Two independent datasets were utilized in this study. Participants in Datasets 1 and 2 underwent MRI scans and neuropsychological tests at Samsung Medical Center and Gachon University Gil Medical Center, respectively. Table 1 details the demographic and clinical information for each dataset.

Dataset 1 included 116 cognitively unimpaired (CU) individuals, 198 patients with amnestic mild cognitively impairment (MCI), and 212 patients with AD. Patients with MCI and AD were further divided into two subgroups: 57 patients with early MCI (EMCI) and 141 patients with late MCI (LMCI) for the MCI group; and 173 patients with mild AD (MildAD) and 39 patients with moderate-to-severe AD (ModAD) for the AD group. These subgroups were categorized based on clinical criteria, such as diagnostic criteria for MCI/AD and neuropsychological tests. See the previous study for more information on participant recruitment and subgroup division (Kim et al., 2021). Dataset 2 consisted of 63 CU individuals and 92 AD patients. Similarly, AD patients in Dataset 2 were identified according to clinical diagnostic criteria, which were described in the previous study in conjunction with the recruitment and inclusion/exclusion criteria (Lee et al., 2021b).

CU participants were further divided into two subgroups based on their ages: young CU (YC) if their age at recruitment was greater than or equal to 65, and old CU (OC) otherwise. Patients with MCI and AD were also subdivided based on onset age: early-onset MCI (EOMCI) or early-onset AD (EOAD) if symptoms developed before age 65, and late-onset MCI (LOMCI) or late-onset MCI (LOAD) otherwise. According to these criteria, individuals in Dataset 1 were classified into 46 YC, 69 EOMCI, 75 EOAD, 70 OC, 129 LOMCI, and 137 LOAD; individuals in Dataset 2 were classified into 33 YC, 51 EOAD, 32 OC, and 41 LOAD.

For Dataset 1, both T1-weighted MRI and resting-state functional MRI (rsfMRI) data were acquired using a 3.0-Tesla Intera Achieva MRI scanner (Philips Medical Systems, Best, the Netherlands) as previously described (Kim et al., 2016, 2021).

For Dataset 2, the T1-weighted MRI data were acquired using a 3.0-Tesla MRI scanner (Verio, Siemens, Erlangen, Germany) as previously described (Lee et al., 2021b). The rsfMRI data was acquired for 9 min using gradient-echo echo planar imaging (EPI) with the following parameters: TR = 3,000 ms, TE=30 ms, and voxel size = 3.4 × 3.4 × 3.4 mm³. During the acquisition of rsfMRI data, participants were instructed to keep their eyes open, not move their heads, and refrain from falling asleep.

The T1-weighted MRI data were preprocessed according to the standard pipeline in FreeSurfer v5.1 to obtain intracranial volume (ICV). The rsfMRI data were preprocessed using FEAT (FMRI Expert Analysis Tool) and FAST (FMRIB's Automated Segmentation Tool) in FSL (FMIRB's Software Library) v5.0 (Jenkinson et al., 2012) as described in the previous study (Kim et al., 2021).

Participants in Dataset 2 also underwent [¹⁸F]-Flutemetamol positron emission tomography (PET) scans with a Siemens Biograph 6 Truepoint PET/computed tomography (CT) scanner (Siemens, Knoxville, Tennessee, United States) using a list-mode emission acquisition. We computed the global amyloid standardized uptake value ratio (SUVR) from each PET image by averaging AD-related regions, including the prefrontal, superior/inferior parietal, lateral temporal, and anterior/posterior cingulate cortices with pons as the reference region. Amyloid positivity was defined as the global SUVR > 0.62. Detailed information on PET imaging parameters and SUVR computation are demonstrated in the previous study (Lee et al., 2021b).

A whole-brain functional connectivity network (FCN) for the i-th participant was mathematically modeled as a finite, simple, undirected, and vertex-labeled graph Gi=(V,Ei), where V is a set of vertices and Ei∈V×V is a set of edges. V was defined as the volumetric regions of interest (ROIs) determined using the Automated Anatomical Labeling (AAL) brain atlas (Tzourio-Mazoyer et al., 2002). The ROIs consist of 40 cerebral cortical regions and five subcortical regions for each hemisphere, resulting in |V|=90. The presence of an edge e∈Ei, with a weight of c_e, representing its connection strength, was determined by temporal associations between regional blood oxygenation level dependent signals, which were computed by averaging the signals of the voxels included in each ROI. Pearson product-moment correlation coefficient (Pearson's r) was used for the association measure, followed by the Fisher r-to-z transformation. A negative coefficient was set to zero, as used in our previous studies (Kim et al., 2017, 2021), because of its ambiguous biological interpretation (Fox et al., 2009; Murphy et al., 2009; Rubinov and Sporns, 2010; Cao et al., 2014). Though, our framework described below is not limited to this thresholding criterion. For convenience, we considered the nonexistent edge e∉Ei to be equivalent to the edge e∈Ei with c_e = 0.

