# NBS: Network-based statistic for brain MRI data In brainGraph: Graph Theory Analysis of Brain MRI Data

## Description

Calculates the network-based statistic (NBS), which allows for family-wise error (FWE) control over network data, introduced for brain MRI data by Zalesky et al. Accepts a three-dimensional array of all subjects' connectivity matrices and a `data.table` of covariates, and creates a null distribution of the largest connected component size by permuting subjects across groups. The covariates `data.table` must have (at least) a Group column.

Print a summary of NBS analysis

## Usage

 ```1 2 3 4 5 6 7 8``` ```NBS(A, covars, con.mat, con.type = c("t", "f"), X = NULL, con.name = NULL, p.init = 0.001, N = 1000, perms = NULL, symm.by = c("max", "min", "avg"), alternative = c("two.sided", "less", "greater"), long = FALSE, ...) ## S3 method for class 'NBS' summary(object, contrast = NULL, digits = max(3L, getOption("digits") - 2L), ...) ```

## Arguments

 `A` Three-dimensional array of all subjects' connectivity matrices `covars` A `data.table` of covariates `con.mat` Numeric matrix specifying the contrast(s) of interest; if only one contrast is desired, you can supply a vector `con.type` Character string; either `'t'` or `'f'` (for t or F-statistics). Default: `'t'` `X` Numeric matrix, if you wish to supply your own design matrix (default: `NULL`) `con.name` Character vector of the contrast name(s); if `con.mat` has row names, those will be used for reporting results (default: `NULL`) `p.init` Numeric; the initial p-value threshold (default: `0.001`) `N` Integer; number of permutations to create (default: 5e3) `perms` Matrix of permutations, if you would like to provide your own (default: `NULL`) `symm.by` Character string; how to create symmetric off-diagonal elements (default: `max`) `alternative` Character string, whether to do a two- or one-sided test (default: `'two.sided'`) `long` Logical indicating whether or not to return all permutation results (default: `FALSE`) `...` Other arguments passed to `brainGraph_GLM_design` `object` A `NBS` object `contrast` Integer specifying the contrast to summarize; defaults to showing results for all contrasts `digits` Integer specifying the number of digits to display for p-values

## Details

The graph that is returned by this function will have a `t.stat` edge attribute which is the t-statistic for that particular connection, along with a `p` edge attribute, which is the p-value for that connection. Additionally, each vertex will have a `p.nbs` attribute representing 1 - the p-value associated with that vertex's component.

## Value

An object of class `NBS` with some input arguments in addition to:

 `X` The design matrix `removed` Character vector of subject ID's removed due to incomplete data (if any) `T.mat` List of numeric matrices (symmetric) containing the statistics for each edge `p.mat` List of numeric matrices (symmetric) containing the P-values `components` List containing data tables of the observed and permuted connected component sizes and P-values

## Author(s)

Christopher G. Watson, [email protected]

## References

Zalesky A., Fornito A., Bullmore E.T. (2010) Network-based statistic: identifying differences in brain networks. NeuroImage, 53(4):1197-1207.

`brainGraph_GLM_design, brainGraph_GLM_fit_t`
Other Group analysis functions: `IndividualContributions`, `brainGraph_GLM`, `brainGraph_boot`, `brainGraph_mediate`, `brainGraph_permute`, `mtpc`
 ```1 2 3 4``` ```## Not run: max.comp.nbs <- NBS(A.norm.sub[[1]], covars.dti, N=5e3) ## End(Not run) ```