PMC:4620161 / 40749-47973 JSONTXT

{"target":"http://pubannotation.org/docs/sourcedb/PMC/sourceid/4620161","sourcedb":"PMC","sourceid":"4620161","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4620161","text":"Results with experimental data\nHow do the testing approaches perform when applied to real data? Would their performances be consistent with the simulations? To address these questions, we ran 3dMVM on the ESM data presented in the Introduction section with n = 50 (2 groups: 21 children and 29 adults), m = 20 (2 conditions with each having 10 component estimates at 10 TR grids) and design matrix X of q = 4 columns in the MVM (1): all ones (intercept associated with the average effect across groups), effect coding for the two groups, the average age effect between the two groups, and the interaction group:age (or group difference in age effect). The age values were centered within each group so that the group effect can be interpreted as the difference between the two groups at their respective average age. The effect of interest was on the interaction of group and condition: Did the two groups have the same HDR profile difference between the two conditions? Five F-statistics from MVT, XUV (with sphericity correction), AUC, L2D, and XMV, were obtained and then, due to different degrees of freedom, converted to Z-values for direct comparisons (Figure 2A). To take advantage of the geometrical representation in Table 1 when interpreting the effect of interest, we reduce the within-subject factor Condition to the contrast between the two conditions, so that the interaction effect essentially becomes the group contrast in terms of the HDR profile difference between the two conditions (Figure 2C).\nFigure 2 Analysis results of experimental data. (A) Five tests for ESM and ASM are illustrated at an axial slice (Z = 54 mm) at p = 0.05 level with the radiological convention (left is right). To demonstrate the subtle differences among the methods, the raw results are shown here without multiple testing correction applied. When family-wise error correction through Monte Carlo simulations was adopted, a minimum cluster of 140 voxels for a voxel-level significance of 0.05 led to a surviving cluster at the crosshair (Voxel 1) for XUV for ESM and XUV for ASM. For the cluster labeled with blue circles (Voxel 2), the surviving tests were AUC for ESM, AUC and β0 for ASM. (B) The power differences (p-values in blue when below 0.05) among the five tests are demonstrated at Voxels 1 and 2, whose approximate locations (left postcentral gyrus and left precuneus) are marked with the green crosshair and blue circle respectively in the axial views in (A). (C) The estimated HDRs through ESM are shown for the two conditions (first two columns) and their differences (third column) at Voxels 1 and 2. Each HDR profile spans over 11 TRs or 13.75 s. The profile patterns at Voxels 1 and 2 are shared by their neighboring voxels in their respective clusters. In addition to the statistical significance in (A) and (B), the HDR signature profiles provide an extra evidence for the associated effects at these voxels. Consistent with the simulation results, XUV achieved the highest detection power in most regions (Figure 2A top) while L2D showed low power (and likely high FPR) due to no differentiation between the positive and negative effect estimates for ESM. All the other three methods, MVT, AUC, and XMV, were generally less powerful than XUV. The strong performance of XUV can be seen in the estimated HDR curves at Voxel 1 (Figures 2B left,C) extracted from a cluster (left postcentral gyrus). More specifically, the adults had roughly the same HDR profile between the two conditions except for a faster recovery phase under the Congruent condition than the Incongruent condition; in contrast, the upstroke and peak were more elevated under the Congruent condition in the children than the Incongruent condition except for the recovery phase during the last 3 TRs. Geometrically, the interaction effect between Group and Condition at Voxel 1 is represented by the fact that the HDR profiles of condition difference were intersecting between the two groups (Figure 2C). MVT and XMV achieved a moderate power while AUC and L2D failed to reach the significance level of 0.05 at Voxel 1 (Figure 2B left). On the other hand, the detection failure of XUV at Voxel 2 (left precuneus) was caused by the fact that the condition contrast was roughly parallel between the two groups (Figure 2C), as geometrically demonstrated in Table 1. MVT, AUC, and XMV showed their auxiliary role when XUV failed (Figure 2B left).\nWith the ASM analysis results, five tests were performed using 3dMVM. First, the popular approach of focusing on the effect estimate β0 associated with the first basis (canonical) function through the hypothesis (6b) was adopted (Figure 2A bottom). Secondly, the L2D approach (7) was used on the first two basis functions (not shown here) as well as all three. Thirdly, MVT was performed using (2b) with the three coefficients. Lastly, the HDR curve at each condition was reassembled for each subject using the three coefficients, and the reconstructed effect estimates only at the first 10 TRs were analyzed with 3dMVM for two reasons: a) with the three SPM curves covering 32 s or 25 TRs, the model would contain too many parameters relative to the data size; b) the effect estimates after the first 10 TRs were mostly negligible. Two tests, XUV and AUC, were performed while MVT and XMV were impossible because the rank was 3 among the 10 effect estimates from the linearly reconstructed HDR per condition.\nThe detection power for both β0 and L2D with ASM was very low (Figure 2A bottom), illustrating the fact that focusing on the peak or the combined effects associated the two or three basis functions would largely fail to detect subtle differences during the BOLD uprising and recovery phases. In contrast, MVT (with the coefficients from three basis functions of ASM), XUV and AUC (with the reconstructed HDRs from ASM) outperformed the conventional approaches of β0 and L2D in SPM. Such failure of ASM is specifically demonstrated at Voxel 1 where the peak alone or the summarized values from the three coefficients were not as powerful as the reassembled HDR profiles (Figure 2B right). It is noteworthy that XUV with ASM was less powerful than its ESM counterpart, showcasing the coarser characterization with three parameters in ASM than the estimation at every time point in ESM. Furthermore, for both ESM and ASM, even though XUV was mostly more powerful than the alternatives, MVT and AUC (as well as XMV for ESM and β0 for ASM) played a supplementary role when XUV failed (Voxel 2 in Figure 2B right).\nTo recapitulate the performance of the five testing methods in situations when LME cannot be applied, ESM provided a more accurate estimation for the HDR curves than ASM, leading to a higher success in detection power. In addition, with the typical sample size in most studies, XUV as an approximate approach had the lowest power loss at the group level compared to other dimensional alternatives as well as the test with the most accurate hypothesis formulation, MVT. However, MVT plus the lesser accurate approximations such as AUC and XMV may play an auxiliary or even irreplaceable role in situations when XUV suffers from power loss (e.g., Table 1 or Voxel 2 in Figure 2).","divisions":[{"label":"title","span":{"begin":0,"end":30}},{"label":"p","span":{"begin":31,"end":1514}},{"label":"figure","span":{"begin":1515,"end":2927}},{"label":"label","span":{"begin":1515,"end":1523}},{"label":"caption","span":{"begin":1525,"end":2927}},{"label":"p","span":{"begin":1525,"end":2927}},{"label":"p","span":{"begin":2928,"end":4427}},{"label":"p","span":{"begin":4428,"end":5437}},{"label":"p","span":{"begin":5438,"end":6546}}],"tracks":[]}