COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented

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

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