To validate whether the framework performs well when D is measured on a continuous or ordinal scale, we identified connectivity-based biomarkers related to various stages of AD and Aβ deposition from whole-brain FCNs using the optimal values of t and λ determined by K-fold CV. We also computed the corresponding BASIC scores using the entire dataset. Table 2 provides detailed information on the experimental settings. The optimal value of t was determined by computing the generalized association performance of sub-networks containing 0.1–10% of the total number of possible edges (i.e., from four to 401) for values within its range because the NBS is ineffective and has a low statistical power at too high or too low threshold (Zalesky et al., 2010).

When D was measured on a dichotomous scale, we compared the BASIC scores with scores determined by the logistic model, where the score function was defined as s = g ◦ f with a sigmoid function g(x) = 1/(1 + e^−x). In contrast to the BASIC score, where w satisfies the objective with respect to the summarizing function f, the logistic model-based scores were obtained by minimizing the BCE between s(Gi[F])=g(f(Gi[F];w)) and d_i ∈ {0, 1} as the target variable. For D with continuous values, we compared the BASIC scores with scores determined by optimizing the least-square form of the classical canonical correlation with Laplacian regularization (Sun et al., 2008).

As an example of a neurodegenerative disorder, we first computed the BASIC scores associated with the presence or absence of AD for Dataset 1, (Experiment 1). By examining the distribution of estimated scores for all CU individuals and AD patients, we found that the likelihood of intermediate scores was comparable to that of extreme CU or AD scores (Figure 2A). This phenomenon differed from the biomarker abnormality scores computed using the logistic model (Experiment 1-1), demonstrating a higher likelihood of extreme CU and AD scores and a very low likelihood of the intermediate scores (Figure 2B).

Upon estimating the distributions for CU and AD individuals, the distribution of BASIC scores in each group was completely distinguished, as maximizing Kendall's τ_b with a dichotomous variable equivalent to maximizing the area under the receiver operating characteristic (AUROC) curve (Hanley and McNeil, 1982; Brossart et al., 2018). However, the score distributions of the CU and AD groups were differently shaped for each method. In contrast to the logistic model-based scores, we discovered that the BASIC scores were evenly distributed within each score range for each group.

When scores of MCI patients in Dataset 1 were calculated with the parameters of the summarizing function obtained for CU and AD individuals in Dataset 1, their BASIC scores had the highest likelihood in the mid-scores (gray-shaded area in Figure 2A). Patients with MCI were expected to be distributed between CU and AD. In contrast, a higher likelihood was observed in the score range close to AD in the logistic model-based scores (gray-shaded area in Figure 2B). A similar trend was observed when the scores were computed for Dataset 2 (Figures 2C,D). This demonstrates that BASIC scores reflect disease progression along the AD continuum more accurately than logistic model-based scores.

AD is characterized by the gradual progression of cognitive deficits along a continuum, and its progression can be discretized into more than two consecutive stages. The proposed framework is applicable to this situation, producing BASIC scores that are associated with disease progression. Figure 3 depicts the estimated distributions when the stages on the AD continuum are three (CU, MCI, and AD; Experiment 2) and five (CU, EMCI, LMCI, MildAD, and ModAD; Experiment 3). In each instance, the distributions of scores for CU individuals and AD patients were more naturally at their boundaries than when scores were determined using only two groups. The MCI patients' scores exhibited a bell-shaped distribution, with the highest likelihood between the CU and AD scores. When using five groups, the median difference between LMCI and MildAD was larger than that between EMCI and LMCI or between MildAD and ModAD, indicating that BASIC scores can reflect monotonic nonlinear changes across disease stages.

We performed correlation analyses between the BASIC scores determined using different numbers of stages on the AD continuum and cognitive functioning scores directly related to AD (Figure 4). When BASIC scores were calculated using only two stages, there were significant correlations for all participants as well as only patients with dementia (including both MCI and AD patients). However, within each of the MCI and AD groups, no significant correlation was found. All associations were strengthened when disease stages were further subdivided, particularly within the MCI and AD groups, implying that the greater the number of disease stages utilized, the more truthful the biomarker score.

