Test GCM(s) for statistical significance

The function tests whether graphlet correlations (entries of the GCM) are significantly different from zero.

If two GCMs are given, the graphlet correlations of the two networks are tested for being significantly different, i.e., Fishers z-test is performed to test if the absolute differences between graphlet correlations are significantly different from zero.

Usage

testGCM(
  obj1,
  obj2 = NULL,
  adjust = "adaptBH",
  lfdrThresh = 0.2,
  trueNullMethod = "convest",
  alpha = 0.05,
  verbose = TRUE
)

Arguments

obj1

object of class GCM or GCD returned by calcGCM or calcGCD. See details.

obj2

optional object of class GCM returned by calcGCM. See details.

adjust

character indicating the method used for multiple testing adjustment. Possible values are "lfdr" (default) for local false discovery rate correction (via fdrtool), "adaptBH" for the adaptive Benjamini-Hochberg method (Benjamini and Hochberg, 2000), or one of the methods provided by p.adjust.

lfdrThresh

defines a threshold for the local fdr if "lfdr" is chosen as method for multiple testing correction. Defaults to 0.2 meaning that differences with a corresponding local fdr less than or equal to 0.2 are identified as significant.

trueNullMethod

character indicating the method used for estimating the proportion of true null hypotheses from a vector of p-values. Used for the adaptive Benjamini-Hochberg method for multiple testing adjustment (chosen by adjust = "adaptBH"). Accepts the provided options of the method argument of propTrueNull: "convest" (default), "lfdr", "mean", and "hist". Can alternatively be "farco" for the "iterative plug-in method" proposed by Farcomeni (2007).

alpha

numeric value between 0 and 1 giving the desired significance level.

verbose

logical. If TRUE (default), progress messages are printed.

Value

A list with the following elements:

gcm1	Graphlet Correlatoin Matrix GCM1
pvals1	Matrix with p-values (H0: gc1_ij = 0)
padjust1	Matrix with adjusted p-values

Additional elements if two GCMs are given:

gcm2	Graphlet Correlatoin Matrix GCM2
pvals2	Matrix with p-values (H0: gc2_ij = 0)
padjust2	Matrix with adjusted p-values
diff	Matrix with differences between graphlet correlations (GCM1 - GCM2)
absDiff	Matrix with absolute differences between graphlet correlations (|GCM1 - GCM2|)
pvalsDiff	Matrix with p-values (H0: |gc1_ij - gc2_ij| = 0)
pAdjustDiff	Matrix with adjusted p-values
sigDiff	Same as diff, but non-significant differences are set to zero.
sigAbsDiff	Same as absDiff, but non-significant values are set to zero.

Details

By applying Student's t-test to the Fisher-transformed correlations, all entries of the GCM(s) are tested for being significantly different from zero:

H0: gc_ij = 0 vs. H1: gc_ij != 0,

with gc_ij being the graphlet correlations.

If both GCMs are given or obj1 is of class GCD, the absolute differences between graphlet correlations are tested for being different from zero using Fisher's z-test. The hypotheses are:

H0: |d_ij| = 0 vs. H1: |d_ij| > 0,

where d_ij = gc1_ij - gc2_ij

Examples

# See help page of calcGCD()
?calcGCD