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

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):

# Multivariate Distance Matrix Regression (MDMR)
mdmr:

  # Used to determine if Multivariate Distance Matrix Regression (MDMR) will be added to the pipeline or not.
  run:  [0]

  # Inclusion list text file listing the participant IDs you wish to include in the MDMR analysis. If left as None, will include all subjects.
  inclusion_list : None

  # Path to a mask file. Voxels outside of the mask will be excluded from MDMR.
  roi_file: /path

  # Path to a CSV file containing the phenotypic regressor.
  regressor_file:

  # Name of the participants column in your regressor file.
  regressor_participant_column: ''

  # Columns from the CSV file indicating factor variables. Other columns will be handled as covariates. Separated by commas.
  regressor_columns: ''

  # Number of permutation tests to run on the Pseudo-F statistics.
  permutations:  15000

  # Number of Nipype nodes created while computing MDMR. Dependent upon computing resources.
  parallel_nodes:  10

  # If you want to create zstat maps
  zscore: [1]

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)