Supplementary Material
Summary of Scan Success Rates Reported by Yerys et al (continued)
Yerys et al [41] reported that, on average, only 50% of all ADHD patients (both on and off MPH) were able to complete an entire fMRI study, compared to an 88% completion rate for controls. They also reported that 95% of both the medicated and unmedicated ADHD subjects successfully completed at least one session in an fMRI battery. Furthermore, the percentage of ADHD children who successfully completed at least one session in an fMRI battery was higher than both the epilepsy group (93%) and the ASD group (81%).
Further Considerations on the Practicalities of Scanning Children and Adolescents
Excessive head motion is the most common cause of failure of fMRI scanning. Yerys et al. [41] reported that medicated ADHD patients had the lowest percentage of failed runs due to excessive head motion, including when compared to healthy controls. Unfortunately, the reason why the medicated ADHD patients’ overall success rate was equal to the unmedicated ADHD patients’ overall success rate is not clear, as medicated ADHD patients failed a larger number of sessions classified by the authors as due to “other” reasons. When reviewing the literature of fMRI studies in ADHD it was discovered that 16.4 children and adolescents with ADHD and 15.3 controls (including only those used in the analysis) were included, on average, in the thirty-two studies investigated (a full list of the ADHD subjects scanned in the thirty-two fMRI studies is shown in Supplementary Table 1). The largest number of ADHD patients scanned in a study was 52 [41], the smallest number of ADHD patients scanned (not including patients that were scanned but later excluded from the study) was 7 [15]. Desmond and Glover [12] suggest that including 12 subjects in an fMRI scanning study would be adequate to find voxel differences at a low significance threshold of p<0.05, however this depends entirely on the effect size of interest (smaller numbers of subjects result in a lower power to detect differences that are actually present, therefore an increased risk of type II errors). They also suggest the number of subjects must be doubled if a higher level of significance is required. As the average number of ADHD patients and controls in the thirty-two studies reviewed was 31.7 subjects then it is clear that some studies may have required more subjects to obtain higher statistical power [9]. Consequently studies which have a low number of subjects and find negative results are of less interest as a null result could be due to a lack of statistical power. However, a study which rejects the null hypothesis, regardless of the number of subjects, is of more interest as the result is significantly different from what would have been expected by chance. Statistical power is notoriously difficult to estimate for neuroimaging studies as it varies from brain region to brain region; some brain regions (e.g. medial orbitofrontal cortex, inferior temporal lobes) adjacent to air filled spaces in the head (e.g. nasal sinuses, ear canals) are additionally affected by signal dropout (the ‘susceptibility’ artefact), and statistical power is further affected by other factors such as poor image quality (see the main text). For individual subject MVPA studies it is generally thought that even more subjects are required to achieve high accuracy and generalisability of predictions. In all fMRI studies considered here, the total duration for an fMRI study was restricted to 30 minutes or less.
Group Level Univariate Analyses of Scanning Data
An example of a common conventional technique for analysing brain images from clinical populations is the use of t-tests, at each voxel, to test the null hypothesis of no significant difference between groups [21]. In this statistical test, each small volume (voxel) of the brain is compared with the corresponding voxel for all subjects in each of the groups (e.g. patient and control). The mean and standard deviation values at each voxel (which correspond to grey matter probabilities in a grey matter segmented image) are computed for both groups and a t-score is calculated at each voxel. Voxels with a t- score exceeding a given significance threshold (typically p = 0.05 or p = 0.01), given the degrees of freedom, are evidence of brain regions for which the null hypothesis can be rejected. It should be noted that this method involves a large number of simultaneous tests and therefore a significance correction for multiple testing is required. Long established neuroimaging methods include the Family Wise Error (FWE), False Discovery Rate (FDR), and cluster-based methods [21]. This combination of pre- processing and making group level statistical inferences using structural brain scans is referred to as Voxel-Based Morphometry (VBM) http://www.fil.ion.ucl.ac.uk/spm/doc/papers/john_vbm_methods.pdf. Two meta-analyses of VBM studies of ADHD reported significant grey matter reductions in the putamen/globus pallidus [16] and lentiform nucleus extending to the caudate nucleus [26]. The most often reported decreases in child and adolescent ADHD also include the dorsolateral prefrontal cortex, cerebellum and white matter of the corpus callosum [34]. Abell et al [1] reported grey matter decreases in the right paracingulate sulcus and the left inferior frontal gyrus in young adults with autism when compared with controls. Increases in grey matter were also found in the amygdala/peri-amygdaloid cortex, middle temporal gyrus, and inferior temporal gyrus [1].
