A trichotomy method for defining homogeneous subgroups in a dementia population

Abstract Introduction Diagnosis of dementia in the aging brain is confounded by the presence of multiple pathologies. Mixed dementia (MX), a combination of Alzheimer's disease (AD) proteins with vascular disease (VD), is frequently found at autopsy, and has been difficult to diagnose during life. This report develops a method for separating the MX group and defining preclinical AD (presence of AD factors with normal cognition) and preclinical VD subgroups (presence of white matter damage with normal cognition). Methods Clustering was based on three diagnostic axes: (1) AD factor (ADF) derived from cerebrospinal fluid proteins (Aβ42 and pTau), (2) VD factor (VDF) calculated from mean free water and peak width of skeletonized mean diffusivity in the white matter, and (3) Cognition (Cog) based on memory and executive function. The trichotomy method was applied to an Alzheimer's Disease Neuroimaging Initiative cohort (N = 538). Results Eight biologically defined subgroups were identified which included the MX group with both high ADF and VDF (9.3%) and a preclinical VD group (3.9%), and a preclinical AD group (13.6%). Cog is significantly associated with both ADF and VDF, and the partial‐correlation remains significant even when the effect of the other variable is removed (r(Cog, ADF/VDF removed) = 0.46, p < 10−28 and r(Cog, VDF/ADF removed) = 0.24, p < 10−7). Discussion The trichotomy method creates eight biologically characterized patient groups, which includes MX, preclinical AD, and preclinical VD subgroups. Further longitudinal studies are needed to determine the utility of the 3‐way clustering method with multimodal biological biomarkers.


Introduction
In 2015 more than 45 million people suffered from Alzheimer's disease and related dementia (ADRD), and this number is expected to dramatically increase to 75 million by 2030, and further to 132 million by 2050. 1,2Multiple pathological processes contribute to cognitive impairment in the aging brain and overlapping syndromes confound clinical diagnosis, which can be improved with biomarkers from imaging, cerebrospinal fluid (CSF) and blood.][8][9] Clinical trials that include homogeneous patient groups targeting a specific pathophysiological process are more likely to succeed with fewer participants for adequate statistical power. 10The formula, amyloid (A), tau (T), and neurodegeneration (N), improves diagnosis of AD. 11 While using this formula has improved the diagnosis of AD, it fails to capture several other contributory factors (e.g., vascular disease and synucleinopathy).To remedy that deficiency, an expanded formula that includes other diagnoses, ATXN, has been proposed, where "X" represents novel candidate biomarkers for additional pathophysiological mechanisms. 12Adding biomarkers from CSF and positron emission tomography (PET) improves biological diagnosis, advancing AD research, it is magnetic resonance imaging (MRI), especially diffusion imaging that identifies white matter damage, making it a surrogate for vascular damage, but they can be caused by other pathologies as well. 13The presence of WMH does not confirm presence of cerebral small vessel disease (CSVD).At present, neuropathology of postmortem brains is the only sure confirmation for the presence of vascular disease, and large differences exist between white matter damage seen in MRI images and CSVD seen in neuropathology. 14We know that white matter damage is not unique to CSVD, hence studies that combine MRI-based markers of white matter damage with fluid biomarkers to give a CSVD diagnosis would be useful.The recent STRIVE-2 criteria have endorsed both mean free water (mFW) in white matter [15][16][17] and peak width of skeletonized mean diffusivity (PSMD) 18 calculated from diffusion tensor imaging, as among the best currently available indicators of microvascular damage to the white matter. 19We combined AD proteins in CSF with MRI markers to show white matter injury in a double-dichotomy clustering classification method that made the diagnosis of MX possible during life and separated dementia patients into four groups. 20However, our prior report had several drawbacks, including the small sample size from a single center and lack of a cognitive dimension.In this report we expanded the number of subjects to over 500 with the Alzheimer's Disease Neuroimaging Initiative (ADNI) database and added a cognitive dimension to the double-dichotomy, forming a three-dimensional "trichotomy" clustering method that improved homogeneity by creating eight patient groups.
The ATN framework was based on each axis being defined by the three different pathological processes appropriate for AD diagnosis. 11Our proposed system uses three-axes based on the goal of distinguishing Alzheimer's and vascular disease, and to further distinguish subjects with normal and low cognitive performance.Our proposal combines the "AT" of ATN into one Alzheimer's disease factor (ADF) and adds two other independent measures to characterize vascular disease, a vascular disease factor (VDF) and a composite cognition (Cog) measure of executive and memory function.They are defined as functions of appropriate biomarkers with their range in [0,1] and a cut-point = 0.5.The three scores are plotted orthogonally and the threshold of 0.5 divides the subjects into eight groups.

