This vignette documents the implementation of NBR 0.1.3 for linear models.
We will analyze the
frontal3D dataset, which contains a 3D volume of 48 matrices, each matrix representing the functional connectivity between 28 nodes (in the frontal lobe). Phenotypic information (
frontal_phen) includes diagnostic GROUP (patient or control), sex, and age. We will test for a GROUP effect.
library(NBR) <- NBR:::frontal3D # Load 3D array cmx <- NBR:::frontal_roi # Load node labels brain_labs <- NBR:::frontal_phen # Load phenotypic info phen dim(cmx) # Show 3D array dimensions #>  28 28 48
We can plot the sample average matrix, with
library(lattice) <- apply(cmx, 1:2, mean) avg_mx # Set max-absolute value in order to set a color range centered in zero. <- max(abs(avg_mx)[is.finite(avg_mx)]) flim levelplot(avg_mx, main = "Average", ylab = "ROI", xlab = "ROI", at = seq(-flim, flim, length.out = 100))
As we can observe, this is a symmetric matrix with the pairwise connections of the 28 regions of interest (ROI)
brain_labs. The next step is to check the phenotypic information (stored in
phen) to perform statistic inferences edgewise. Before applying the NBR-LM, we check that the number of matrices (3rd dimension in the dataset) matches the number of observations in the
head(phen) #> Group Sex Age #> 1 Control F 8.52 #> 2 Control M 16.16 #> 3 Patient M 17.75 #> 4 Control M 12.27 #> 5 Control F 12.07 #> 6 Patient F 8.71 nrow(phen) #>  48 identical(nrow(phen), dim(cmx)) #>  TRUE
The data.frame contains the individual information for diagnostic group, sex, and chronological age. So, we are all set to perform an NBR-LM. We are going to test the effect of diagnostic group with a minimal number of permutations to check that we have no errors.
set.seed(18900217) # Because R. Fisher is my hero <- Sys.time() before <- nbr_lm_aov(net = cmx, nnodes = 28, idata = phen, nbr_group mod = "~ Group", thrP = 0.01, nperm = 10) #> Computing observed stats. #> Computing permutated stats. #> Permutation progress: .... <- Sys.time() after show(after-before) #> Time difference of 10.3054 secs
Although ten permutations is quite low to obtain a proper null distribution, we can see that they take several seconds to be performed. So we suggest to paralleling to multiple CPU cores with
set.seed(18900217) library(parallel) <- Sys.time() before <- nbr_lm_aov(net = cmx, nnodes = 28, idata = phen, nbr_group mod = "~ Group", thrP = 0.01, nperm = 100, cores = detectCores()) <- Sys.time() after length(nbr_group)
NBR functions return a nested list of at least two lists. The first list encompasses all the individual significant edges, their corresponding component and statistical inference (p < 0.01, in this example). In this case all the significant edges belong to a single component.
# Plot significant component <- array(0, dim(avg_mx)) edge_mat $components$Group[,2:3]] <- 1 edge_mat[nbr_grouplevelplot(edge_mat, col.regions = rev(heat.colors(100)), main = "Component", ylab = "ROI", xlab = "ROI")
show(nbr_group$fwe$Group) #> Component ncomp ncompFWE strn strnFWE #> 1 1 28 0 64.52926 0
As we can observe, significant edges are displayed in the upper triangle of the matrix, and the second list (
fwe) contains, for each term of the equation, the probability of the observed values to occur by chance, based on the null distribution.