brainconn.nbs.nbs_bct

nbs_bct(x, y, thresh, k=1000, tail='both', paired=False, verbose=False)[source]

Performs the NBS for populations X and Y for a t-statistic threshold of alpha.

Parameters:
  • x (NxNxP numpy.ndarray) – matrix representing the first population with P subjects. must be symmetric.
  • y (NxNxQ numpy.ndarray) – matrix representing the second population with Q subjects. Q need not equal P. must be symmetric.
  • thresh (float) – minimum t-value used as threshold
  • k (int, optional) – number of permutations used to estimate the empirical null distribution
  • tail ({'both', 'left', 'right'}, optional) – enables specification of particular alternative hypothesis ‘left’ : mean population of X < mean population of Y ‘right’ : mean population of Y < mean population of X ‘both’ : means are unequal (default)
  • paired (bool, optional) – use paired sample t-test instead of population t-test. requires both subject populations to have equal N. default value = False
  • verbose (bool, optional) – print some extra information each iteration. defaults value = False
Returns:

  • pval (Cx1 numpy.ndarray) – A vector of corrected p-values for each component of the networks identified. If at least one p-value is less than alpha, the omnibus null hypothesis can be rejected at alpha significance. The null hypothesis is that the value of the connectivity from each edge has equal mean across the two populations.
  • adj (IxIxC numpy.ndarray) – an adjacency matrix identifying the edges comprising each component. edges are assigned indexed values.
  • null (Kx1 numpy.ndarray) – A vector of K sampled from the null distribution of maximal component size.

Notes

The NBS[R5426218f292b-1]_ is a nonparametric statistical test used to isolate the components of an N x N undirected connectivity matrix that differ significantly between two distinct populations. Each element of the connectivity matrix stores a connectivity value and each member of the two populations possesses a distinct connectivity matrix. A component of a connectivity matrix is defined as a set of interconnected edges.

The NBS is essentially a procedure to control the family-wise error rate, in the weak sense, when the null hypothesis is tested independently at each of the N(N-1)/2 edges comprising the undirected connectivity matrix. The NBS can provide greater statistical power than conventional procedures for controlling the family-wise error rate, such as the false discovery rate, if the set of edges at which the null hypothesis is rejected constitues a large component or components.

The NBS comprises fours steps:

  1. Perform a two-sample T-test at each edge indepedently to test the hypothesis that the value of connectivity between the two populations come from distributions with equal means.
  2. Threshold the T-statistic available at each edge to form a set of suprathreshold edges.
  3. Identify any components in the adjacency matrix defined by the set of suprathreshold edges. These are referred to as observed components. Compute the size of each observed component identified; that is, the number of edges it comprises.
  4. Repeat K times steps 1-3, each time randomly permuting members of the two populations and storing the size of the largest component identified for each permuation. This yields an empirical estimate of the null distribution of maximal component size. A corrected p-value for each observed component is then calculated using this null distribution.

References

[1]Zalesky A, Fornito A, Bullmore ET (2010) Network-based statistic: Identifying differences in brain networks. NeuroImage. 10.1016/j.neuroimage.2010.06.041