Subjects
The participants were selected from the Alzheimer's Disease Neuroimaging Initiative (ADNI2 and ADNI3) database (http://adni.loni.usc.edu) if they had, (a) CSF measurements of Aβ42 and pTau, (b) MRI diffusion and FLAIR measurements, and (c) composite scores for memory (ADNI_MEM) and executive function (ADNI_EF).The ADNI was initiated in 2003 by NIH under the leadership of Dr. Weiner.The primary objectives of ADNI were to identify biomarkers to measure progression of mild cognitive impairment (MCI) and early identification of AD (www.adni-info.org).Institutional review board approval was obtained from each of the multicenter sites, and an informed consent was obtained for each study participant.We maintained the original ADNI diagnostic classification for reference with a change in the naming convention to distinguish the original clinical diagnosis from our proposed biological diagnosis.ADNI classifies the subjects into three groups based on a clinical and neuropsychological evaluation: (a) cognitively normal (aCN), (b) mild cognitive impairment (aMCI), and (c) Alzheimer's disease (aAD).The subject demographics are in Table 1.
The eight biologically defined groups are summarized in Table 2.In the earlier work 20 the bCN group (cognitively normal with no AD or VD factors) was diagnosed separately and was not part of the double-dichotomy analysis.The four groups shared with the double-dichotomy methods are, bMX = biological mixed dementia, bAD = biological Alzheimer's disease, bVD = biological vascular disease, and bCN VD = biological leukoaraiosis (normal cognition with white matter changes on FLAIR).The three new groups are, bCL = cognitively low performers with no AD or VD factors, bCN MX = cognitively normal with both AD and VD factors, and bCN AD = cognitively normal with only AD factors.The cognitively normal groups with AD or VD factors may be important in a longitudinal study of disease progression.

Biochemical assessments
ADNI used the Elecsys system for measuring Aβ42 (pg/ mL) and pTau (pg/mL) values in CSF.We obtained these values from the ADNI database.Several previous studies have determined suitable cutoff values by comparing these CSF-based measurements to 18 F PET studies. 21,22There are other studies that have shown that using ratios (Aβ42/Aβ40, pTau/Aβ42, pTau/Aβ40) is better than using individual biomarkers for predicting clinical progression of AD or for predicting 18 F PET status. 21,23,24 uses a composite score based on the ratio pTau/Aβ42 to characterize AD.A larger value of the composite score captures the low concentration of Aβ42 and the high concentration of pTau present in AD.A cutoff value of 0.022 was used to define AD-positive subjects. 21

Composite cognitive scores
The methods of obtaining composite memory function and executive function scores and the advantages of using composite scores have been previously summarized. 25

MRI acquisition
The MRI protocol details are available (https://adni.loni.usc.edu/).The ADNI2 dataset has thick slices for the FLAIR sequence and larger voxel size for the diffusion sequence.All diffusion calculations were only done with shells b = 1000 s/mm 2 and b = 0 s/mm 2 , with higher order shells excluded (ADNI3 advanced protocol).This minimized the difference between diffusion measures calculated from different ADNI datasets.The white matter hyperintensity volume (WMHV), mFW in white matter, 15 and PSMD 18 were calculated based on methods described earlier, 28 and the scripts available on the MarkVCID website (https://markvcid.partners.org/consortium-protocols-resources).In all regression analyses a protocol variable was used to account for differences across ADNI protocols.