To determine which edge had the greatest impact on biomarker scores, we defined edge importance as the square of the parameter values on edges, similar to how feature importance is calculated in linear regression (Grömping, 2015). As a representative example, the profile of edge importance in constructing BASIC scores associated with AD progression represented by the five stages is illustrated in Figure 5. Connections with high edge importance were incident to a set of regions, including the opercular/orbital parts of the left inferior frontal gyrus, left thalamus, right parahippocampal gyrus, right supramarginal gyrus, and right precuneus, where functional connectivity is altered as AD progresses (Grady et al., 2001; Wang et al., 2007; Zhou et al., 2013; Li et al., 2017).

AD can be subdivided according to various criteria, one of which is the subtype divided by onset age: EOAD and LOAD. Previous research has shown that EOAD and LOAD can be distinguished by their distinct pathological and clinical characteristics, including patterns of cortical atrophy, white matter disruption, and cognitive impairment (Panegyres and Chen, 2013; Mendez, 2019; Lee et al., 2021b). In this study, our proposed framework provided BASIC scores for EOAD-related biomarkers based on EOAD trajectory (YC-EOMCI-EOAD) and LOAD-related biomarkers based on LOAD trajectory (OC-LOMCI-LOAD), respectively (Experiment 4a and 4b). BASIC scores for the EOAD-related and LOAD-related biomarkers were sensitive to disease progressions of each subtype (left parts of Figures 6A,B).

Notably, individuals in the LOAD trajectory had relatively high BASIC scores for the EOAD-related biomarkers; in contrast, individuals in the EOAD trajectory had relatively low LOAD-related biomarker scores (gray-shaded areas in Figures 6A,B). Similar tendencies were observed for individuals in Dataset 2 when their BASIC scores were calculated using the parameters estimated from Dataset 1 (Figures 6C,D). This is in line with previous results that found that LOAD has a typical memory-disorder manifestation, whereas EOAD is characterized by deficits in the non-memory domain, such as visuoconstructional skills, executive function, and memory function (Joubert et al., 2016; Tellechea et al., 2018). In other words, the symptoms of EOAD are more extensive than those of LOAD, and features contributing to the EOAD-related biomarker score may also be present in LOAD, resulting in relatively high EOAD-related biomarker scores for individuals in the LOAD trajectory. Similarly, the LOAD-related biomarker score may be lower in EOAD because LOAD-related scores do not include all characteristics associated with EOAD. It is also worth noting that comparing the score distributions of stages on different disease trajectories, beyond comparing degrees of increases for the trajectories, may not be meaningful, because age or other demographic/clinical variables are not considered when constructing the score. These variables can distort the level of biomarker abnormality due to their association with disease manifestation; their effect can be controlled in further analyses that use the scores.

There is a need to identify biomarkers associated with continuous pathological changes, which are sometimes the direct criteria for brain disorders. For instance, amyloid deposition is a necessary condition for diagnosing AD (Jack et al., 2018); consequently, determining whether an individual is amyloid-positive or amyloid-negative is essential for distinguishing AD from other neurodegenerative disorders, which can be determined by global retention values obtained from amyloid PET. We identified a brain connectivity-based biomarker and computed its score in relation to the global amyloid SUVR (Experiment 5). The BASIC scores were significantly correlated with the SUVR (Figure 7A). In addition, the distributions of scores in the amyloid-negative (Aβ-) and amyloid positive (Aβ+) groups were smoothly connected, with scores also present near the boundary between the two groups (Figure 7B).

We also performed a classification analysis between Aβ- and Aβ+ groups using BASIC scores derived from FCNs and structural connectivity networks (SCNs) from a previous study (Lee et al., 2021b). When classification was performed using BASIC scores obtained by maximizing Kendall's τ_b, the two groups were distinguished with a five-fold CV accuracy of 0.8987 (Figures 7C,D). However, BASIC scores obtained by maximizing the canonical correlation coefficient, or equivalently, Pearson's r (Experiment 5-1) demonstrated poorer classification performance (5-fold CV accuracy of 0.7504), with a high rate of misclassification for the Aβ+ group (Figures 7E,F). This indicates that the association between the global amyloid SUVR and connectivity-based biomarkers cannot be explained solely by a linear relationship. This nonlinear relationship can be detected more effectively using Kendall's τ_b than Pearson's r.