## 4 Quantitative Methods for the Detection of AD
### General Linear Models and Statistical Parametric Mapping
At this point, statistical inference may proceed as described above. The contrast vector may be used to generate SPMs of the hypo- or hypermetabolic regions in FDG-PET images at the level of the patient or the group. This can be used to detect AD in two primary ways. First, a visual inspection of the statistically significant regions can be performed. These statistically significant clusters may be displayed on a glass brain in the application viewer, but they may also be visualized over an anatomical template, or on subject-specific MR images. SPM will also generate tables of statistics for each significant cluster and any existing sub-clusters and allow for the modification of relevant thresholds. SPM has some notable and well-known disadvantages when compared to other methods. SPM-based analysis assumes sphericity between all possible pairs of groups under consideration. Being a mass univariate methodology, it also suffers from the multiple comparison problem, which must be adequately corrected to avoid dramatic type I errors. SPM also locates statistically significant clusters (see Equation (4)) based on a facsimile of the signal-to-noise ratio--a contrast of parameter values to their standard error--which may introduce artifactually large parameter values in regions of low noise, such as outside the brain, unless corrected with brain masking and/or intensity thresholding. SPM also assumes that the error variance-covariance is stationary under the null hypothesis. SPM and many other methodologies also require elaborate preprocessing procedures to ensure exact voxel-wise spatial correspondence between images/groups. SPM also presupposes the use of relatively arbitrary thresholds for statistical significance. Furthermore, SPM maps are best suited for subjective visual interpretation; however, masks of any statistically significant clusters may be used as a form of dimensional reduction on whole images. Figure 2: Sample output of SPM12. A group-wise comparison was performed on FDG-PET scans of AD patients and healthy controls, and the results were compared by \(t\)-testing. Regions of statistically significant differences between the groups (\(p=0.05\) with family-wise error adjustment) are shown as dark clusters on the white glass brain. Red arrow points to the global maximum. It has been demonstrated that SPM-aided FDG-PET readings can improve the differentiation of AD patients from healthy controls (HC), sMCI, or pMCI patients [79; 80; 81; 82; 83; 84]. SPM-aided readings may also improve the differentiation between different neurodegenerative disorders. [PERSON] et al., found that when given SPM-generated maps, specialists performed significantly better in diagnosing dementia and were better able to differentiate between several forms of DSD, including MCI [81]. [PERSON] et al., published a novel use of the GLM using the vector of response parameters (\"beta map\") over each voxel in the image. The dot product of this with the voxel values of the proportionately scaled FDG-PET images was used to create subject-specific scores representing the similarity of the subject's FDG-PET image to the group-derived beta map. Using this technique, they were able to reliably differentiate AD patients and HCs with sensitivity = 86.2%, specificity = 85.6%, and area-under-curve (AUC) = 0.922 [85]. [PERSON] et al., discovered, by use of a GLM, that female subjects exhibited significantly greater accumulation of tau neurofibrillary tangles in the MCI stage compared to male subjects if they possessed the _APOE-e4_ genetic mutation [86]. [PERSON] et al., used a GLM to explore the effects of short-term (<1 year) conversion rates from MCI to AD states by combining FDG-PET, amyloid-PET, CSF markers, structural MRI, and neuropsychological testing information. They discovered that FDG-PET and hippocampal volume combined with neuropsychological testing best predicted short-term conversion from MCI to AD, and that neither amyloid-PET nor CSF markers were able to predict conversion [87].