Modified test statistics by inter-voxel variance shrinkage with an application to f MRI

Shu Chih Su, Brian Caffo, Elizabeth Garrett-Mayer, Susan Spear Bassett

Research output: Contribution to journalArticlepeer-review


Functional magnetic resonance imaging (f MRI) is a noninvasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of f MRI studies is to identify localized brain regions where neuronal activation levels vary between groups. Single voxel t-tests have been commonly used to determine whether activation related to the protocol differs across groups. Due to the generally limited number of subjects within each study, accurate estimation of variance at each voxel is difficult. Thus, combining information across voxels is desirable in order to improve efficiency. Here, we construct a hierarchical model and apply an empirical Bayesian framework for the analysis of group f MRI data, employing techniques used in high-throughput genomic studies. The key idea is to shrink residual variances by combining information across voxels and subsequently to construct an improved test statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances toward a common value. The shrunken estimator for voxel-specific variance components on the group analyses outperforms the classical residual error estimator in terms of mean-squared error. Moreover, the shrunken test statistic decreases false-positive rates when testing differences in brain contrast maps across a wide range of simulation studies. This methodology was also applied to experimental data regarding a cognitive activation task.

Original languageEnglish (US)
Pages (from-to)219-227
Number of pages9
Issue number2
StatePublished - Apr 2009


  • General liner model
  • Group analysis
  • Hierarchical models
  • Image analysis
  • Shrinkage estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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