Lepsien, J.

Lohmann, G.

Mueller, K.

Möller, H.

English

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Introduction Methods  In a recent manuscript, Eklund et al. [1] reported inflated false positive rates in functional magnetic resonance imaging (fMRI) using common software packages including SPM, FSL, and AFNI.  Briefly, a nominal family-wise error rate of 5% in the parametric statistical evaluation was shown to be conservative for voxel-wise inference but not for cluster-wise inference.  As a cause of the observed invalid cluster inferences, the authors suggested that the spatial autocorrelation functions do not follow the assumed Gaussian shape.  We would like to draw attention to an important aspect that was not addressed in this publication: Statistical inferences obtained using the Gauss random field approach depend heavily on a pre-processing parameter that was not included in the analysis performed by Eklund et al. [1], namely the spatial resolution to which the data are resampled and interpolated during pre-processsing.  We analyzed 47 resting-state fMRI data sets, each acquired at a nominal spatial resolution of 3×3×4 mm3 with 300 volumes.  Using a strategy analogous to that of Eklund et al. [1] we imposed various fake designs including block- and event-related types.  Analysis was performed using SPM12.  Normalization included a resampling with three different voxel sizes: 3×3×3 mm3, 2×2×2 mm3, and 1×1×1 mm3.  Two normalization pipelines: (a) normalizing the raw data and performing the individual statistics with normalized data, and (b) normalizing the contrast images.   Using a family-wise error (FWE) correction for multiple comparisons based on the Gauss Random Field approach, we first evaluated each data set separately. Thereafter, we performed a group-level inference in which all 47 data sets were pooled.  Inflated false positive rates in fMRI depend on the voxel size  of normalized images Karsten Mueller1 , Jöran Lepsien1 , Harald E Möller1 , Gabriele Lohmann2,3 1Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, 2Max Planck Institute for Biological Cybernetics, Tuebingen, Germany,  3Department of Biomedical Magnetic Resonance, University Hospital Tübingen, Tübingen, Germany karstenm@cbs.mpg.de Results & Discussion Figure 1. Orthogonal brain sections showing brain activity differences between two experimental conditions A and B using a fake design with resting-state fMRI data. During normalization into the standard space, data were scaled to 3x3x3 mm3 , 2x2x2 mm3 , and 1x1x1 mm3 . Family-wise error (FWE) corrected p-values become smaller when using a higher upscaling. The white box shows the FWE-corrected p-value of a selected cluster that reaches significance that is a false positive result. References [2] Flandin G, Friston KJ. Analysis of family-wise error rates in statistical parametric mapping using random field theory, arXiv 2016;1606.08199v1 [stat.AP], 27 Jun 2016, http://arxiv.org/pdf/1606.08199.pdf [1] Eklund A, Nichols TE, Knutsson H. Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates, Proc Natl Acad Sci U S A. 2016;113(28):7900-7905. doi:10.1073/pnas.1602413113 [3] Hopfinger JB, Büchel C, Holmes AP, Friston KJ. A study of analysis parameters that influence the sensitivity of event-related fMRI analyses, Neuroimage 2000;11(4):326-333. doi:10.1006/nimg.2000.0549  Eklund et al. [1] used the common default setting of 2×2×2 mm3.  In response to the paper by Eklund et al., Flandin and Friston [2] used a different setting of this parameter, namely 3×3×3 mm3. Together with a more stringent initial cluster-forming threshold, they did not observe inflated false positive rates.  However, a spatial resolution of 2×2×2 mm3 is the default value in two major software packages (SPM, FSL) and, hence, it is likely to be used for processing fMRI data by these packages.  In previous work, Friston and colleagues [3] stated that resampling to 2×2×2 mm3 renders the analysis “more sensitive”.  It is, thus, completely unclear what a valid setting for this parameter should be. Therefore, it is of substantial relevance to systematically assess its influence on statistical inference. A < B,   p<0.001 x = 30 z = 8 y = 0 3 mm 2 mm 1 mm 0.065 0.031 0.025  On the individual level, we found that with higher resampling resolutions, the FWE-corrected p-values decrease systematically so that more and more false positives occur.   As expected by our null hypothesis, we did not obtain any positive clusters with 3×3×3 mm3 resolution. However, with 2×2×2 mm3, the p-values are already smaller leading to a significant cluster. With a resolution of 1×1×1 mm3, the p-value decreased again.   Figure 1 shows the effect using a fake event-related design with two experimental conditions.   We obtained the same effect when using an arbitrary on/off-design with a block length of 20 s.   It appears that there is a systematic dependence of the false positive rate on the resampling parameter with smaller voxel sizes leading to smaller FWE-corrected p-values and hence more false positives.   While some dependence on pre-processing para-meters may be inevitable, a systematic dependence of this type is clearly worrisome, because researchers may be tempted to interpolate their data until the desired statistical significance level is reached.   Statistical inference should certainly not depend in such a systematic way on a pre-processing parameter that can be set ad libitum.   Clearly, this issue requires further in-depth analysis. 

Inflated false positive rates in fMRI depend on the voxel size of normalized images

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