Statistical methods of estimation and inference for functional MR image analysis

Abstract

Two questions arising in the analysis of functional magnetic resonance imaging (fMRI) data acquired during periodic sensory stimulation are: i) how to measure the experimentally determined effect in fMRI time series; and ii) how to decide whether an apparent effect is significant. Our approach is first to fit a time series regression model, including sine and cosine terms at the (fundamental) frequency of experimental stimulation, by pseudogeneralized least squares (PGLS) at each pixel of an image. Sinusoidal modeling takes account of locally variable hemodynamic delay and dispersion, and PGLS fitting corrects for residual or endogenous autocorrelation in fMRI time series, to yield best unbiased estimates of the amplitudes of the sine and cosine terms at fundamental frequency; from these parameters the authors derive estimates of experimentally determined power and its standard error. Randomization testing is then used to create inferential brain activation maps (BAMs) of pixels significantly activated by the experimental stimulus. The methods are illustrated by application to data acquired from normal human subjects during periodic visual and auditory stimulation.

Multiple testing corrections, nonparametric methods, and random field theory

“…The problem was that fMRI times series' autocorrelation violates a basic assumption needed by permutation, exchangeability. Others had tackled this problem, by decorrelating the fMRI data using the fit of a parametric autocorrelation model (Bullmore et al, 1996;Locascio et al, 1997), however we found this mix of parametric and nonparametric modeling unsatisfactory 17 . However fMRI analysis quickly came to focus on group analysis using a summary statistic approach Mumford & Nichols, 2009), meaning our PET 1-scan-per-subject permutation methods remained relevant.…”

“…Another less-used alternative to FWE is the expected number of false positives (Bullmore et al, 1996). This measure is used in the CamBA software 6 to control the expected number of 4 People often say "FWE is conservative", but that's like saying a meter is too short.…”

Reducing vascular variability of fMRI data across aging populations using a breathholding task

“…Significantly active voxels for the saccade task and for the hypercapnia task were identified using a GLM analysis with a Fourier basis set in SPM2 (Bullmore, et al 1996;Handwerker, Daniel A 13 Josephs, et al 1997). For the saccade task, the temporal derivative of the three spatial and three rotational motion correction parameters were included as covariates of no interest.…”

Differential activation of frontal and parietal regions during visual word recognition: An optical topography study

“…The predictors for the GLM were generated by convolving a Gaussian function with each event (Plichta et al, 2007). To estimate the amplitude of the oxygenation response beta-values for each predictor were calculated by a least squares model fitting procedure maximizing model-to-data fitting (Bullmore et al, 1996). The first and second temporal derivative of each prediction term was included to adapt the onset and dispersion of the model functions to the individual's hemodynamic response.…”