Autosomal Dominantly Inherited Alzheimer Disease: Analysis of genetic subgroups by Machine Learning

Abstract

Despite subjects with Dominantly-Inherited Alzheimer’s Disease (DIAD) represent less than 1% of all Alzheimer’s Disease (AD) cases, the Dominantly Inherited Alzheimer Network (DIAN) initiative constitutes a strong impact in the understanding of AD disease course with special emphasis on the presyptomatic disease phase. Until now, the 3 genes involved in DIAD pathogenesis (PSEN1, PSEN2 and APP) have been commonly merged into one group (Mutation Carriers, MC) and studied using conventional statistical analysis. Comparisons between groups using null-hypothesis testing or longitudinal regression procedures, such as the linear-mixed-effects models, have been assessed in the extant literature.

Within this context, the work presented here performs a comparison between different groups of subjects by considering the 3 genes, either jointly or separately, and using tools based on Machine Learning (ML). This involves a feature selection step which makes use of ANOVA followed by Principal Component Analysis (PCA) to determine which features would be realiable for further comparison purposes. Then, the selected predictors are classified using a Support-Vector-Machine (SVM) in a nested k-Fold cross-validation resulting in maximum classification rates of 72–74% using PiB PET features, specially when comparing asymptomatic Non-Carriers (NC) subjects with asymptomatic PSEN1 Mutation-Carriers (PSEN1-MC). Results obtained from these experiments led to the idea that PSEN1-MC might be considered as a mixture of two different subgroups including: a first group whose patterns were very close to NC subjects, and a second group much more different in terms of imaging patterns. Thus, using a k-Means clustering algorithm it was determined both subgroups and a new classification scenario was conducted to validate this process. The comparison between each subgroup vs. NC subjects resulted in classification rates around 80% underscoring the importance of considering DIAN as an heterogeneous entity.

1. Introduction

Alzheimer’s Disease (AD) is neuropathologically defined by the presence of amyloid-β (Aβ)-plaques and by neurofibrillary tangles associated with a suggestive clinical phenotype [1, 2, 3]. Clinically AD is characterized by a progressive loss of memory and other neuropsychiatric changes such as decline in executive functioning and behavioral changes [4, 5].

Since the development of a theoretical model of biomarker changes for AD [6], multiple longitudinal studies about AD have tried to find the exact triggers that could explain the prognosis and evolution of the disease. Clinicopathologic evidence suggests that pathological changes leading to AD such as deposition of Aβ-plaques begin many years prior to onset of cognitive symptoms [7, 8, 9, 10], but it still awaits for further empirical validation. In addition to this, as some more recent works point out, the nature of AD might be mistakenly described until now as different genetic alterations, which are causing the same disease, are expressing themselves through different triggers [11, 12, 13, 14, 3, 15].

Dominantly Inherited Alzheimers Disease (DIAD) only represent about 1% of all AD cases, but it has a marked importance for AD research [16]. This type of AD is caused by known mutations in the Amyloid Precursor Protein (APP) [17], Presenilin-1 (PSEN1) [18, 3] (most frequently found), or Presenilin-2 (PSEN2) [19] genes. DIAD is quite similar to the more common Late Onset AD (LOAD) in many features including clinical presentation and disease course [20, 21, 22, 23, 3, 24]. In this sense, the main difference between DIAD and LOAD is in the age at onset, family history and co-pathologies [25].

To facilitate the study of DIAD and its comparison with LOAD, the National Institute on Aging (NIA) funded the Dominantly Inherited Alzheimer Network (DIAN) [26]. This study assesses people at risk of inheriting an autosomal dominant AD mutation and monitor their evolution through a standardized procedure which includes clinical, cognitive, neuroimaging, CSF and plasma tests among others.

Currently, the DIAN study presents more than 450 subjects with 90 different mutations in multiple genes¹.

The reason why DIAN is so important for AD research is related to the understanding of the disease natural history. It is certain that a person with DIAD will develop AD in the future, so a follow-up of different biomarkers from DIAD subjects (specially during their initial stages as asymptomatic carriers) could provide a great deal of information which may later be used to make a model of the disease [27, 28]. Findings obtained from DIAD can be extrapolated to the sporadic LOAD so it is expected that better treatments will be prescribed at pre-clinical stages of the disease when damage is minimal and pathogenesis can be slowed down or even prevented from progressing [7, 29, 30, 31, 24, 5].

DIAD research has played an important role in the fact that it is now well-accepted that AD pathogenesis starts 20–30 years before the onset of clinical symptoms [5]. Previous works dedicated to decipher the time course of DIAD have made use of regression models to explore the evolution of AD markers based on a predicted variable called AAOE (Age At Onset Estimated) and its equivalent EYO (Estimated Years to Onset) which is predicted considering the disease onset age of their first-degree relatives [32, 22] or the average age of onset for each mutation type [25].

Over the last decades, neuroscience has transitioned from qualitative reports of case studies from abnormal conditions to quantitative statistical maps to characterize the global pattern of disease. With the inclusion of classical statistics, pathological models were obtained based on classical statistical assumptions on data, which are not always fulfilled [33], making interpretation of the results arguable. Fortunately, the recent use of Machine Learning (ML) techniques in the analysis of different neurological disorders [34] is having a noticeable impact on diagnosis and prognosis of diseases, such as Parkinson’s Disease (PD) or AD, even though their complex pathological models are not yet completely understood in limited sample sizes. This conforms a potentially useful screening tool in the diagnosis of unseen subjects or in the development of new treatments. The latter, combined with the emergence of highly detailed databases like DIAN, might result in an accurate model of AD disease courses, despite the definition of AD as a mixture of different AD subtypes [35].

With this aim, the work presented here proposes a DIAD analysis based on ML techniques to discern between Non-Carriers (NC) and Mutation-Carriers (MC) participants grouped by which gene is causing (or will cause) the disease. This give us 3 main hypothesis including 1) to check whether all data modalities are necessary for DIAD diagnosis including: Non-Imaging Biomarkers (NIB) such as Aβ_4(0,2) amyloid, τ protein or the apolipoprotein APOE among others; and imaging features extracted from PiB PET (PIB), FDG PET (FDG) and MRI scans (MRI); 2) to validate if reducing the MC heterogeneity via separating the mutations by their responsible gene has a significative impact on the DIAD diagnosis accuracy; and 3) to determine if the model generated using ML can be used to determine in which period before the symptoms onset group differences are larger.