Calculation of normalized composite scores
The four steps for calculating CS norm are summarized in Figure 1 and the mathematical details are described in the Supplementary Materials.We (1) select the biomarkers for defining the composite score, (2) define the mathematical formula for calculating the raw composite score (CS raw ) and a cutoff (cth) based on a classification algorithm (for VDF raw and Cog raw ) or an independent study (for ADF raw ), (3) calculate f CS raw ð Þ, the probability density function of CS raw , and (4) calculate a uniform normalization transform (UNT, a function f CS raw ð Þ) to map CS raw to CS norm in the range (0,1) and the cutoff to 0.5.CS norm is a monotonically increasing function of CS raw , which maintains the relative order of individual scores, and CS norm is approximately uniformly distributed in the range (0,1).The method to calculate CS raw was slightly different for the three biomarkers (VDF, Cog, and ADF), while the same algorithm transformed CS raw to CS norm for all three biomarkers.The method for calculating CS raw and the details of mapping CS raw to CS norm are described with greater detail in the Supplemenatry materials.
VDF raw was calculated as a linear function of white matter mFW and PSMD calculated from a diffusion image.The linear function was defined by linear discriminant analysis (LDA) of separating the UNM cohort into controls and subcortical ischemic vascular disease (SIVD) groups (Fig. 1A).The UNM data were used for calculating VDF raw because they had recruited subjects with clinically diagnosed vascular cognitive impairment and included a more extensive range of white matter damage than the ADNI dataset.White matter hyperintensity volume (WMHV) was excluded for calculating the composite scores because it did not improve the classification of subjects into control and patient groups, both mFW and PSMD had higher correlation with executive function than WMHV, and they do not depend on a binary threshold to detect white matter lesions and can continuously monitor white matter changes.The classification accuracy of the LDA algorithm for separating the controls from the SIVD group in the UNM cohort was 88.3% (Supplementary Materials for further details).VDF raw is given by, Cog raw was calculated was calculated as a linear function of ADNI_MEM and ADNI_EF.The ADNI data (538 subjects) were used to define a linear discriminant function that best separated subjects with normal cognition (aCN) and those with some cognitive impairment (aMCI + aAD).An independent dataset was not available in this case for calculating Cog raw .The previous LDA method was used, and additionally we validated the stability of the Cog raw by leave-one-out cross-validation method (Fig. 1B).Cog raw is given by, This classification rule had 82.2% accuracy for separating the ADNI group aCN from the combined aMCI + aAD groups.
ADF raw was based on the results of an independent study, which used the ratio of Aβ42 to pTau and calculated a cutoff that best matched the PET results for AD presence 21 (Fig. 1C).ADF raw is given by, with cth ¼ Log 10 0:022 ð Þ¼À1:66: All the three raw scores, VDF raw , Cog raw and ADF raw were converted to normalized scores VDF norm , Cog norm , and ADF norm by the table based UNT method described in Supplementary Materials (Fig. 1G-I).

Relationships between Biomarkers
Table 3 summarizes the linear regression results of the relationships between the biomarkers with age, sex, education, protocol differences, and an additional variable as indicated, treated as a covariate.The partial correlation was calculated between the residuals after removing the effect of covariates from each variable.
The relationship of the individual biomarkers across modalities was different.VDF was not significantly associated with pTau, while it was significantly associated with Aβ42 (Rows 4-5).Similarly, ADF was not significantly associated with PSMD, while it was associated with mFW (Rows 6-7).Although the pair pTau and Aβ42, and the pair mFW and PSMD are correlated with each other, they do contribute with independent information in defining the composite measures.The composite (Cog) and the individual cognitive measures (ADNI_MEM, ADNI_EF) are significantly associated with both ADF and VDF, with ADF having a higher correlation then VDF (Rows 8-13).Although ADF and VDF are significantly correlated with each other (Row 14), the partial correlation between the cognitive measures and VDF remains significant, even after the effects of ADF are removed (for example, r(Cog, VDF/ADF removed) = 0.29 p < 10 À7 ), and similarly the partial correlation between the cognitive measures and ADF remains significant after the effects of VDF are removed (for example, r(Cog, ADF/ VDF removed) = 0.42), p < 10 À28 ) (Rows 15-20).ADF had higher correlation with memory than with the executive function (ADNI_EF) (Rows 10-11 and 17-18), while VDF had higher correlation with the executive function than with memory (Rows 12-13, and 19-20).
The variables mFW and PSMD are highly correlated, and we examine their relative value in predicting Cog.This calculation shows that in subsequent versions of the method, mFW should be sufficient.This conjecture must be examined over other datasets which include subjects with increased amounts of vascular disease.