Mathematical overview of the linear SVM
This section will briefly outline the main mathematics applied in SVM as simply as possible. If there are N subjects in a training set then {xi,yi} where i = 1…N, xi represents a vector of the selected voxels from one subjects image, and yi represents a subject’s class label (i.e. -1 or 1 – class labels are arbitrarily assigned to either number). As described in the main text, the SVM algorithm identifies the decision boundary which best separates the two classes using the training set. This decision boundary (or hyperplane) can be described by w. x + b = 0 where w is normal to the hyperplane and b/ || w || is the perpendicular distance from the hyperplane to the origin. If the classes are linearly separable, there exists a vector w and a scalar b such that the inequalities:
w.xi b 1 if yi 1 (Eq. 1) w.xi b 1 if yi 1 are consistent throughout the training set. In order to classify data which is not linear separable Cortes and Vapnik [10] introduced a slack variable, ξi (where i = 1…N ), which allows for misclassified points:
w.xi b 1i if yi 1
w.xi b 1 i if yi 1 (Eq. 2)
i 0 i which can be combined into:
y(w.xi b) 1 i 0 where i 0 i (Eq. 3)
The SVM optimises the hyperplane by minimising the classification errors and maximising the margin (the distance between the hyperplane and the closest subject (of either class label). The introduction of the slack variable ‘soft-margin’ allows classification to be performed even when there are subjects located on the incorrect side of the margin as it penalises each misclassified subject as a function of the distance from the hyperplane [10, 20]. Without including the derivation (see Bishop [4], Cristianini & Shawe-Taylor [11], Fletcher [20] for derivation) the hyperplane is found by minimising:
N 1 2 min w Ci (Eq. 4) 2 i1 such that Eq. 3 is satisfied. The parameter C corresponds to the soft-margin parameter outlined in the main text. Once the SVM has identified the optimal hyperplane from the training data (assuming a suitable soft-margin parameter has been selected as described in the main text) the novel training data can then be classified. Using a linear kernel, a new subject {x*,y*} is classified by:
N * * f (x ) wi xi b (Eq. 5) i1 where the sign of f(x*) determines which class label the subject is predicted to have. In general, the main equation for classifications using SVM (and RVM) is:
N f (x) wi K(x, xi ) b (Eq. 6) i1
where K(x,xi) describes the kernel function which has been selected (e.g. linear, polynomial, radial basis function, etc) [4]. Supplementary References
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Neuroimage 40:110-120 Supplementary Table 1: The number of ADHD subjects in a selection of fMRI studies. fMRI Study Number of ADHD patients Number of controls included included in the analysis in the analysis Adler et al [2] 11 (bipolar + ADHD) 11 (bipolar only) Anderson et al [3] 10 6 Booth et al [5] 12 12 Brotman et al [6] 18 37 Cao et al [7] 12 13 Cao et al [8] 19 23 Durston et al [15] 7 7 Durston et al [14] 11 11 Durston et al [13] 22 22 Epstein et al [17] 20 9 Epstein et al [18] 10 14 Fassbender et al [19] 12 13 Hoekzema et al [22] 19 0 Kobel et al [23] 14 12 Konrad et al [24] 16 16 Mostofsky et al [25] 11 11 Passarotti et al [27] 11 15 Peterson et al [28] 16 20 Pliszka et al [29] 17 15 Rubia et al [33] 20 20 Rubia et al [31] 13 13 Rubia et al [30] 20 20 Rubia et al [32] 14 20 Shafritz et al [35] 15 14 Solanto et al [36] 20 0 (comparing ADHD subtypes) Suskauer et al [37] 25 25 Vaidya et al [38] 10 10 Van ’t Ent et al [39] 27 27 Wang et al [40] 19 20 Yerys et al [41] 52 32 matched with the ADHD group (137 total) Zang et al [42] 13 12 Zhu et al [43] 9 11