Time Series Analysis of Biomarkers of Progression in Neurodegenerative Diseases

Time Series Analysis of Biomarkers of Progression in Neurodegenerative Diseases Íñigo Sanz Ilundain Degree in Computer Science Faculty of Computer Science and Engineering Complutense University of Madrid Degree Thesis in Computer Science May 30 2022 Tutor/s and/or colaborator/s: Laura Hernández Lorenzo José Luis Ayala Rodrigo Resumen en castellano Las enfermedades neurodegenerativas son enfermedades complejas y temporalmente dependientes. Entre ellas, la más común es la enfermedad de Alzheimer, en la que los pacientes atraviesan una serie de estados sintomáticos antes de llegar al diagnóstico de demencia causada por el Alzheimer. Debido a sus características, es necesario estudiar los biomarcadores asociados a esta enfermedad desde el punto de vista de las series temporales. En este trabajo, exploramos exhaustivamente los biomarcadores encontrados en la cohorte de Alzheimer’s Disease Neuroimaging Initiative (ADNI), aplicando una colección de algoritmos de clustering, tanto temporales como no temporales. Se han aplicado estos modelos a varios conjuntos de datos: considerando un solo biomarcador, combinándolos por pares y utilizando las regiones MRI. Los resultados obtenidos con estos conjuntos de datos fueron evaluados desde un punto de vista computacional, al igual que uno clínico, este último correspondiendo a los resultados esperados. Estos resultados muestran que, desde un punto de vista computacional, los modelos no temporales suelen obtener mejores resultados que los modelos temporales. Adicionalmente, los conjuntos de datos combinando biomarcadores con características similares incrementan el valor del resultado. Mientras tanto, desde un punto de vista clínico, el resultado influye mucho del algoritmo y del conjunto de datos utilizado: los modelos no temporales suelen obtener mejores resultados en conjuntos de datos que contengan biomarcadores como AV45 o ABETA, pero obtienen peores cuando se usan otros biomarcadores como TAU o PTAU, un límite que se puede superar usando modelos temporales. Este trabajo pone de manifiesto un enorme potencial en el clustering de series temporales en el conocimiento de las enfermedades dependientes del tiempo, como las neurodegenerativas. Palabras clave Enfermedad de Alzheimer, biomarcadores, deformación dinámica del tiempo, clustering Abstract Neurodegenerative diseases are complex and highly time-dependent diseases. Among them, the most common is Alzheimer’s Disease (AD), in which the patient goes through a series of symptomatic stages before receiving the diagnosis of dementia caused by AD. Due to its temporal characteristics, it is necessary to study the biomarkers associated with the AD from a time series point of view. In this work, we have exhaustively explored the biomarkers found on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort applying a wide array of clustering algorithms both temporal and non-temporal. These models were applied to several biomarker datasets: implying one biomarker only, combining them in pairs as well as making use of the MRI regions. The results obtained with these dataset types were evaluated using a computational and a clinical standpoint, where the latter corresponded very clearly with its expected outcomes. Results show that from a computational perspective, non-temporal models generally obtain greater outcomes than temporal models. Moreover, datasets combining biomarkers with similar properties also increase the resulting score. Contrarily, from a clinical standpoint, the outcome depends greatly on the algorithm and the dataset used: non-temporal models obtain better results in datasets containing AV45 or ABETA but struggle when used with TAU or PTAU, a limitation that can be surpassed by making use of temporal models. The present work raises enormous potential found in time series clustering to discover knowledge in time-dependent diseases such as the neurodegenerative ones. Keywords Alzheimer’s Disease, biomarkers, dynamic time warping, clustering Contents Índice i Agradecimientos ii Dedicatoria iii 1 Introduction 1 2 Materials and Methods 6 2.1 Databasedescription ............................... 6 2.2 Datafiltering ................................... 10 2.3 Datapreprocessing ................................ 13 2.3.1 Missingvalues............................... 13 2.3.2 Data transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Unsupervised classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Agglomerative Hierarchical Clustering . . . . . . . . . . . . . . . . . 16 2.4.2 K-Means.................................. 19 2.4.3 Density-Based Spatial Clustering of Application (DBSCAN) . . . . . 20 2.4.4 Self Organizing Maps (SOM) . . . . . . . . . . . . . . . . . . . . . . 21 2.4.5 Dynamic Time Warping with Hierarchical Clustering . . . . . . . . . 23 2.4.6 Dynamic Time Warping with DBSCAN . . . . . . . . . . . . . . . . . 26 2.5 EvaluationMetrics ................................ 27 3 Results 29 3.1 Non-Temporalmodels .............................. 29 3.1.1 Non-Temporal models with separated biomarkers . . . . . . . . . . . 30 3.1.2 Non-Temporal models with pairs of biomarkers . . . . . . . . . . . . 33 3.1.3 Non-Temporal models with MRI regions . . . . . . . . . . . . . . . . 34 3.2 Temporalmodels ................................. 35 3.2.1 Temporal models with separated biomarkers . . . . . . . . . . . . . . 36 3.2.2 Temporal models with pairs of biomarkers . . . . . . . . . . . . . . . 39 3.2.3 Temporal models with MRI regions . . . . . . . . . . . . . . . . . . . 