Trichotomy-based subgroups
The trichotomy defined sub-groups (Table 2), along with the subject distribution across the eight groups is shown in Figure 2. A dichotomy based on cognition, splits the ADNI group into two parts based on Cog <= 0.5 (Fig. 2A) and Cog >0.5 (Fig. 2B). Figure S1 in the Online Appendix shows the six figures based on the dichotomy of Cog, ADF, and VDF, respectively.The numerical distribution of the subjects across our eight biologically defined groups and the ADNI groups (aCN, aMCI, and aAD) is shown in Table S1.
Overall, 9.3% of ADNI subjects were classified as mixed dementia (bMX), while in the Alzheimer's ADNI group (aAD) 22 of 69 subjects (31.9%) had mixed dementia.In 102 of 283 (36.0%) cognitively normal ADNI subjects (aCN) Alzheimer's or vascular disease factors were Partial correlation is calculated from the residuals after removing the effects of the covariates from Biomarker1 and Biomarker2.present.Finally, 107 of 186 (57.5%) of mild cognitively impaired ADNI subjects (aMCI) had AD factors (groups bMX, bAD, bCN MX, and bCN AD ).
We consider preclinical to be those with normal cognition but having biological factors (bCN VD , bCN AD , and bCN MX ).Overall, 3.9% of the subjects were classified as bCN VD (21 out of 538 subjects), 13.5% were classified as bCN AD (73 out of 538 subjects), and 2.6% were classified as bCN MX (14 out or 538 subjects).

Biomarker properties for the ADNI subgroups
We first discuss the variation of the six biomarkers used in defining the composite scores across the eight groups (Fig. 3).Next, we discuss the difference across the eight groups for six additional biomarkers that were not used in defining the composite scores (Fig. 4).
The differences in cognition, Alzheimer's disease factors, and vascular disease factors across the eight groups are shown in Figure 3.The variation of the biomarkers across the eight groups follows the expected differences based on how the groups were created.In Figure 3F there are subjects in the bAD group with large PSMD values that were not classified as bMX.This occurs because the composite VDF score primarily depends on mFW (Eq.1), and mFW is small for these subjects.In the groups with normal cognition there was minimal effect of disease on ADNI_EF and none on ADNI_MEM.ADNI_EF (bCN) was significantly greater than ADNI_EF (bCN AD + bCN MX + bCN VD ) with p < 0.02).On the other hand, in the cognitively low performance groups the presence of VDF decreased ADNI_EF, while the presence of ADF decreased ADNI_MEM.ADNI_EF (bCL + bAD) was significantly greater than ADNI_EF (bVD + bMX) with p < 0.02, and ADNI_MEM (bCL + bVD) was significantly greater than ADNI_MEM (bAD + bMX) with p < 1e-5.The groups based on differences in cognition are G1, G4, and G5, while those based on differences in vascular disease (VD) are G2, G6, and G7, and those based on differences in Alzheimer's disease (AD) are G3, G8, and G9.We find the presence or the absence of vascular disease does not make a difference in the biomarkers considered (G2, G6, G7).In the presence of disease, the difference in cognition is more pronounced if AD is present (G5) then if VD is present (G4).If the disease status is ignored then for differences in cognition, every hypothesis was significant (G1).The groups based on the presence or absence of AD factors were different for all the hypotheses, except for sex and BA (G3 and G8).HV was different in greater number of groups and with higher significance than BA.

