Multivariate Distance Matrix Regression (MDMR)

Introduction & Background

Connectome-wide Association Studies (CWAS) allow researchers to explore relationships between patterns of functional connectivity (the functional connectome), behavior, and phenotypic factors. The CWAS method that is implemented in C-PAC (Shehzad et al., 2014) examines the correlation among patterns of functional connectivity and phenotypes using the Multivariate Distance Matrix Regression (MDMR; Reiss et al., 2010). Compared to traditional univariate techniques which require rigorous correction for multiple comparisons, a multivariate approach significantly reduces the number of connectivity-phenotype comparisons needed to run a CWAS (Shehzad et al., 2014).

Computation and Analysis Considerations

Computation steps for CWAS are listed below as described by Shehzad and colleagues (2014).

  1. For each subject, C-PAC computes the correlation of BOLD signals between every possible pair of gray matter voxels, resulting in a V x V correlation matrix for each subject (where V is the number of gray matter voxels).
  2. To determine individual differences, patterns of whole-brain connectivity for each voxel are compared to the connectivity pattern for the same voxel between all possible pairs of subjects. A distance matrix is then computed which represents the dissimilarity between whole-brain connectivity patterns for any pair of subjects.
  3. MDMR is then used to test whether, for each voxel, whole-brain connectivity patterns tend to be more similar for individuals with like phenotypes (within-group) than individuals with unlike phenotypes (between-group). This quantifies how well phenotypic variables explain the distances between participants in the distance matrix.
  4. The significance of these similarities and differences is assessed with a permutation test. This identifies brain regions whose whole-brain pattern of connectivity is significantly predicted by a particular phenotypic variable.

The figure below (taken from Shehzad et al., 2010) outlines these steps. For more detail on how C-PAC handles these computations, please see the CWAS section of the developer documentation.

_images/cwas_shehzad_schematic.png

It is important to note that the results of MDMR analysis do not contain information about the direction of connectivity-phenotype relationships, nor the specific connections underlying these connectome-wide associations. Follow-up analysis using seed-based correlation analysis (or similar methods) is required to discover this information (Shehzad et al., 2014). To avoid bias caused by ‘double-dipping’ your data (Kriegeskorte et al., 2009), this analysis should always be performed on an independent sample (Shehzad et al., 2014). Further, the results of these follow-up analyses should take into account existing knowledge about brain anatomy and physiology before being considered definitive (Shehzad et al., 2014).

Applications and Recommendations

As C-PAC is one of the first public software packages to implement CWAS, it has yet to be utilized by more than a few researchers. The most notable use to date is the analysis performed by Shehzad and colleagues, who found robust associations between functional connectivity and a number of phenotypic characteristics including age, ADHD diagnosis, IQ, and L-dopa administration.

_images/cwas_shehzad_brains.png

As CWAS examines connectivity across the whole brain, it may have reduced sensitivity to highly-localized sets of connections related to a phenotype. This issue can be addressed by limiting analysis to connectivity between specific anatomical regions (Shehzad et al., 2014), which can be accomplished by defining an ROI mask during C-PAC setup.

Configuring CWAS

Using the GUI

_images/cwas.png
  1. Run CWAS - [Off, On]: Used to determine if CWAS will be added to the pipeline or not.
  2. Mask ROI File - [path]: Path to a mask file. Voxels outside of the mask will be excluded from CWAS.
  3. Regressor File - [path]: Path to a text file containing the phenotypic regressor.
  4. Regressor Participant Column Name - [string]: Name of the participants column in your regressor file.
  5. Regressor of Interest columns - [string]: Columns of the regressor of interest in your regressor file.
  6. Permutations - [integer]: Number of permutation tests to run on the Pseudo-F statistics.
  7. Parallel Nodes - [integer]: Number of Nipype nodes created while computing CWAS. Dependent upon computing resources.

Configuration Using a YAML File

To configure CWAS options within a YAML file, add the following lines to your file (with appropriate substitutions for paths):

runCWAS = [0]
cwas_roi_file = '/path/to/cwas_mask_file'
cwas_regressor_file = '/path/to/cwas_regressor_file'
cwas_regressor_participant_column = 'ID
cwas_regressor_columns = ['FIQ', 'VIQ', 'PIQ']
cwas_permutations = 500
cwas_parallel_nodes = 3

References

Reiss, P.T., Stevens, M.H.H., Shehzad, Z., Petkova, E. & Milham, M.P. On distance-based permutation tests for between-group comparisons. Biometrics 66, 636–643 (2010).

Shehzad, Z., Kelly, C., Reiss, P.T., Craddock, C.R., Emerson, J.W., McMahon, K., Copland, D.A., Castellanos, F.X., & Milham, M.P. An Analytic Framework for Connectome-Wide Association Studies. Neuroimage, 93 Pt 1, 74–94 (2014).

Kriegeskorte, N., Simmons, W.K., Bellgowan, P.S.F. & Baker, C.I. Circular analysis in systems neuroscience: the dangers of double dipping. Nat Neurosci 12, 535–540 (2009)