40 4 Discussion 42 5 Conclusion 53 Bibliography 56 i Agradecimientos Quiero agradecerle a toda mi familia el apoyo incondicional que me han dado. A mis padres, a mi tía Piluca y a mi tío Carlos por apoyarme en los momentos más complicados. Muchas gracias a Berta, a Víctor, y al grupo de teatro de la Complutense, Triaca, por haberme acompañado tan de cerca durante todos estos años. Estoy especialmente agradecido a mis tutores Laura y José, no solo por haberme enseñado tanto sobre las enfermedades neurodegenerativas y guiado inmensamente a lo largo del año, sino también por su invaluable apoyo durante la elaboración de este trabajo. No habría sido posible realizar este trabajo sin vosotros. ii Dedicatoria A mi abuela, a mis padres y a mis hermanos. iii Chapter 1 Introduction Neurodegenerative diseases are complex diseases that take place in the patient’s brain, causing the progressive loss of neurons and its structure, a biological process known as neurodegeneration. A wide variety of neurodegenerative diseases exist, and the interceptions and treatments differ greatly from one disease to another. These diseases cause a great sanitary cost, as the affected patients need to be in constant monitorization both prior and after neurodegeneration begins in order to slow down the cell loss rate. Neurodegenerative diseases also have an economic impact, since the treatments employed are complex and thus expensive. Lastly and more importantly, the social impact of these diseases. Because of the cognitive impairment, patients with neurodegeneration cannot live their life in a normal way, depend on caretakers to perform their daily life activities and can ultimately end up developing dementia, something that impacts in their psychology, reducing their chances to slow cognitive decline, and also their social environment. Therefore it is essential to understand how neurodegeneration takes place and develop accurate techniques to diagnose and prevent it. Unfortunately, most neurodegenerative diseases are extremely complex and anticipating and curing their biological mechanisms is generally unknown. Examples of these neurodegenerative diseases are Parkinson’s or Huntington’s diseases, although the most common one is Alzheimer’s Disease, where one in 10 Americans are affected by it.1 Alzheimer’s Disease (AD) is a brain disease that mainly affects cognitive functions, beginning with mild memory loss, worsening to the extent of being unable to respond to 1 the environment. As stated, these symptoms are caused by neurodegeneration meaning a loss of neurons and its inter-connections, resulting in brain atrophy. This particular disease is characterized by three main clinical stages: preclinical AD, mild cognitive impairment (MCI), and finally dementia due to AD2. Depending on the current stage, diverse changes take place on the brain, with no or varying degrees of cognitive symptoms. Figure 1.1 shows these stages as well as the cognitive symptoms for each one of them. Mild and unnoticed symptoms No symptoms Severity of symptoms depends on degree of Dementia PRECLINICAL AD MILD COGNITIVE IMPAIRMENT DEMENTIA DUE TO AD Figure 1.1:Three main stages and symptoms in Alzheimer’s disease continuum. Note that the preclinical stage is the ideal stage to anticipate Dementia before the biological mechanisms take place. These stages and their particularities can be studied with the use of certain biomarkers present among the affected individuals as well as other assessments. Biomarkers are substances that indicate a biological status which are used to detect diseases before they take place as well as evaluate their progression once they have. Said biological status can be static measures such as the genotype of a person, or a varying measure, for instance molecular tests. The biological features of AD are described by the accumulation of two proteins in their pathogenic forms: beta-amyloid and Tau, forming plaques and neurofibrillary tangles, respectively. Therefore, one example of a very common biomarker is the progression of increased beta-amyloid levels in Positron Emission Tomography (PET) scans. However, similarly to the other neurodegenerative diseases, AD’s main challenge is to foresee when these mechanisms will take place and their evolution in time. All these mechanisms already trigger in the preclinical stage, long before any symptoms start taking place. Consequently, it is essential to study these mechanisms and anticipate their progression over time and implication at the clinical level, for instance the diagnosis transitions and their potential 2 relation with other important biomarkers such as in individuals’ genetics. While these diseases are extremely complex, the medicine field has also made advances such as reseaching new possible ramifications of medicine. It is the case of “P4 medicine”3, an approach to make medicine more predictive, preventive, personalized and participatory, with the major objective of improving wellness and anticipating the appearance of a disease’s symptoms. This has benefited the treatment of neurodegenerative diseases, especially the personalized approach. Due to the complexity of AD, placing each patient in one of three specific stages in the Alzheimer’s Disease continuum is limiting at best, as a considerable amount of information is lost and the differences between patients at a given stage are significant. Therefore, instead of visualizing stages, a more personalized perspective is the use of a gradient, where patients with similar biomarkers are placed close to each other. Because of the complexity in patient diagnosis and the amount of people affected by Alzheimer’s Disease, a very efficient tool to compare patients together is the use of Machine Learning techniques. Machine Learning is a discipline of Artificial Intelligence that allows systems to make observations and learn from patterns in data without any kind of human intervention or assistance. Its many applications range from data processing software in fields such as finance and data security to robotics capable of performing operations on patients with the use of sensors. Machine Learning has many uses due to the three types of classifications it is capable of, these being unsupervised, supervised and reinforcement learning. Unsupervised learning or clustering is a technique that is based on grouping together samples with similar characteristics. Therefore it is a useful tool in clinical applications because it permits to find new related groups of patients with the disease, which ultimately offers new knowledge about how the disease occurs without biasing the result towards previous knowledge about it. When treating with AD, clustering is the most interesting technique as it learns from the input data without the use of labels, which in our application field would represent the patients’ diagnoses. Moreover, this technique is also beneficial as it avoids taking into 3 patients had a MCI diagnosis and 791 (33.62%) suffered from Dementia, with the same 35 (1.49%) previous patients that did not have a set diagnosis. As we can see, the number of patients with Dementia has increased since the baseline, therefore this database is suitable to study the progression of AD among these patients. 