Discussion
Cognitive loss in aging results from a heterogeneous group of diseases.Biomarkers can be used to separate The distribution of the biomarkers that were not used for calculating the composite scores is compared across the eight trichotomy groups.The statistical differences between the groups are discussed in Table 5.There is a greater proportion of males in cognitively low groups with presence of AD.In subjects with AD and low cognition there was a greater proportion of subjects present with (a) both alleles present (Fig. 3B), (b) higher values of CDRSB (Fig. 3C) and (c) higher values of ΔCDRSB/year (Fig. 3D), as seen by the green bars.Hippocampal volume was less in groups with AD and it was more sensitive than brain atrophy to group differences (Fig. 3E,F).cognitively impaired patients into more homogeneous groups to reduce the number of subjects needed in a clinical trial and improve the likelihood of success.We have previously developed a clustering classification method, which we called the double-dichotomy method by plotting an Alzheimer's disease score on one axis and a vascular disease score on the other. 20We made two modifications in this report: (1) we used the Alzheimer's disease neuroimaging initiative (ADNI) database to increase the number of participants, and (2) we added cognitive scores to identify those with and without impairment.This potentially improved subject homogeneity, with each group having well-characterized biological markers.
Adding the third dimension of cognitive status to the plots created the "trichotomy method" with the benefit of clarifying participants in the MX (bMX) and the preclinical groups (bCN VD , bCN AD , and bCN MX ).Diagnosing these patients during life can be done by measuring amyloid beta (Aβ) and phosphorylated tau (pTau) in the CSF or with PET to form an Alzheimer's disease factor (ADF) and using the diffusion MRI scan to indicate vascular Table 5.We test the significance of nine hypothesis based on the distribution of the six variables (Fig. 4) across the eight biological groups.(A) Gives the different combination of groups being compared based on the eight biological groups.(B) Gives the nine hypotheses being tested based on the Figure 4  1811 damage to form a vascular disease factor (VDF).Neither the ADF nor the VDF directly provide an indication of cognition, leaving out a critical factor for the classification of patients.
Cognitive status and vascular injury are not explicitly considered in the ATN framework.The trichotomy method defines the preclinical groups more clearly, as they have normal cognition, and presence either of AD and/or of VD factors.The bCN VD group is only 3.9% of the ADNI dataset and may represent preclinical vascular cognitive impairment.Similarly, there is the bCN AD group with normal cognition, low VDF, and elevated ADF (13.6%), which would be considered preclinical AD or Stage 1 or 2 disease according to current guidelines. 29he MX group (bMX) is more clearly defined as abnormal cognition with elevated ADF and VDF (9.3% in ADNI).The percentage of bMX subjects in the ADNI cohort are lower than the 25% of the subjects in the UNM cohort, 20 because the ADNI's exclusion criteria reduced recruitment of subjects with significant vascular disease while the UNM cohort involved an enriched number of vascular patients.
It is rare to find a single pathologic process in the brains of demented patients with more than two being the norm and as high as four different pathological processes not uncommon. 30This could explain the high failure rate in clinical trials where only one pathological process was treated.This would argue for using a more precise classification process based on biomarkers derived from the underlying brain pathology.
This biomarker approach has not undergone rigorous testing in longitudinal studies with large groups of patients.While the use of the amyloid and tau proteins is widely accepted, studies with a marker for the N component of the formula ATN are few.A recent study also shows how the selection of a biomarker and cutoff for "N" in ATN results in different estimated prevalence of neurodegeneration. 31A stronger argument can be made for the inclusion of a vascular factor "V" in the ATN formula because of the ability of MRI to indicate injury to the white matter, which is a strong indicator of vascular injury.However, the optimal set of biomarkers to determine white matter damage remains to be determined.
The large number of subjects with all the data necessary to perform the trichotomy analysis being available in the ADNI database is a strength of the study.Another strength is the proposed method for calculating the normalized composite scores for easier comparison among subjects.
There are several limitations of the study in addition to the lack of longitudinal data.ADNI lacks diversity being mainly composed of white, non-Hispanic and college educated group of participants and the cutoff values are mainly appropriate for that population.Another limitation is the selection of the variables to include in the vascular disease factor.Inclusion of other vascular measures, such as lacunar infarcts, perivascular space enlargement, and microbleeds would have provided additional validity to the VDF.Recent work has reviewed the role of perivascular spaces in AD, 32 and elucidated its contribution to early cognitive decline based on the ADNI data. 335][36] Similarly, there are other factors that could have been included in the cognitive factor.
While the trichotomy separates MX patients from those with AD by including quantitative MRI data, it leaves unresolved the significance of the bCN VD group; the presence of white matter hyperintensities on FLAIR in elderly may be a consequence of aging.8][39] Ultimately the goal of this research is to provide biomarkers that can be used in a clinical setting.We have not intended for this method to be readily translated into a clinical procedure.However, the MRI biomarkers selected can be obtained from a clinical 3T MRI that is available at most medical centers.Therefore, extracting the PSMD and mFW should be possible.Further work will have to be done to obtain cut-points for the three axes, and use of other datasets will be needed to bring this into routine clinical work.
Our study provides a roadmap for other centers with large datasets and statistical support.The fluid biomarkers were obtained from the CSF, which is not optimal.Although the current state of fluid biomarker research is showing that the plasma-based biomarkers are undergoing validation against ones from CSF and PET.This will make more widespread the determination of the AD axis and with neuropsychological testing and MRI, the other two axes could be calculated.We expect that in the nottoo-distant future this type of an approach to classification will become available for clinical research studies and the emerging treatment trials that are based on biomarkers.This approach will be useful with other dementia causing diseases, such as Lewy body disease, limbicpredominant age-related TDP43 encephalopathy (LATE), aging-related tau astrogliopathy (ARTAG), or argyrophilic grain disease (AGD) when appropriate plasma-based biomarkers are available for them.An improved method of classification has the potential of reducing the numbers of patients needed for a clinical trial.The other advantage of this approach is that it can be used to include patients in rural settings at a distance from the research medical centers. 40In summary, we propose that the trichotomy framework can be applied to plasma-based biomarkers and clinical MRI, making it useful for population-based studies.
An added advantage is the ability to identify MX during life with multimodal biomarkers and to show different rates of progression of neurodegenerative and vascular disease pathways, providing a guide to which pathway to initiate treatment and when to begin treatment of the second pathway.In this way biomarkers with statistical clustering methods will be the gateway to precision medicine in dementia.

Figure 1 .
Figure 1.The top row summarizes the four steps required for calculating a normalized composite score.The next three rows show details of the steps required for calculating the three different composite scores: (1) Vascular disease factor (VDF), (2) Cognition (Cog), and (3) Alzheimer's disease factor (ADF).The black line in (A-C) defines the cut-off for the three examples, with the colors being the contour plots of the raw composite score.(A) is the contour diagram of the raw score, VDF raw ¼ 0:135Log 10ÂÂ PSMDÂ1e 4 À Á þ 0:991Log 10 mFW Â 1e 2 À Á À1:474, with the black line being VDF raw ¼ 0, and contour lines being VDF raw ¼ 0:1 apart, with red being the positive score.(B) is the contour diagram of the raw score, Cog raw ¼ À0:076ADNI_EFÀ0:997ADNI_MEM þ 0:519, with the black line being Cog raw ¼ 0, and contour lines being Cog raw ¼ 1 apart, with red being the negative score.(C) is the contour diagram of the raw score, ADF raw ¼ Log 10 pTau=Aβ42 ð Þ , with the black line being ADF raw ¼ Log 10 0:022 ð Þ , and contour lines being ADF raw ¼ 0:2 apart, with red being the positive score.The contour lines are at an angle because ADF raw is the ratio of the two variables.

Figure 4
compares the distribution of the six variables that were not used in defining the composite scores.These being (a) sex, (b) APOE4, (c) CDR sum of boxes (CDRSB) (d) annual change of CDR sum of boxes (ΔCDRSB/year), (e) hippocampus volume (HV), and (f)

Figure 2 .
Figure 2. The trichotomy plot (VDF, ADF, Cog) was divided into two figures, based on a dichotomy on cognition, Cog ≤0.5 (A) and Cog >0.5 (B).The colors distinguish the original ADNI classification (aCN, aMCI, and aAD).This figure reflects the characteristics of the ADNI database.Majority of the subjects fall in bCN and bAD groups (57.6%, bCN + bAD) with considerably lower number of subjects have the vascular disease factor (18.4%, bCN MX + bCN VD + bMX + bVD).This analysis identifies subjects with mixed dementia (bMX) and those with preclinical VD (bCN VD ) and preclinical AD (bCN AD ).
brain atrophy (BA).Chi-squared test was used to test for equivalence of proportions in two groups and two-sample t-test was used to compare means.Except for HV and BA, the other measures are proportion of subjects.The nine pairs of groups that we compare are summarized in

Figure 3 .
Figure 3.The distribution of the biomarkers that were used for calculating the composite scores is compared across the eight trichotomy groups.The variation of each marker is as expected based on how the groups were constructed.The memory is not affected by AD or VD factors within the cognitively normal groups, but within the cognitively low performance groups (bCL + bVD + bAD + bMX), the memory function is significantly lower in those with AD factors (bAD + bMX) than those without (bCL + bVD).

Figure 4 .
Figure 4.The distribution of the biomarkers that were not used for calculating the composite scores is compared across the eight trichotomy groups.The statistical differences between the groups are discussed in Table5.There is a greater proportion of males in cognitively low groups with presence of AD.In subjects with AD and low cognition there was a greater proportion of subjects present with (a) both alleles present (Fig.3B), (b) higher values of CDRSB (Fig.3C) and (c) higher values of ΔCDRSB/year (Fig.3D), as seen by the green bars.Hippocampal volume was less in groups with AD and it was more sensitive than brain atrophy to group differences (Fig.3E,F).

1810 ª 2023
The Authors.Annals of Clinical and Translational Neurology published by Wiley Periodicals LLC on behalf of American Neurological Association.

1812 ª 2023
The Authors.Annals of Clinical and Translational Neurology published by Wiley Periodicals LLC on behalf of American Neurological Association.
This study ª 2023 The Authors.Annals of Clinical and Translational Neurology published by Wiley Periodicals LLC on behalf of American Neurological Association.

Table 1 .
Demographics of participants.aCN, aMCI, aAD are the three groups defined in the ADNI database as cognitively normal, mild cognitive impairment, and Alzheimer's disease.
Summaries are mean (SD) [25%, 75%] for numeric values, and percent for categorical values.1804 ª 2023 The Authors.Annals of Clinical and Translational Neurology published by Wiley Periodicals LLC on behalf of American Neurological Association.

Table 2 .
The classification criteria and the nomenclature of the eight biologically defined subgroups is described below.The groups closest to clinically accepted definitions of subcortical ischemic vascular disease (SIVD) is indicated in the table.The definition of preclinical AD is the presence of AD factors but being cognitively normal, and similarly preclinical VD is the presence of white matter damage due to normal aging with no cognitive decline.

Table 4 lists
R 2 and Akaike Information criteria (AIC) for the model, predicting Cog based on Log 10 mFW ð Þ, and Log 10 PSMD ð Þ.The value of R 2 always decreases with increased number of variables, but a lower value of AIC indicates a parsimonious model-fit, because it penalizes increased number of variables.There is a slight increase in the explained variance if both the variables, mFW and PSMD are included for predicting Cognition.The AIC suggest that the increased complexity of adding PSMD is not justified in a model to predict Cog based on Log 10 mFW ð Þ and on Log 10 PSMD ð Þ.

Table 3 .
Results of linear regression and partial correlation after taking into effects of age, sex, education, and an additional covariate if present are shown.

Table 4 .
The relative importance of mFW and PSMD in predicting cognition is compared.
ª 2023 The Authors.Annals of Clinical and Translational Neurology published by Wiley Periodicals LLC on behalf of American Neurological Association.

Table 5A
and the nine hypothesis we test are summarized in Table5B.Table5Cgives the p-values for testing each hypothesis being different across each pair of groups.The unadjusted p-values were multiplied by 81 for Bonferroni multiple-comparison correction.
biomarkers.(C) Gives the multiple-comparison corrected p-values for testing each hypothesis.
ª 2023 The Authors.Annals of Clinical and Translational Neurology published by Wiley Periodicals LLC on behalf of American Neurological Association.