Final results presented a high performance in classification rates when using PET features with subgrouping MC gene expression even though there may not yet be cognitive symptoms (EYO greater than 5 and 10 years), as well as when clustering asymptomatic PSEN1 MC into two groups: a first group quite similar to the NC group and a second group totally different. The application of a ML approach to these new subsets has resulted in a novel model of the disease and it is expected to have a great impact on DIAD knowledge.

2. Material & Methods

2.1. Participants

DIAN project was founded by Washington University School of Medicine in 2008. This study has been approved by the local institutional review boards of each participating site from United States, Canada, France, Spain, United Kingdom and Australia among other places. Full details of participating sites, enrollment, assessment protocol and infrastructure of DIAN were published in [26]. The inclusion criteria list includes statements such as be aged 18 (inclusive) or older and the child of an affected individual (clinically or by testing) in a pedigree with a known mutation for DIAD; to have two persons who are not their full-blooded siblings who can serve as collateral sources for the study; or be fluent in a language approved by the DIAN Coordinating Center.

In this work, we have made use of data results from the DIAN Observational Study Data Freeze 11 but excluding previously those participants with least one of the following diagnosed diseases: cerebral stroke (3 subjects), transient ischemic attack (1 subject), dementia by alcoholism (4 subjects), Parkinson’s disease (1 subject), traumatic brain injury with chronic deficit/dysfunction (3 subjects), dementia with Lewy bodies, vascular dementia, dementia by unknown causes (3 subjects), frontotemporal dementia, primary progressive aphasia, progressive nonfluent aphasia, semantic dementia, other types of dementia (e.g. logopenic, anomic or transcortical), progressive supranuclear palsy, corticobasal degeneration, Huntington’s disease, prionic dementia, Down syndrome, hydrocephalus and central nervous system neoplasm. Besides, in order not to increase the heterogeneity in symptomatic subjects, LOAD cases in DIAN study have been also discarded (13 subjects). As a result, our average dataset consists of a total of 442 subjects (184 males, 41.63%) with an age at baseline of 38.71 ± 10.98 years². Other disorders such as B12 vitamin deficit, depresion, alcoholism, abuse of other substances, seizures and traumatic brain injury without chronic deficit/dysfunction or thyroid problems have been included due to the large amount of participants with at least one of those diagnostics.

2.2. Genetic groups

Mutations in the APP, PSEN1 and PSEN2 genes were identified in DIAN from DNA extracted from peripheral blood samples as described in [36]. Among all the included participants, 265 were DIAD Mutation Carriers (MC): 202 PSEN1, 22 PSEN2 and 43 APP; while 173 were Non-Carriers (NC) subjects. The 2 remaining subjects were labelled as Unknown and they were not included in the analysis.

2.3. Non-imaging markers

In the models proposed in [20, 8], fibrillar amyloid-β (Aβ) depositions play a key role in the development of AD [37]. Once amyloid Aβ depositions begin to accumulate, many other biomarkers such as CSF τ protein also becomes abnormal. This stage is followed by a brain atrophy (measured by volumetric MRI tests) and cognitive symptoms.

As mentioned in section 1, several works suggest that there are differences in pathogenesis between DIAD and LOAD [38, 39]. Following recent works [40], and based on availability, we decided to include in this study markers such as Aβ₄₂, Aβ₄₀, Aβ₄₂:Aβ₄₀ ratio, τ and p-τ as non-imaging biomarkers (NIB) available ro most of our subjects (table 1).

Table 1:

Non-imaging markers.

Marker	Type of test	Assay protocols [9]
Aβ42	CSF	INNO, xMAP
Aβ40	CSF	INNO
Aβ42 : Aβ40 ratio	CSF	INNO
τ	CSF	xMAP
p-τ	CSF	xMAP
Aβ42	Plasma	PL_xMAP
Aβ40	Plasma	PL_xMAP
Aβ42 : Aβ40 ratio	Plasma	PL_xMAP
APOE	Genetic	Alleles ϵi,j with i, j=2,3,4

Detailed information about data preparation is available from: https://dian.wustl.edu˜/our-research˜/observational-study/.

2.4. Imaging markers

DIAN dataset includes a wide range of imaging variables from MRI and PET images for each participant. Two classes of PET imaging are available for Data Freeze 11: FDG (PET imaging using Fluorodeoxyglucose F18 for imaging of the brain metabolism) and PiB (PET imaging using Pittsburgh Compound B for imaging of amyloid depositions). This section gives some details about data acquisition and complementary tools.

2.4.1. MRI acquisition

MRI acquisition was carried out following the Alzheimer Disease Neuroimaging Initiative (ADNI) protocol [6]. Each participant received an accelerated 3D sagittal T1-weighted MPRAGE on a 3T scanner. Resulting images presented a voxel size of 1.1×1.1×1.2 mm and an adquisition time of approximately 5–6 minutes. All scans have been acquired with a Siemens BioGraph mMR PET-MR 3T scanner or a Siemens Trio 3T MRI scanner depending on the center where tests have been obtained.

All MRI sessions have been processed using the FreeSurfer, v5.3 analysis suite including all patches, for cortical reconstruction and volumetric segmentation [41]. The technical details of these procedures are described in prior publications [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]. More information is available on the website (http://surfer.nmr.mgh.harvard.edu/).

The MRI preprocessing pipeline includes: motion correction and segmentation of the subcortical white matter and deep gray matter volumetric structures on T1 combined with T2 images [48]; intensity normalization; registration to a spherical atlas which utilizes individual cortical folding patterns to match cortical geometry across subjects [45]; and parcellation of the cerebral cortex into units based on gyral and sulcal structure [54]. For each vertex on the cortical surface, thickness was calculated as the shortest distance from the gray/white boundary to the gray/csf boundary [55].

2.4.2. FDG and PiB acquisition

Amyloid imaging was performed with a bolus injection of approximately 15 mCi of [11C]PiB. Dynamic imaging acquisition started either at injection for 70 minutes or 40 minutes post-injection for 30 minutes. For analysis, the PiB PET data between 40 to 70 minutes were used. Metabolic [18F]FDG-PET imaging that assess the neurodegenerative processess in AD [56, 57, 58], was performed with a 3D dynamic acquisition. It began 40 minutes after a bolus injection of approximately 5 mCi of FDG and lasted for 20 minutes.

PET images were motion corrected and registered to their MRI using the methods described in [59, 60]. For each region-of-interest³, standardized uptake value ratio (SUVR) was calculated using a cerebellar reference.

Dynamic PET scans are divided into early, middle, and late frames and registered to correct for head motion. The T1 weighted MRI scans are registered to the Talairach atlas and to the PET images, and transformed into an atlas space. Since PET imaging has a spatial resolution around 6 mm, the regional activity measured directly from PET is a linear combination of activity from different regions. This phenomenon is known as the partial volume effect [63, 64] so, it was compensated through the use of a regional spread function for partial volume correction in the analysis [65].

2.5. Summary of input variables

Considering both imaging and non-imaging variables available in DIAN database, a final set of 1755 features were considered in this work including 10 NIB tests and 1745 imaging features (521 FDG, 184 MRI and 1040 PiB).

2.6. Symptomatology

Separability between symptomatic and asymptomatic subjects have been carried out taking into account the Clinical Dementia Rating (CDR) scale [66, 67]. While asymptomatic or preclinical subjects are those whose CDR results are equal to 0, sympomatic subjects can be divided according to CDR scale into early symptomatic (CDR = 0.5), mild dementia (CDR = 1), moderate dementia (CDR = 2) and severe dementia (CDR = 3) [68]. Table 2 gives a description of DIAN participants as a function of their baseline CDR results.

Table 2:

CDR in baseline.

	Asymptomatic	Symptomatic
		Early	Mild	Moderate	Severe
NC	173	0	0	0	0
APP	29	9	4	1	0
PSEN1	122	51	20	5	4
PSEN2	20	2	0	0	0

2.7. Experiments Definition

To cover all the questions proposed for this work, three experiments have been described as follows:

2.7.1. Experiment 1 - Between-group discrimination ability by data type

Until now, most of the works proposed for DIAN database analysis were focused on the separability between MC and NC subjects using conventional statistical tests like t-Test. As mentioned in section 1, although some of these works have pointed out the relevance of considering the MC separately according to their mutation, we have decided to include a direct comparison between MC and NC as our reference baseline case to improve. It is expected that resulting conclusions could help with the clinical practice for two main reasons: 1) if focusing only on statistically relevant features, to be able to discard non significant ones, it could be reduced the amount of time and costs associated to these kind of tests; and 2) based on this reduced dataset, it could be established a simplified model for DIAD progression. According to these two ideas, the first experiment proposed in this work makes a between-group discrimination to discern between MC and NC to determine which features give a better classification performance (diagnosis) and which of them might be discarded from the point of view of a Machine Learning analysis.

2.7.2. Experiment 2 - Assessment of group heterogeneity in mutation carriers

Once determined which features get a better performance when comparing MC vs. NC, next step will be to determine if subgrouping the MC set according to the affected genes (PSEN1, PSEN2, APP) improves classification accuracy. With the exception of defined analysis made in PSEN1 MC subjects subgroups [69, 4, 28, 3], there is no statistical evidence as yet that DIAD should be studied as an homogeneous entity including all subjects with at least one of those genes regardless the kind of mutation they present or treat each mutation separately. With this aim, we have made a binary classification between NC vs. PSEN1 carriers as the most populated MC subgroup and a multiclass classification comparing NC vs. PSEN1 vs. PSEN2 and vs. APP with particular attention to those features which gave better results in experiment 1.

2.7.3. Experiment 3 - Comparisons based on EYO

Having fitted the best model of DIAD according to the affected genes, a temporal comparison of these groups was performed. For that, several classifications of subjects subgrouped according to their EYO in steps of 5 years [EYO ≥ 15, EYO ≥ 10, EYO ≥ 5] are also carried out. The objective here is to determine at which range of EYO differences between MC and NC are maximized even when participants do not present any kind of AD cognitive symptom.

2.7.4. Extension of Experiment 2 - Clustering PSEN1-MC

To go deeper into the subject of data heterogeneity in DIAN database, an extra comparison has been added. As most of the asymptomatic MC participants (with special focus on PSEN1 MC) are quite similar to any NC subject, maybe this is resulting in a mixture of two different groups (clusters) including both: subjects quite similar to NC cases and those whose prognosis is clearly different. If it is proven this theory, it will reinforce the explanation of why classification results are so low in comparison with the proposed experiments even regardless the AAEOE value given for any subject.

2.8. Balance of subjects

For the comparisons proposed for each experiment and considering different cohorts of subjects, the total number of participants (NC and MC) in each experiment has been summarized as follows in Table 3:

Table 3:

Balance of subjects in DIAN database for each experiment.

Exp	Description	NC	MC
1	NC/MC	164	281
	NC/MC **	164	170
2	NC/PSEN1/PSEN2/APP	164	217/20/44
	NC/PSEN1/PSEN2/APP **	164	122/19/29
	NC/PSEN1	164	217
	NC/PSEN1 **	164	122
3	NC/PSEN1	164	217
	NC/PSEN1 **	164	122

Used ** to represent only asymptomatic cases.

2.9. Feature preparation

A general diagram of the data processing pipeline is shown in Figure 1 and it is organised as follows: first, a cross-validation procedure splits input data into two groups (training and test). Second, these subsets are standardized and used as inputs of a feature selection procedure based on an ANOVA test. And finally, once were selected features that matched with the previous conditions, a Principal Component Analysis (PCA) was used in order to reduce the number of features that will be used for their posterior classification.

Figure 1:

General diagram.

2.9.1. Data standardization

In order to avoid having input variables with larger ranges that will affect to a posterior multivariate analysis [70], a feature standardization procedure based on rescaling using the z-score formula (1) was performed.

$$z_i=\frac{x_i-{\mu }_{x_i}}{{\sigma }_{x_i}}i=1,2,\dots ,N$$ (1)

when x_i is defined to be the original feature i, ${\mu }_{x_i}$ its mean, and ${\sigma }_{x_i}$ its standard deviation.

2.9.2. Missing data

Some of the test results in DIAN study are not available for all the subjects. In these cases, it was decided not to include subjects with unknown tests results in our analysis.

2.9.3. Analysis of variance (ANOVA)

The feature selection consists of two phases: the first one is a feature selection algorithm based on an ANOVA test [71, 72] to remove non-informative features for classification. Using this approach, two classes with N observations in each class are compared. For that, suppose x_i,j denotes the j-th observation (j = 1, 2, …, N) of a feature for the i-th class. As only considering experiments in which two classes are compared, for this work i only could take two possible values: i = 1, 2. Using this notation, group means ${\overline{x}}_i$ and global mean $\overline{x}$ are defined as follows:

$${\overline{x}}_i=\frac{1}{N}\sum _{j=1}^N{x}_{i,j}\overline{x}=\frac{1}{2N}\sum _{i=1}^2\sum _{j=1}^N{x}_{i,j}$$ (2)

Then, the estimated total variance of the sample ${\widehat{\sigma }}_{\text{Total}}^2$ is descomposed into within class variance ${\widehat{\sigma }}_{\text{within}}^2$ and the between class variance ${\widehat{\sigma }}_{\text{between}}^2$ as:

$$\begin{gathered} {\widehat{\sigma }}_{\text{Total }}^2={\sum }_{i,j}{\left(x_{i,j}-\overline{x}\right)}^2 \\ {\widehat{\sigma }}_{\text{within }}^2={\sum }_{i,j}{\left(x_{i,j}-{\overline{x}}_i\right)}^2 \\ {\widehat{\sigma }}_{\text{between }}^2=N{\sum }_i{\left({\overline{x}}_i-\overline{x}\right)}^2 \end{gathered}$$ (3)

Using the one-way ANOVA feature selection method which tests the null hypothesis that means obtained from the two classes are equal, and calculating the expected values of equation (3), two new estimators for the variances can be obtained:

$$\begin{gathered} {\widehat{S}}_{\text{within }}^2=\frac{{\widehat{\sigma }}_{\text{within }}^2}{2(N-1)} \\ {\widehat{S}}_{\text{between }}^2=\frac{{\widehat{\sigma }}_{\text{between }}^2}{2(N-1)} \end{gathered}$$ (4)

Then, dividing ${\widehat{S}}_{\text{between}}^2$ by ${\widehat{S}}_{\text{within}}^2$, F-statistic is defined. This statistic is therefore used to test the null hypothesis considering an specific significance level α using a one-tailed test of the F-distribution. As highest F_values represent the most part of the variance in the target data, values with a high F_values are selected. Due to the correspondence between F_values and their probability, p-value, to reject the null hypothesis, only those features with p-value below a significance level (α) should be selected.

2.9.4. Principal Component Analysis (PCA)

This mathematical procedure [73, 74] provides an approximation of an input dataset X composed by K participants and M variables in terms of a new set of N_Comp variables with M ≥ N_Comp. This method uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called Principal Components (or loadings). In order to do that, PCA makes use of the eigenvalue decomposition of its covariance matrix as shown in expression (5):

$$X^{T}X=W\Lambda W^T$$ (5)

where the columns of W contain the eigenvectors of X^TX and Λ is a diagonal matrix whose diagonal elements are the eigenvalues of X^TX. Therefore, the k^th subject of the original data x_k can be projected to the new space defined by W, obtaining its new set of coordinates s_k:

$$s_k=x_k{W}^T$$ (6)

PCA has been commonly used in applications for AD diagnosis assistance [75, 76, 77]. Most direct consequence to these works is that a reduced number of principal components are necessary and enough to describe the information about AD encoded in the input features.

2.10. Classification

All individual classifications performed in this work make use of Support-Vector-Machine (SVM) classifiers [78, 79]. A SVM classifier is a ML algorithm that splits a given set of binary labeled training data into two subsets. It makes use of an hyperplane that maximizes the distance between the two trained classes. Following this idea, a function $f:{ℝ}^p\to \left\{1,0\right\}$ using p-dimensional patterns x_i and class labels y_i is built to classify new examples $(\tilde{x},y)$:

$$\left({\mathbf{\text{x}}}_1,y_1\right),\left({\mathbf{\text{x}}}_2,y_2\right),\dots ,\left({\mathbf{\text{x}}}_R,y_R\right)\in \left({ℝ}^p\times \left\{1,0\right\}\right)$$ (7)

In order to maximize the distance to the decision boundary that separates the two classes (hyperplane), quadratic programming algorithms are used to minimize the margin cost function J as follows in expression (8) subject to the inequality constraints in (9). Note that as feature vectors may belong to one of the next three cases: (a) well-classified feature vectors outside the hyperplane margins, (b) well-classified feature vectors inside the hyperplane margins and (c) missclassificated feature vectors. These three cases can be merged into one when introducing a new set of variables, ε_i, also called ‘slack variables’. Therefore, the objective will be to maximize the hyperplane margins whereas mantaining ε_i ≥ 0 as low as possible including the maximum amount of points well-classified.

$$J\left(w,w_0,\epsilon \right)=\frac{1}{2}\Vert w{\Vert }^2+C\sum _{i=1}^l{\epsilon }_i$$ (8)

$$y_i\left[w^T{x}_i+w_0\right]\ge 1-{\epsilon }_i,{\epsilon }_i\ge 0,i=1,2,\dots ,l$$ (9)

The linear combination of a vectors subset (support vectors) conforms the solution of this problem.

2.11. Cross-validation strategy

To validate the classification results, each dataset has been splited into two groups: a training data group, which was used to train the prediction model, and a test data group, that is then used to measure the classifier’s performance. In this work, as the number of participants is large enough, an N-fold cross-validation strategy with N = 10 has been selected [80]. In addition to these traditional/empirical methods for the evaluation of the classification performance, it was analyzed the upper bounds of the empirical error based on the theory of uniform convergence of means to their expectations [81], since their competitive performance in heterogeneous data applications, such as the field of neuroscience and neuroimaging. A recent advance in this regard, based on the “in general position” assumption of the data distribution, allows to obtain tighter upper bounds effectively connecting the empirical and actual risks for linear classifiers within a small confidence interval [82].

3. Results

Following the schema proposed in Figure 1 and the comparisons defined in Table 3, several simulations were performed to obtain the number of PCA components (N_Comp) which maximize the classification performance considering a previous ANOVA analysis which discards non-significant features for a significance level α.

Depending on the type of input data, four feature selection and classification procedures for each experiment were defined: one for the NIB tests and three for imaging features (FDG, MRI and PiB). Once discarded participants without all tests results for each experiment; discarded all tests with a variance equal to 0; having standarizated all remaining columns using the z-score formula as described in (1); and regardless the experiment considered; a total of 10 NIB, 520 FDG, 184 MRI and 1040 PiB results were included as input features for each stack.

Moreover, in order to check if these characteristics were suitable for a later ANOVA analysis, Kolmogórov-Smirnov test was applied [83]. The objective of this test was to determine the percentage of features from each group which can be assumed to present a normal distribution. In this work, for all experiments at least 50%−75% of the features matched this condition. Thus, it was admited the use of ANOVA for feature selection.

At this point, for each experiment, the feature selection procedure (ANOVA + PCA) is carried out over training data and evaluated following the 10-fold cross-validation schema. Classification is performed using an SVM classifier with Linear Kernel. All these experiments are calculated considering the 50 most significant features of each input data class using the ANOVA analysis and up to 20 number of components for PCA: N_Comp = 1, 2,…, 20.

In the case of experiment 1, it was first decided to make a comparison between NC and MC participants regardless of their CDR. However, and as depicted in Figure 2 (upper), due to the overall small differences obtained following this idea with classification rates not better than 60.39% for FDG and less than 60.08% for PiB, it was finally decided to compare only asymptomatic subjects for both groups. Moreover, as one of the main objectives for this work was to determinate if subgrouping MC participants in terms of their responsible gene, a second comparison of NC vs asymptomatic PSEN1 vs asymptomatic PSEN2 vs asymptomatic APP was proposed. In that case, the problem was related to the size of each class (only 20 asymptomatic PSEN2 and 29 asymptomatic APP cases) which limits the generalization ability of each classifier⁴. Thus, it was finally decided only to focus on the most populated group and make a direct comparison between NC vs asymptomatic PSEN1 (Experiment 2) which has led to an increase in classification performance above 11.31% when N_Comp = 15 as shown in Figure 2 (down). Note that performance represented has been defined in terms of balanced accuracy which is equal to the arithmetic mean of sensitivity (true positive rate) and specificity (true negative rate).

Figure 2:

Classification results for experiments 1 and 2 using a SVM classifier with Linear Kernel and considering different types of input data for each N_Comp in PCA analysis.

As most of the values obtained showed low classification results, it was analyzed the upper bounds of the empirical error based on the theory of uniform convergence of means to their expectations like explained in section 2.11 for some of the components computed for PCA. In Table 4, it has been included both upper bounds of the empirical error and cross-validation classification performance for a given set of N_Comp and each kind of input data from experiment 2. Note that, in order not to overload the table, only some of these combinations have been depicted.

Table 4:

Classification results for NC vs asymptomatic PSEN1 comparison. Neither FDG nor NIB showed significant results.

Input data	NComp	CV accuracies (%)	re-Substitution (%)	Upper bounds (%)(*)	h
PIB	3	50.00	62.70	16.34	Reject
	10	57.46	85.38	28.21	Accept
	15	71.40	87.50	29.31	Accept
	20	64.60	89.48	30.35	Accept
MRI	3	56.41	61.21	16.34	Reject
	10	57.60	65.82	28.21	Reject
	15	56.83	68.01	29.31	Reject
	20	56.90	69.83	30.35	Reject

^(*)Reference levels obtained from [82]. CV accuracies column is expressed in terms of the balanced accuracy.

In regard of the results obtained, it was decided to use N_Comp = 15 as our reference level for PCA analysis. Using this value, different levels of EYO have been processed from the same point of view (experiment 3) as a way to determine how EYO has an effect on the classification outcome. As depicted in Figure 3, best performance results in terms of balanced accuracy were obtained for: MRI at EY O ≥ 15 years (70.00%); PiB at EY O ≥ 10 years (63.75%); and PiB at EY O ≥ 5 years (60.00%).

Figure 3:

Classification results for experiment 3 depending on the Estimated Years to Onset (EYO) when comparing NC vs. PSEN1 (only asymptomatic cases).

For each experiment and considering all the imaging data types, ROC curves have been calculated as shown in Figure 4 with the exception of EYO analysis which has been included as Supplementary Material. These curves can be used to check whether a fixed number of features selected by ANOVA analysis and a particular value for PCA N_Comp might involve a robust solution for the computer aided-diagnosis system. Moreover, to reinforce this idea, Area Under the Curve (AUC) has also been computed as represented in Figure 5 for PiB⁵ with maximum levels AUC = 0.679 at N_Comp = 15 when comparing directly PiB features from NC subjects vs asymptomatic PSEN1 participants.

Figure 4:

ROC curves obtained considering different types of input features for experiments 1 and 2.

Figure 5:

AUC obtained for each comparison performed for experiments 1, 2 and 3 when only using PiB imaging features.

In order to show the PCA results at a more detailed level, analysis of its variance has also been carried out. As depicted in Figure 6 for imaging markers, both FDG, MRI and PiB reach the 90% of their total variance within the 405 interval N_Comp ∈ [0, 10]. Thus, it can be assumed that increasing N_Comp will not provide significant differences in classification. This is the reason why N_Comp has been choosen as a value in the [0, 20] interval.

Figure 6:

Cumulative variance of PCA relative to N_Comp.

Apart from the proposed schema using ANOVA + PCA + SVM methods, a direct characterization of biomedical tests has also been presented here considering only those features which present a significance level for ANOVA below a certain threshold. Figure 7 shows the most significant imaging features for experiment 2 in terms of ANOVA analysis as example⁶. Moreover, in addition to this plot, a graphical representation of p-value for the first two experiments and considering a significance level for ANOVA α = 0.05 has also been included as shown in Figure 8. Note that as lower p-values represent more highlighted differences between groups comparisons, we have made use of the log(p-value) instead of p-value.

Figure 7:

Violinplots and Boxplots for the 6 most significant features of each input group (NIB, FDG, MRI and PiB) when comparing NC vs asymptomatic PSEN1 MC.

Figure 8:

Atlas plot of significant brain regions using the log(F_value) measure. Threshold referred to the significance level 0.05.

To complete this section, a comment about the study case presented in section 2.7.4 is also provided. When it was considered the scenario where NC and asymptomatic PSEN1 MC were compared, it was analyzed the distribution of the most significative features from both NC and PSEN1 MC classes. As shown in Figure 9, the histograms obtained from each marker revealed two similar distributions⁷ with no many differences between them.

Figure 9:

Histograms obtained from the 8 most significative FDG imaging markers when comparing NC vs asymptomatic PSEN1 MC.

Although this analysis could be ended here, shapes and sizes of both distributions suggested the existence of at least two subclasses within each group with special emphasys when considering the PSEN1 MC class. Making use of the Akaike Information criterion [85] for k-Means to determine the minimum number of clusters in a class as well as the k-Means algorithm itself, they were computed the two clusters within the PSEN1 subset. As shown in Figure 10, one of the PSEN1 subsets (violet) is usually displaced in relation to the centre of NC class (yellow) unlike the second subset (turquoise). This behaviour remains the same regardless also including symptomatic PSEN1 MC.

Figure 10:

Clustering obtained from FDG imaging markers when comparing NC vs asymptomatic PSEN1 MC. This 3D figure has been generated by representing the N_Comp = 3 components obtained from PCA analysis step.

In this scenario, the new classification rates obtained when comparing NC vs asymptomatic PSEN1 MC from the first cluster, and the NC vs asymptomatic PSEN1 MC from the second cluster showed significant differences between them. In fact, following the same procedure as perfomed for previous experiments, this resulted in classification rates above 73.56% (first cluster) and 66.08% (second cluster) when using N_Comp = 15 as our reference in previous experiments. This difference is even more highlighted when also including symptomatic cases: 77.69% (first cluster) and 65.44% (second cluster) as depicted in Figure 11.

Figure 11:

Classification rates obtained from FDG imaging markers when comparing NC vs PSEN1 MC. These results underscore the similarity between second PSEN1 cluster with respect NC whereas the first cluster is clearly more differentiated.

4. Discussion & Conclusions

A deep characterization of the clinical and preclinical stages of AD is critical to develop new lines of treatment for the disease [86, 24, 5]. As many works point out, AD should not be considered as a single entity [87]. Some of the AD subtypes, including the rare autosomal dominant form might evolve differently and require different ways to face up with the disease. However, most of the current clinical trials carried out to test interventions for AD did not discriminate between disease subtypes (mainly defined genetically in the case of DIAD).

For this work, the 3 experiments as described in section 2.7 section have been carried out with the aim to explore the possibilities offered by ML in analyzing DIAN dataset. In all the experiments presented here, a set of healthy control and non-carriers subjects have been compared with a group of mutation-carriers considering as inputs biomedical markers (NIB) and imaging markers (FDG, MRI, PiB). Due to the particular cases considered, experiments are discussed individually as follows in the next subsections. Then, a final section summarizes all the key points in common between them.

4.1. Experiment 1 - NC vs MC

Experiment 1 makes a comparison between NC and MC first considering all posible mutation types at every stage. Discussion about this experiment can be started from the analysis of classification rates obtained with a maximum balanced accuracy of 60.39% when using FDG imaging markers and 60.08% for PiB. If focusing on the other kind of tests, this rate decreases to even lower rates regardless of the number of input features selected from the ANOVA analysis or the combination ANOVA+PCA. To this aim, in a second step, it was decided to use only asymptomatic participants as a way to reduce the heterogeneity between subjects. This resulted in classification rates slightly higher than 60% when using PiB but still to far away from our objective. In this scenario, although PiB presented a better behaviour, results obtained have to be treated with caution since the low rates obtained and the lack of robustness shown in Figure 4: PiB curves present a considerable difference with respect the diagonal line but with a low AUC (maximum AUC equal to 0.6138 when using a high N_Comp for PCA). In the light of these findings, it can be assumed that PiB features ensure an appropriate separation of MC and NC but within a noisy environment in which missclasification errors happen very often. If unmasking data heterogeneity, better classification rates are expected to be obtained.

Despite of having some highly significant brain regions obtained from the ANOVA analysis selection such as those highlighted in Figure 8; superposition and data heterogeneity is limiting effectiveness of ML analysis for this experiment. Nevertheless, these results are quite similar to obtained in other works with special attention to central brain and right hemisphere. For example, [86] proved significant differences for carriers at temporal lobe (both medially in the region of the hippocampus and laterally in the temporal neocortex), cuneus, precuneus, cingulate, putamen and thalamus also referred by [88, 89, 16].

4.2. Experiment 2 - NC vs subgrouped MC

As a way to highlight the relevance of better comparing NC vs subgrouped MC in future DIAN studies, a second comparison between NC vs PSEN1 vs PSEN2 vs APP MC was performed. However, due to the low number of subjects in PSEN2 and APP classes as depicted in 2, it was finally decided only to compare NC vs PSEN1 MC participants among them.

In regard of Figure 2 results for NC vs asymptomatic PSEN1 MC, when selecting a high N_Comp for PCA, classification results increase up to 71.4% (PiB features). This supposes an increase above 13.16% with respect the NC vs asymptomatic MC comparison. In fact, regardless of the Estimated Years to Onset (EYO) from any patient, this difference in PiB and MRI scans is susceptible of being used to determine whether a new subject is more likely to be developing DIAD or if this assumption still remains far in time.

Finally, owing to AUC results in Figure 5, the solution proposed shows a robust behaviour. A clear illustration of this can be seen in the region between N_Comp = 4 and N_Comp = 15 where the increasing in AUC values take place in a linear way. Indeed, even considering a N_Comp out of these margins, none of the AUC values raise (or lower) dramatically.

As depicted in Figure 8, now the most highlighted regions are located at: cerebellum, entorhinal, cingulate (both caudal-ant., isthmus, post. and rostral-ant.), medial orbitofrontal, frontal pole, middletemporal, parahippocampal, corpus callosum (both ant., mid-ant. and post.), pars triangularis, precentral, ventral DC, brain-stem and insula. In comparison with the current literature related to this experiment, [4] described a significant deposition of Aβ amiloid in WM but it did not specified which were the particular regions where these results were obtained. Only [69] referred changes at cerebellum corresponding with one of our most significant regions for PiB markers. Note that as those works only were referred to PSEN1 MC but without specifying ther CDR grade, these results are not totally comparable to ours. The only work that presented a similar comparison was [28] where making use of brain imaging and fluid biomarkers, they characterized 18 asymptomatic children with E280A PSEN1 mutation. In that case, it was proven that MC children were distinguished from control individuals by higher levels in Aβ₄₂ and Aβ₄₂ : Aβ₄₀ ratio plus differences measured in precuneus area, post. cingulate, medial temporal lobe and hippocampus. These results also correspond with the presented here although NIB result have not been significant for our ML model.

4.3. Experiment 3 - NC vs asymptomatic PSEN1 MC (EYO consideration)

Once it has been proven that comparing NC vs MC subgrouped by their responsible gene is more effective from the point of view of ML analysis specially for PiB features, next step has been to determine if this significance is variable in time. For that, considering different levels of EYO applied to asymptomatic PSEN1 MC, input features have been classified and compared among them as shown in Figure 3.

In view of the results obtained, what first calls the attention is the lack of classification results for PiB and NIB at EY O ≥ 15 years. In [20], authors referred changes for signaling findings at neostriatum area. However, using our balanced muestral size of [35, 35] participants, not enough differences between NC and asymptomatic PSEN1 MC with EY O ≥ 15 years were found. The same reasoning applies to NIB features despite findings given by other works such as [20, 89, 9, 14, 90] where it was stated that Aβ depositions (and increasing of CSF τ levels and brain atrophy) occurs at least 15 years before symptoms onset when comparing NC vs MC. On the contrary, both MRI and FDG classifications have returned classification rates above 70.50% specially when considering FDG scan results. Indeed, ANOVA analysis carried out has underscored the following brain regions: paracentral, postcentral, insula, putamen, cingulate (both. caudalant. and rostral-ant.), fusiform gyrus, medial orbitofrontal, parahippocampal, corpus callosum (both central, mid-ant. and post.), choroid-plexus, accumbens, inf. lat. vent., inf. temporal, frontal pole, cuneus, pars orbitalis, lingual and supramarginal. Some of these areas corresponds with the findings discovered by other works like [20] using MRI scans at this stage.

At a posterior stage of DIAD pathogenesis, when introducing EY O ≥ 10 cases ([64, 64] participants), the first data patterns using PiB features and/or NIB begin to be significant and SVM classifiers start to discern between NC and MC cases⁸.

It is known that hippocampal volume reductions are observed as early as 10 years before expected onset [86, 20]. Moreover, there are also references to changes in FDG and PiB located at: precuneus, entorhinal, precentral, parietal lobule (both lateral and post-central) and post. cingulate regions; as well as significant changes for MRI features related to atrophy of accumbens and amygdala [32, 89]. Most of these patterns fit with the majority of the highlighted regions by our ANOVA analysis but also including: poscentral, frontal pole, paracentral, corpus callosum, pericalcarine, cerebellum, inf. lat. vent., choroid-plexus, pars opecularis, lateral orbitofrontal, insula, supramarginal and middletemporal. With reference to NIB features, although [9] pointed out significant concentrations of Aβ₄₂, τ and p-τ markers in MC group at very early EYO points, these results have not been relevant in this case.

Finally, with respect EY O ≥ 5 results, it is well known that decreased volumes of the thalamus, caudate, temporal lobe, parietal lobe and occipital lobe are reported in presymptomatic PSEN1 mutation carriers about 5 years before symptom onset [86, 13, 90]. Other works such as presented in [20, 89, 14] confirm these results, add new regions like precuneus and entorhinal areas to the list, and even suggest significant changes in cerebral hypometabolism and hippocampal atrophy during this stage of the disease. All of these results are consistent with ours but extending our findings to: cerebellum, ventral DC, corpus callosum, accumbens, choroid-plexus, pars opecularis, insula, amygdala, caudal middlefrontal, precentral, paracentral, poscentral and post. cingulate.

4.4. Extension of Experiment 2

One last question that remains to be answered is if classification results for experiments 1, 2 and 3 could be improved. Although it has been proved 1) that PET scans are the most suitable kind of test for DIAD, and 2) that reducing the heterogeneity of the disease (for example by differentiating participants according to their responsible gene) we can get a more precise model of the pathology; similarity between NC and asymptomatic MC at early stages of the disease should be further explored. This is the main reason why the extension of experiment 2 proposed in section 2.7.4 has been suggested as a way to measure the relationship between NC subsets and those without any kind of mutation. In this scenario, distribution analysis of the most significant features for DIAD could be a good starting point. As shown in Figure 9 for FDG, a preliminary assessment of NC and PSEN1 distributions suggests that both classes are very similar. Although this behaviour was not as good as expected, in view of the distribution tails from PSEN1 distributions it was stated that maybe this shape might be related to a mixture of two/more distributions. To confirm this idea, a clustering approach based on the use of k-Means algorithm was applied to the data as a way to determine if one/more of these PSEN1 subclasses could belong to the same distribution of NC participants or if they could be considered as an independent entity. Fortunately, as depicted in Figure 11 when using FDG imaging markers⁹, the second statement was confirmed. In fact, whereas one of the PSEN1 clusters is hard to distinguish from NC with classification rates barely above 64%, the other one improve these rates with balanced accuracy rates close to 80%. This procedure has been also repeated for NIB, MRI and PiB confirming this trend though not as much margin as using FDG including both symptomatic and asymptomatic cases. For example, when only using asymptomatic PSEN1 MC cases, PSEN1 subclasses got a difference margin up to 6.1% whereas FDG got 7.5%.

Relative to demographics extracted from each cluster, both populations are closely similar between them in terms of sex, age or MMSE as summarized in Table 5 (both symptomatic and asymptomatic cases) and Table 6 (only asymptomatic). This fact reflects that clustering is not based on the separation of participants according to their sex, age, or even their degree of disease; but only about activation measures. Although no significant differences were found with respect their first-degree relatives age at onset or the average age at onset obtained for the PSEN1 group, a further analysis of these subgroups is proposed for future work.

Table 5:

Demographics obtained from the two clusters computed with k-Means for NC vs PSEN1 MC.

Cluster	Group	N	Age	MMSE
First	Male	18	40.17 ± 11.38	26.67 ± 5.04
	Female	28	38.61 ± 10.88	26.68 ± 6.03
	Both	46	39.21 ± 11.10	26.67 ± 5.67
Second	Male	23	42.65 ± 10.57	26.65 ± 4.98
	Female	51	39.37 ± 9.76	26.81 ± 4.74
	Both	74	40.39 ± 10.14	26.76 ± 4.82

Table 6:

Demographics obtained from the two clusters computed with k-Means for NC vs asymptomatic PSEN1 MC.

Cluster	Group	N	Age	MMSE
First	Male	16	41.69 ± 10.70	26.94 ± 5.32
	Female	21	37.38 ± 9.72	26.71 ± 5.60
	Both	37	39.24 ± 10.38	26.81 ± 5.48
Second	Male	20	44.20 ± 10.43	26.65 ± 4.98
	Female	37	39.27 ± 9.16	26.81 ± 4.74
	Both	57	41.00 ± 9.91	27.79 ± 4.68

4.5. General conclusions

When this work was proposed, its main objective was to answer three questions: first, which kind of clinical test was the most relevant for DIAN diagnosis; second, considering MC subjects all together or separately (3 genes whose mutation is responsible of DIAD) if this could aid us to improve the model of the disease; and third, to confirm if these ideas could be used for a longitudinal analysis from the point of view of ML algorithms and to test its validity. In this sense, there is no other work trying to perform a ML analysis using this database so any conclusion stated here can be used for future works in the study of DIAN.

Owing to classification results obtained from each experiment performed, the first conclusion that we can assume is that all the imaging tests can provide relevant information concerning the DIAD prognosis and/or its pathogenesis with special emphasis on PiB features. This is indicating that even subtle differences in Aβ plaques deposited in neuronal tissue are more related to a higher separation between MC and non-MC than any other kind of test considered for this work. In fact, regardless the experiment under consideration, differences between NC and MC are larger using PiB than any other kind of input marker with an exception: results obtained whe comparing NC vs asymptomatic PSEN1 MC with EY O ≥ 15 years in experiment 3. Nevertheless, these results should be taken with care due to the kind of input markers used: SUVR values obtained using the analysis suite FreeSurfer. It is no exaggeration to state that a proper image preprocessing particularly designed for AD study might bring new evidences about pathogenesis and prognosis of the disease better than SUVR values do. Indeed, an specific analysis of those regions might be also important for future works even when a no direct evidence of AD has appeared yet (asymptomatic subjects) [14].

With respect to the improvement achieved when subgrouping DIAD participants in DIAN study, it is obvious that comparisons using subgrouped MC outperforms the results obtained for NC vs MC from experiment 1. Although it would have been desirable to compare NC vs PSEN1 vs PSEN2 and APP MC in a multiclass classification schema, the improvement reached when comparing NC vs asymptomatic PSEN1 MC instead of just using NC vs asymptomatic MC has been noteworthy (11.31% of classification increase for experiment 2). Further, if taking into account the results obtained for the extension of experiment 2, it has been demonstrated that even comparisons within PSEN1 MC with respect the control group (NC) show a strong differentiation among two PSEN1 subclasses in terms of imaging response. This fact has not been described before beyond the proposal made by [3] who suggested the existence of two or more differenciated groups for PSEN1 MC from the point of view of their symptomatology. Now, as this assumption was mathematically confirmed, this result constitutes an important milestone for the understanding of AD for two simple reasons: 1) it helps to corroborate findings in previous works, and 2) it establishes the basis for future comparisons even despite the low discriminative information extracted from DIAD markers but with special emphasis on PET imaging markers.

In conclusion, despite subjects with an inherited autosomal dominant AD mutation represent less than 1% of AD persons, the study carried out by DIAN initiative constitutes a strong impact in the understanding of AD with special emphasis on the disease course [26, 30]. As exposed during the discussion of all experiments, merging all MC subtypes as one unique MC group (even regardless the stage of their pathogenesis) might lead to a loss in statistical power. In the current work, it has been shown that our model fits better with DIAD progression even at its earliest stages. In this sense, since the proposal of a theoretical biomarker changes model for AD by [6], though several works have pointed out the relevance of different markers even 20 years before first symptoms onset, the application of deeper mathematical tools like ML models aid to discard some of them and to concentrate only of those clearly relevant. For all these reasons, it is expected that the use of new DIAN database updates joined with a deep image processing of FDG, MRI but, above all, PiB scans; provide insights into DIAD and LOAD and could even potentially be employed as read out in future treatment trials¹⁰.

• A comparison in DIAN by considering the 3 genes and Machine Learning.

• Feature selection based on ANOVA followed by Principal Component Analysis (PCA)

• SVM in a nested k-Fold CV resulted in accuracies of 72–74% using PiB PET features

• PSEN1 subgroups vs. NC provided accuracies of 80%, DIAN as an heterogeneous entity