MODIFIED TEST STATISTICS BY INTER-VOXEL VARIANCE SHRINKAGE WITH AN APPLICATION TO fMRI

Functional Magnetic Resonance Imaging (fMRI) is a non-invasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of fMRI 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 in the statistical analysis of fMRI data is desirable in order to improve efficiency. Here we construct a hierarchical model and apply an Empirical Bayes framework on the analysis of group fMRI 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 in lieu of the classical t-statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances towards a common value. The shrunken estimator for voxelspecific 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 rate 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.

Semiparametric Theory for Causal Mediation Analysis: efficiency bounds, multiple robustness, and sensitivity analysis

Whilst estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of the exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Although powerful semiparametric methodologies have been developed to analyze observational studies, that produce double robust and highly efficient estimates of the marginal total causal effect, similar methods for mediation analysis are currently lacking. Thus, this paper develops a general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables. Our analytic framework is particularly appealing, because it gives new insights on issues of efficiency and robustness in the context of mediation analysis. In particular, we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects, and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable.