). The MST of the weighted
undirectional graph created from the samples is found.
The nodes of the MST are ranked based on their position in the MST. The MST
is rooted at the node with largest geodisic distance (rank 1) and then nodes
are ranked in the High Directed Preorder (HDP) traversal of the tree
(Rahmatallah et. al. 2012). The mean deviation between the cumulative
distribution functions (CDFs) of sample ranks in two conditions is calculated.
The null distribution of the test statistic is estimated by permuting sample
labels nperm
times and calculating the test statistic for each.
Pvalue is calculated as
p.value = \frac{∑_{k=1}^{nperm} I ≤ft[ D_{k} ≥q D_{obs} \right] + 1}{nperm + 1}
where D_{k} is the test statistic for permutation k
, D_{obs} is the
observed test statistic, and I
is the indicator function.
When pvalue.only=TRUE
(default), function MDtest
returns
the pvalue indicating the attained significance level. When
pvalue.only=FALSE
, function MDtest
produces a list of
length 3 with the following components:
statistic 
the value of the observed test statistic. 
perm.stat 
numeric vector of the resulting test statistic for

p.value 
pvalue indicating the attained significance level. 
This function invokes function HDP.ranking
which does not
work properly if there is any node in the MST with more than 26 links.
However, this situation is almost impossible for a dataset composed of a few
hundreds or less of samples.
Yasir Rahmatallah and Galina Glazko
Rahmatallah Y., EmmertStreib F. and Glazko G. (2012) Gene set analysis for selfcontained tests: complex null and specific alternative hypotheses. Bioinformatics 28, 3073–3080.
Friedman J. and Rafsky L. (1979) Multivariate generalization of the WaldWolfowitz and Smirnov twosample tests. Ann. Stat. 7, 697–717.
KStest
, WWtest
, RKStest
,
RMDtest
, HDP.ranking
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## generate a feature set of length 20 in two conditions
## each condition has 20 samples
## use multivariate normal distribution
library(MASS)
ngenes < 20
nsamples < 40
## let the mean vector have zeros of length 20 both conditions
zero_vector < array(0,c(1,ngenes))
## set the covariance matrix to be an identity matrix for both conditions
cov_mtrx < diag(ngenes)
gp < mvrnorm(nsamples, zero_vector, cov_mtrx)
## apply a mean shift of 3 to half of the features under condition 2
gp[1:20,1:10] < gp[1:20,1:10] + 3
dataset < aperm(gp, c(2,1))
## first 20 samples belong to group 1
## second 20 samples belong to group 2
pvalue < MDtest(object=dataset, group=c(rep(1,20),rep(2,20)))

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