2.2 Data filtering We divided the entire dataset into smaller subsets, each being biomarker specific to meet with all the filtering criteria, since a patient that might have all their datapoints available for a given biomarker, may also contain only a few for the rest of the biomarkers. Hence, each patient’s time series in the dataset has to go through a filtering process in order to make sure it is accurate and does not show ambiguities. Figure 2.3 shows the filtering steps carried out in this work. ... ... ... ... P1 P2 Pn n patients P have a time series each ... We discard patients with less than 3 points in time We discard patients with no variability in their time series We discard patients with unfeasable diagnosis transitions P1 P2 Pm INPUT DATASET m patients P, with m ≤ n Each time series has length 5 ... We fit each patient into a specific time series based on a given biomarker Figure 2.3:Description of each stage in the filtering process. Regarding this biomarker division, and the distribution of datapoints shown in the previous Section, we plotted in Figure 2.4 the number of datapoints available for each of the biomarkers used in this work as predictor variables. As it can be seen in Figure 2.4, for each biomarker, the number of available points has a different frequency of measurement over time. Therefore, we selected for each biomarker dataset the patients that had at least three measurements over time for that given biomarker. The threshold value of three visits was 10 Data points distribution over time for each biomarker (a): AV45 data points distribution over time (b): TAU data points distribution over time (c): PTAU data points distribution over time (d): ABETA data points distribution over time (e): FDG data points distribution over time (f): MRI data points distribution over time Figure 2.4:Distribution of the amount of data points in function of the VISCODE for each biomarker. Note that only patients with at least 3 points over time have been taken into account, since those with less points are not considered when defining the timeseries. decided due to two main reasons. In the first place, selecting a smaller number of needed measurements (1 or 2) would make our data more inaccurate. Moreover, selecting a bigger number as the threshold (e.g. at least 4 points) would have left us with barely any patients when combining biomarker datasets. Secondly, we removed patients with no variability in their biomarker measurements, which kept their progression constant. 11 Thirdly, we discarded patients depending on their diagnosis transitions. The diagnosis transition is defined by their diagnosis at baseline and last medical visits. We removed subjects that stayed with a normal cognitive profile during all visits (CN to CN). We also removed patients that presented unfeasible diagnosis transitions, different from those shown in Figure 2.2, such as going from Dementia to MCI, from Dementia to CN, or transitioning between diagnoses more than twice during their whole timeline. Finally, we selected a relevant time series for each biomarker; e.g, measurements taken every six months. This time series was defined taking into account how frequently the patients’ measurements are updated for each biomarker (Figure 2.4) and as described in ADNI’s protocol in their webpage8. Datapoints outside this time series were not considered since they would only be available in a small proportion of the total amount of patients, and it is crucial that all patient time series among a given biomarker have the same timeline. As a result of the filtering step, Table 2.2 shows the number of datapoints before and after the filtering process described above as well as the corresponding time series (in months) for each biomarker. Table 2.2:Number of data points before and after the filtering process and corresponding timeseries for each biomarker Biomarker Before filt. After filt. Timeseries TAU 2370 1180 (bl, 12, 24, 36, 48) PTAU 2369 1175 (bl, 12, 24, 36, 48) ABETA 2370 1175 (bl, 12, 24, 36, 48) AV45 2678 1645 (bl, 24, 48, 72, 96) FDG 3605 1760 (bl, 6, 12, 18, 24) Ventricles (MRI) 8955 6805 (bl, 12, 24, 36, 48) Hippocampus (MRI) 8317 6335 (bl, 12, 24, 36, 48) Midtemp (MRI) 7907 5975 (bl, 12, 24, 36, 48) Entorhinal (MRI) 7907 5975 (bl, 12, 24, 36, 48) Fusiform (MRI) 7907 5975 (bl, 12, 24, 36, 48) WholeBrain (MRI) 9210 6930 (bl, 12, 24, 36, 48) 12 2.3 Data preprocessing We then performed multiple preprocessing steps over all datasets meaning missing values processing and several data transformations. 2.3.1 Missing values As described in Section 2.2, by fitting each biomarker into a given time series specified by ADNI8and described by the dataset we considerably reduced the number of points without measurements, known as missing values. However, even with the recommended time series for each biomarker, some measurements over time were still missing. We input these missing values depending on the time point they were found. For missing values at the baseline time point (t= 0) for a given biomarker, we input the mean of all available patients’ values in baseline for that biomarker. This way, the variance of the dataset is kept constant, which will be useful when we begin using unsupervised classification. Missing values found at non-baseline and last time points were filled using the methods known as ’forward filling’ and ’linear filling’9, respectively. Figure 2.5 summarizes both of these methods. Missing values appearing at non-baseline and non-last time points were filled using ’linear-filling’9. This method uses linear interpolation in order to keep the progression linear, which works as follows. Let ybe the missing value and xits position in the time series. Moreover, let y0,x0be the same parameters for a known point before x; and y1, x1the same parameters for a known point after x. As long as there are two known points in