Last release: 1.0.0beta
(May 17, 2013)

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# Local analysis¶

Differences at the single connection level can be revealed by a local analysis. In this analysis, tests between the two groups are performed for each connection. Atom wise analysis (AWA) are methods that compute p-values separatly for each edge or node, apply a correction method and report the ones whose p-value is lower than a significant threshold. Given the tremendous number of tests, the correction comes with a high cost in statistical power. Subtle differences at the connection or node scale are then difficult to establish.

## Relaxation methods¶

In order to increase the statistical power of local analysis procedures, Meskaldji adapted a method proposed by Benjamini and Heller (2007) to the analysis of connectomes at the local scale.

This method, referred to as a two step multiple comparison procedure for positively dependent data, takes into account the positive dependance between affected nodes or edges. In overall, the first step is a subnetwork analysis, where the M edges or nodes are pooled into m subnetworks. A mean summary statistic is computed for each subnetwork, and the corresponding p-values are corrected for m multiple comparisons. This results into two sets of subnetworks: significant (positive) subnetworks with p-value lower than a significant threshold, and non-significant (negative) subnetworks whose p-value is greater than the threshold. Decreasing the number of tests from M to m increases the power of the test.

The second step corresponds to an atom wise analysis, but the p-values of the connections or edges belonging to positive (negative) subnetworks are modified by a “relaxation” (“tightening”) coefficient before the application of correction procedures. The computation of the relaxation or tightening coefficient takes into account the information provided by the subnetwork analysis, introducing the positive dependance between affected nodes or edges into the local analysis.

The two step procedure can either apply a correction method in the first step (“Relaxed Method With Correction” or RMWC) or apply no correction (“Relaxed Method with No Correction” or RMNC). The control of the whole procedure is inherited from the correction method used in the second step, which can be any correction method described in the litterature (Bonferroni, FDR, BH95, etc...).