the time series, all other points in between can be computed via interpolation with the formula: y=y0+ (x−x0)∗(y1−y0) (x1−x0) This method can be used for any time series in our dataset since the baseline is always present (if it is not, it is filled in as explained above) and there are at least two other known 13 0 1 2 3 4 5 Time y 6 Time 0 1 2 3 4 5 6 Value of feature y y0 y1 N/A N/A y4 N/A N/A Point present in dataset Missing point filled using linear-filling Missing point filled using forward-filling if point at baseline is missing, fill with the mean of all other patients' y value if available Figure 2.5:Explanation of the methods ’forward filling’ and ’linear filling’ used to fill in missing values. values in the time series. Lastly, missing values appearing at the end of the time series (last visit) were filled using ’forward-filling’9, in order to keep the remainder of the time series constant. Let yibe the last known value in our time series of length nand xiits position in the series, with i < n. Let also [yi+1, . . . , yn−1, yn]be missing points after yi. With ’forward-filling’, yk=yiwhere k∈[i+ 1, n]. 14 2.3.2 Data transformations We performed several data transformations regarding the clinical adjustements needed for some measures and the type of datasets we wanted to build. For the datasets involving the MRI variables, the brain regions’ volumes in a patient are all dependent on their intracranial volume (ICV). This means that while two patients may have an identical volume on a certain brain region, they in fact depend on their ICV. Therefore, we normalized at each point in the timeline, the patients’ brain region volumes by their own ICV. Because we wanted to take into account the temporality of the data while keeping them in tabular format, we carried out the following transformation for AV45, ABETA, TAU, PTAU, FDG and MRI biomarkers. We calculated their polynomial coefficients to perform a feature extraction. For this, we fit each time series into the equation ax2+bx +c, with a, band cpolynomial coefficients. Regarding datasets combining different biomarkers, since each biomarker has its own range, we normalized the values of each biomarker in order to keep them in the interval [0,1], therefore biomarkers with higher values will not add greater weight during the clustering decisions than biomarkers with a smaller range of values. Lastly, when the unsupervised classification algorithm applied needed it, we standardized the data so that it had a mean of 0 and a standard deviation of 1. 2.4 Unsupervised classification The aim of this study is to group these patients together by means of unsupervised classification or clustering. As such we used the following algorithms with tabular-formatted datasets: (i) Agglomerative Hierarchical Clustering, (ii) K-Means, (iii) Density-Based Spatial Clustering of Application with Noise (DBSCAN) and (iv) Self-Organizing Maps (SOM). Regarding time series datasets, we used Dynamic Time Warping combined with (v) Hierarchical or (vi) DBSCAN clustering methods. 15 Regarding all Section 2.3, we built six different types of datasets which will be evaluated in Chapter 3using the described unsupervised classification algorithms. The datasets names and the unsupervised classification methods applied to each of them are shown in Table 2.3. Table 2.3:Datasets and unsupervised algorithms applied in this work. Biomarker type Biomarkers employed Algorithm Tabular One biomarker AV45, ABETA, TAU, PTAU, FDG, MRI KMeans Hierarchical SOM Tabular Pair of biomarkers AV45-ABETA, AV45-TAU, AV45-PTAU, AV45-FDG, ABETA-TAU, ABETA-PTAU, ABETA-FDG, TAU-PTAU, TAU-FDG, PTAU-FDG KMeans Hierarchical SOM Tabular Several biomarkers MRI regions: Ventricles, Hippocampus, Entorhinal, Fusiform, Midtemp, WholeBrain KMeans Hierarchical SOM Polynomial transformation One biomarker AV45, ABETA, TAU, PTAU, FDG, MRI KMeans Hierarchical SOM Polynomial transformation Pair of biomarkers AV45-ABETA, AV45-TAU, AV45-PTAU, AV45-FDG, ABETA-TAU, ABETA-PTAU, ABETA-FDG, TAU-PTAU, TAU-FDG, PTAU-FDG KMeans Hierarchical SOM Polynomial transformation Several biomarkers MRI regions: Ventricles, Hippocampus, Entorhinal, Fusiform, Midtemp, WholeBrain KMeans Hierarchical SOM Timeseries One biomarker AV45, ABETA, TAU, PTAU, FDG, MRI DTW + Hierarchical DTW + DBSCAN Timeseries Pair of biomarkers AV45-ABETA, AV45-TAU, AV45-PTAU, AV45-FDG, ABETA-TAU, ABETA-PTAU, ABETA-FDG, TAU-PTAU, TAU-FDG, PTAU-FDG DTW + Hierarchical DTW + DBSCAN Timeseries Several biomarkers MRI regions: Ventricles, Hippocampus, Entorhinal, Fusiform, Midtemp, WholeBrain DTW + Hierarchical DTW + DBSCAN The next subsections describe all of the mentioned clustering algorithms. 2.4.1 Agglomerative Hierarchical Clustering Hierarchical clustering is a clustering technique that, depending on its type, merges data points into one cluster or divides a cluster into multiple clusters. Both types can be represented as a dendrogram to know which clusters were merged together or split up. Hierarchical clustering can use an agglomerative or bottom-up approach, where each data point is its own cluster and according to their distance with other clusters they are merged together or left alone. Meanwhile, there is the divisive or top-down approach, where all data points 16 are considered one unique cluster and based on their distance with each other they are split up into smaller clusters. While both types of hierarchical clustering yield the same results, we chose the agglomerative type over the divisive one since a bottom-up approach seemed easier to analyze over a top-down one. This explanation can be further visualized in Figure 2.6. BA CD E F Step 1: Data sample of 6 points labeled A-F BA CD E F Step 2: We compute pairwise distances for each pair of points based on a distance metric and a linkage criteria. In this example we use Euclidean distance and single linkage. B A CD E F Step 3: We pick the pair of points with the minimal distance and group them together. B A CD E F Step 4: We continue the process until only one cluster remains. Step 5: obtain the necessary number of clusters from the dendrogram. (e.g 2) A B C D E F 2 clusters AGGLOMERATIVE DIVISIVE Figure 2.6:Explanation of the agglomerative hierarchical clustering method. As mentioned previously, the agglomerative hierarchical clustering first considers all data points as their own clusters and groups them together based on two parameters: the distance 17 metric and the linkage criteria. The distance metric is used to determine the separation between each cluster using one of the available metrics such as the Euclidean distance10, which measures the linear distance between two points, or the Manhattan distance10, which is the sum of the absolute difference between the measures in all dimensions of two points, among many others. The linkage criteria is the basis by which each pair of clusters is grouped together based on their distance. These criteria can be single-linkage -where we group together pairs of clusters that are closest to each other-, complete-linkage -where we group together pairs of clusters that are the furthest from each other-, centroid-linkage -where pairs of clusters are grouped together based on the closest centroid distanceor average-linkage -where we group together pairs of clusters that have the shortest mean distance between pairs of elements from each of the clusters-, among others. The explained linkages are visually detailed in Figure 2.7. BA CD Single linkage: returns minimal distance between clusters BA CD Complete linkage: returns maximal distance between clusters BA CD Average linkage: returns mean of all pair distances between clusters Centroid linkage: returns distance of centroids between clusters BA CD Figure 2.7:Explanation of some of the different types of linkage that can be used in hierarchical clustering. Since there are multiple metrics and linkages that can be used to cluster our data, we 18 performed a grid-search considering each combination metric-linkage. In section 3, we kept for each biomarker the combination that returned the best outcomes based on the evaluation metrics and analyzed the results. 2.4.2 K-Means K-Means11 is a clustering algorithm that clusters data into Kclusters while keeping each cluster’s variance as minimal as possible. The methodology of this algorithm can be visualized in Figure 2.8. Dataset of 13 samples which we want to cluster into 3 groups. Step 1: We initialize each centroid and assign it to a random sample x x x Step 2: Each sample is assigned to a cluster depending on what its nearest centroid is x x x Step 3: Centroid positions are updated according to the new samples present in their cluster x x x repeat Step 2 until centroids no longer change K clusters are now defined x x x Figure 2.8:Explanation of the K-Means clustering method. It functions by separating Nsamples from a dataset into Kdisjoint clusters. Each cluster is defined by a centroid, which is the mean ukof all the samples contained among a cluster. At first, Kcentroids are placed either in Kdifferent samples or initialized randomly in the 19 failed because the threshold was set too high-, or the minimal distance between trajectories is bigger than the threshold. Since we group trajectories together, and a trajectory can either be a time series or a prototype cluster made of two or more timeseries, we must define a specific formula to compute the DTW distance in these specific cases. Let A and B be trajectories of one or more timeseries: DT W(A, B) = op(DT W (∀A, ∀B)) As hierarchical clustering has multiple linkage criteria that need to be considered, the operator op in the formula above depends on the chosen criteria. This operator can be replaced as follows. When we perform complete-linkage, we want to get the maximal possible distance between a pair of points of the two timeseries, therefore we can use max instead. When performing single-linkage, we seek the minimal distance between a pair of points of the timeseries, thus we replace op with min. We also performed average-linkage, by calculating the mean of all the computed distances, by using mean. Finally, we used median-linkage, finding the median of all the computed distances using median instead. Each linkage criteria has been used with each kind of dataset both in uniand multidimensional ones. Regarding multidimensional datasets, for our algorithm to function correctly we modified the dimensionality of the input and used a different method for DTW computation.14 2.4.6 Dynamic Time Warping with DBSCAN We also combined DTW with the DBSCAN algorithm since it excels in datasets with regions of high density and DTW seemed to be a promising lead. We first computed for each pair of trajectories their DTW distance and created a matrix of N×Nwith i,jcorresponding to the distance between the trajectory of patient iand the trajectory of patient j. We then used this distance matrix as input data instead of the patients’ timeseries. In order to obtain the best results, we performed a grid search to find the hyperparameters that worked best 26 with the algorithm, taking into consideration certain filtering criteria, such as a maximum of 20% of patients being considered as outliers, as well as each cluster having a minimum of 10% of total patients. 2.5 Evaluation Metrics To evaluate how well each of our algorithms cluster the data, we have used two metrics: the Silhouette Score (SI), very often used in clustering applications, as well as the Progression Accuracy (PA), a custom metric that indicates the differences among each cluster from a clinical standpoint. The Silhouette Score15 is a useful metric when considering how dense and well defined the resulting clusters are. It ranges from -1 to 1, and the higher the score, the more defined the clusters will turn out to be. If the score is in the negative range, it usually considers the clustering to be incorrect, while a score close to 0 signifies that the clusters are overlapping each other. Since this score only determines how well the clustering algorithm is performed from a computational viewpoint, it is also necessary to evaluate the clustering performance from a clinical point of view. The Progression Accuracy is a metric that aims to compute the quality of the diagnoses separation between clusters. We consider a patient that progresses further in the Alzheimer’s Disease continuum as one that started with a certain diagnosis and has progressed towards a more advanced stage by their final diagnosis. These patients will be considered as active. Contrarily, a patient that has a static diagnosis transition between the baseline and their last visit is considered to have a slower progression towards Dementia. These other patients will be considered as static. Therefore this metric computes the proportion between active and static patients, favoring clustering results that show considerable difference in diagnosis progression between clusters. We want to find the PA value of N clusters. Let S be the combinations of all pairs of 27 clusters without repetitions, such as: S= (i, j)|i∈[0, N], j ∈[0, N], i < j To calculate this metric, we first need to compute the progression ratio (PR) between all pairs of clusters in S. Let Ciand Cjbe two clusters, with Aiand Sibeing the amount of active and static patients for Cirespectively, and Ajand Sjthe amount of active and static patients for Cj. Then, the PR between clusters Ciand Cjcan be considered as: PR(Ci, Cj) = max(Ai+Aj, Si+Sj) Ai+Aj+Si+Sj Thus, in order to find the PA between N clusters: PA(C1, . . . , Cn) = P R(Ci, Cj)with (i, j)∈S We will use these metrics to consider for each clustering both the computational and the clinical standpoints and compare each clustering algorithm with another. When comparing how each dataset worked with each type of algorithm, we will describe the best clustering result in terms of the Progression Accuracy. This description is done from the point of view of diagnosis change and demographic variables as previously described. Additionally, when working with temporal models, we computed for each biomaker the regression line y=Ax+Bof each cluster so that we could measure more precisely how each cluster progressed over time, depending on the value of A. Finally, we analyzed each cluster using the demographical data at our disposal. We performed a t-test for each variable so that, by obtaining its p-value, we could conclude whether there was a significant difference between clusters regarding these demographic variables. A result is considered significant if its p-value between clusters is less than 0.05. 28 Chapter 3 Results As introduced in Section 2.4, we applied a wide array of clustering algorithms to try on our data. Because said array is lengthy, we have separated the following description of the results into two main sections. Firstly, in Section 3.1, we describe algorithms that do not take into account the temporality of the dataset, meaning models that take as input normal tabular datasets where the features represent different timestamps for when the biomarker was measured. Secondly and contrarily, Section 3.2 describes results with algorithms that do take into account the temporality of the dataset. For each type of model, we describe differences in the evaluation metrics between the various clustering algorithms. Next, we report both the biomarker dataset and clustering algorithm that obtained the best progression accuracy score described in Section 2.5. Lastly, we describe the clusters obtained in the best results using the sociodemographic variables we mentioned in Section 2.1. All the percentages shown in this section are calculated over the total number of patients in each cluster. 3.1 Non-Temporal models We applied several canonical clustering algorithms such as KMeans, Hierarchical Clustering and Self Organizing Maps, giving them as input two different datasets: (i) only one feature corresponding to the first biomarkers’ measurement (i.e. baseline visit) available in the timeseries, and (ii) all features available in a patient’s timeseries, meaning each feature 29 represents a patients’ visit to the doctor. The first kind of models could serve us as a reference, showing what we could expect from the very first visit and measurement taken of each biomarker both in terms of clustering and the diagnosis progression. Moreover, we evaluated these two kinds of input datasets using information from (i) only one biomarker (e.g. AV45), (ii) a pair of biomarkers (e.g. AV45+ABETA) or (iii) several biomarkers (MRI). Therefore resulting in six different kinds of datasets evaluated with the abovementioned clustering algorithms. For the sake of understandability we have divided these results in categories involving non-tempral and temporal models. Figure 3.1 displays the proportion of diagnosis transitions between clusters in the non-temporal models that will be described. Meanwhile, Figure 3.2 shows the distribution of the sociodemographic variables for said models. Figure 3.1:Barplots showing the diagnosis transitions for each cluster in the three best clustering results for non-temporal models: (a) best non-temporal model for separated biomarkers (SOM with AV45, all features), (b) best non-temporal model for paired biomarkers (SOM with AV45+FDG, all features) , (c) best non-temporal model for the MRI dataset. (SOM, all features) 3.1.1 Non-Temporal models with separated biomarkers We applied KMeans, Hierarchical and SOM clustering to datasets containing only information of one biomarker using (i) only the baseline visit measurement, and (ii) all the visits’ measurements. Figure 3.3 shows the results obtained in terms of SI score and accuracy. As it can be seen in Figure 3.3a, most of the clustering models obtained a SI score greater 30 Gender APOE e4 status MMSE score at last visit AGE at baseline visit Education years Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Gender APOE e4 status MMSE score at last visit AGE at baseline visit Education years Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 (b) SOM (all) and AV45 + FDG * * * * * * (a) SOM (all) and AV45 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Gender APOE e4 status MMSE score at last visit AGE at baseline visit Education years (c): SOM (all) and MRI * * * * Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Cluster 0 Cluster 1 Figure 3.2:Distribution of five different sociodemographical features by clusters: gender, APOE e4 genotype, MMSE score at the last visit, age at baseline visit, and education years in non-temporal models. Plots that are labeled with an asterisk on top indicate that the sociodemographic variable considered is significantly different (p-value <0.05) between clusters. than 0.5, except for the majority of FDG datasets and algorithms combinations. In three out of five evaluated biomarkers (AV45, ABETA and FDG), K-Means was the algorithm that obtained the best results in terms of SI score, both using only the baseline visit (KMeans 31 AV45 TAU PTAU ABETA FDG Dataset 0 0.2 0.4 0.6 0.8 1 Silhouette Index (a) AV45 TAU PTAU ABETA FDG Dataset 0 0.2 0.4 0.6 0.8 1 Progression Accuracy (b) KMeans baseline KMeans all visits Hierarchical baseline Hierarchical all visits SOM baseline SOM all visits Figure 3.3:Evaluation metrics obtained for each non-temporal model. Figure (a) shows the Silhouette Index Score and Figure (b) shows the Progression Accuracy achieved with unidimensional datasets. baseline, see Figure 3.3a) and all visits (KMeans all visits, see Figure 3.3a). Therefore, KMeans makes more defined clusters in terms of distance regarding non-temporal models. In fact, the highest SI score is obtained with K-Means using the baseline ABETA measurement (SI score of 0.7143). Regarding the progression accuracy defined in Section 2.5, as seen in Figure 3.3b, only datasets using AV45 and ABETA obtained an accuracy greater than 0.60. Overall, AV45 datasets obtained the best progression accuracy values compared to the other biomarkers. In fact, the combination that obtained the best accuracy results in AV45 datasets was the SOM model using all the available features (0.7083). SOM model using all the available AV45 features gave two clusters, containing 115 and 77 patients, respectively. In the smaller cluster, 80.52% (62/77) of the subjects were diagnosed both at the baseline and last visit with MCI, while only 19.48 % (15/77) advanced towards the Alzheimer’s Disease continuum between their initial and last visit. Unlike the smaller group, only 37.39% (43/115) in the bigger cluster stayed on the very same diagnosis, meanwhile a total of 62.61% (72/115) progressed towards a worse diagnosis. Thus, we can clearly see two very different groups, one of them containing mainly patients that stayed on the same stage of AD, and another group with patients that continued to a more advanced stage. These results also correlate with the demographic variables: we obtained a significant 32 difference regarding the number of patients or their mean values in each cluster for four out of the five sociodemographic variables used. Figure 3.2 shows the distribution of these variables in each cluster. The variables that obtained a significant p-value, meaning a significant difference between clusters were (p-values between parentheses): APOE4 (9.30e−08), the MMSE score (7.35e−09), the patients’ age at baseline (AGE, 1.7e−02) and finally the years of education of the patients (PTEDUCAT, 2.5e−02). 3.1.2 Non-Temporal models with pairs of biomarkers The same algorithms were applied in the very same datasets (baseline visits and all visits measurements) combined by pairs, in order to gain a better understanding whether a certain combination of biomarkers favors higher evaluation results. In Figure 3.4a, the Silhouette Index scores obtained with combinations of biomarkers range from scores starting from 0.193 to 0.5743, with the majority above 0.4. The best score is obtained when combining the TAU and PTAU datasets, with a maximum value of 0.5743 when used with KMeans. As for the Progression Accuracy score, in Figure 3.4b, it seems that those pairs of biomarkers that were combined with AV45 obtained a remarkable result when used with Self Organizing Maps, compared to the other two algorithms, with a maximum of 0.741 in AV45 + FDG when using all available features. With most of the other pairs, it also seems like Self Organizing Maps obtains a better result than the other algorithms. When applying SOM in the dataset combining AV45 and FDG, we obtained two clusters, each one containing 27 patients, as such we will name them C0 and C1. C0 only contains a total of 22.2 % (6/27) patients that do not transition towards a more advanced stage. Meanwhile the other 77.8 % (21/27) did suffer from more neurodegeneration. Contrarily, C1 has a total of 70.4 % (19/27) of patients that stay in the same diagnosis, and the remaining 29.6 % (8/27) that do progress towards a more advanced stage. As for the demographic variables, both the APOE4 gene (1.9e−03) and the MMSE score (1.4e−02) are significant. 33 AV45+TAU AV45+PTAU AV45+ABETA AV45+FDG TAU+PTAU TAU+ABETA TAU+FDG PTAU+ABETA PTAU+FDG ABETA+FDG Dataset 0 0.2 0.4 0.6 0.8 1 Silhouette Index (a) AV45+TAU AV45+PTAU AV45+ABETA AV45+FDG TAU+PTAU TAU+ABETA TAU+FDG PTAU+ABETA PTAU+FDG ABETA+FDG Dataset 0 0.2 0.4 0.6 0.8 1 Progression Accuracy (b) KMeans baseline KMeans all visits Hierarchical baseline Hierarchical all visits SOM baseline SOM all visits Figure 3.4:Evaluation metrics obtained for each non-temporal model. Figure (a) shows the Silhouette Index score and Figure (b) shows the Progression Accuracy achieved with multidimensional datasets. 3.1.3 Non-Temporal models with MRI regions Finally, we applied the aforementioned clustering algorithms to a dataset containing all of the cerebral regions described in Section 2.1, with the same variations that the other datasets had, these being (i) only baseline measurements, and (ii) all visits’ measurements. Figure 3.5 shows the results obtained regarding SI scores and Progression Accuracies. As seen in Figure 3.5a, all clustering models obtained a Silhouette Index score similar to 0.3, with a maximum of 0.322 when using K-Means and all available features in the time series. Regarding the algorithm variants, it seems that the algorithms that use all of the available features in the dataset obtain a better score than those that do not. Regarding the accuracies obtained, we can gather from Figure 3.5b that all models obtain an accuracy below 0.6, with Self Organizing Maps and the variant that uses all features obtaining a maximum accuracy of 0.593. As with the Silhouette Index scores, the algorithms that use all of the available features obtain a better accuracy than those that only use the baseline visit measurement. When combining the variant of SOM that uses all the available features with the MRI 34 MRI Dataset 0 0.2 0.4 0.6 0.8 1 Silhouette Index (a) MRI Dataset 0 0.2 0.4 0.6 0.8 1 Progression Accuracy (b) KMeans baseline KMeans all visits Hierarchical baseline Hierarchical all visits SOM baseline SOM all visits Figure 3.5:Evaluation metrics obtained for each non-temporal model. Figure (a) shows the Silhouette Index Score and Figure (b) shows the Progression Accuracy achieved with the MRI dataset. regions, we obtain two clusters, a smaller one containing 374 patients and a bigger one with 462 patients. In the smaller cluster, a total of 61.8 % (255/374) had a static diagnosis transition, while the remaining 38.2 % (119/374) moved to a more advanced stage. Meanwhile, in the bigger cluster, 49.8 % (230/462) of patients stayed in the same diagnosis while the other 50.2 % (232/462) did not. Regarding the sociodemographic variables, four variables were considered significant, these being the APOE4 (2.61e−06), the MMSE score (2.50e−49), the patients’ age (AGE, 4.46e−15) and the patients’ years of education (PTEDUCAT, 4.9e−02) 3.2 Temporal models After applying canonical clustering algorithms to the datasets, we applied other clustering techniques that consider temporality (a) within the datasets, or (b) within the algorithm. Its main purpose is to compare the difference w.r.t the non-temporal models evaluated previously (Section 3.1) to assess whether including any kind of temporal structure to the data could give better results. Firstly, as described in Section 2.4, for each of the five biomarkers, we applied a poly35 Chapter 4 Discussion We have performed an extensive research of combinations between multiple clustering algorithms and biomarkers datasets for the discovery of new clusters related to the progression of AD. Regarding the clustering algorithms, we evaluated several algorithms ranging from those that do not take into account the temporality of the data (Section 3.1) to other algorithms that do use time series (Section 3.2) for grouping patients. Moreover, the array of datasets used started with those that do not have any temporal components to others that do integrate them and also combinated different biomarkers alone and in pairs, as well as the MRI regions. Therefore, we will analyze in this section whether there is a correlation between integrating temporality to the model and obtaining a better result in each of the biomarkers, using the evaluation metrics proposed. In the following paragraphs we employ the term "model" as the application of a certain clustering algorithm with a specific dataset, e.g. K-Means with AV45 dataset. In general, SI scores seemed to vary between models, as some scores reach up to 0.7 and others barely make it to 0.2. Because of the uneven SI scores between models, the following discussion is organized to give an interpretation from different perspectives, differentiating the results obtained between datasets and the algorithms used. Regarding non-temporal models that used individual biomarkers datasets, from a dataset perspective, there is a difference of results between linear algorithms such as K-Means and Hierarchical clustering, and non-linear algorithms like SOM. AV45 and ABETA datasets 42 worked better with linear algorithms, obtaining SI scores higher than 0.6, contrarily to nonlinear algorithms. However, FDG dataset worked better with SOM, obtaining a SI score as good as the ones previously described with linear algorithms. From an algorithmic point of view, both K-Means and Hierarchical clustering algorithms obtained better results than SOM. These results make sense because the former algorithms use an approach completely based on distances between samples, the principle in which SI score is based. Specially, the K-Means algorithm as it is highly distance-based, since it is an algorithm that minimizes cluster variance and therefore favors a good SI score. Meanwhile, SOM integrates the underlying structure of the data and favors a higher distance between neurons, but these neurons do not necessarily imitate the variance of the data, specially because we have performed a feature extraction and some information about the original data will be lost. Moreover, when using AV45 and ABETA datasets, we obtained a better SI score when giving as input only the baseline visit measure. On the contrary, we obtained better SI results when using all features in the TAU or PTAU datasets. As for pairs of biomarkers, from a dataset perspective, the SI scores obtained are generally worse than those acquired when using separated biomarkers. This is probably due to the increased dimensionality when adding another biomarker into the dataset: with the datasets that only focus on the first feature, the dimensionality of each sample becomes 2 since we add the first feature of the other biomarker, meanwhile for those that use all 5 components, the dimensionality increases to 10. This dimensionality increases the distance between samples, and the clusters obtained are less dense, therefore obtained a lower SI score. The dataset that obtained the best score was the TAU+PTAU pair as most of the algorithms that use this dataset obtained a score close to 0.6. A dataset that also performed well is the pair combining the AV45+ABETA biomarkers, which seemingly obtains the second best score out of the other datasets. The reason for obtaining denser clusters with the pairs TAU+PTAU, as well as AV45+ABETA make sense accordingly to the processes that these biomarkers represent. Both TAU and PTAU measure the amount of Tau 43 protein in their normal and phosporilated form, respectively. Moreover, both AV45 and ABETA measure the amount of accumulated beta-amyloid in the brain or in the CSF, respectively. Therefore, there will be a higher correlation between biomarker measurements in these pairs, than between those that are less similar. For example, the pair AV45 and FDG performs the worst between all the datasets, as all of the algorithms that use it obtained a score lower than 0.40. Although both AV45 and FDG are measures obtained through PET scans and measure neurodegeneration, AV45 measures the quantity of beta-amyloid while FDG measures the amount of glucose consumed in the brain, thus they correspond to very different neurodegeneration biological processes. Therefore, it seems that the SI score is highly affected by the nature of the paired biomarkers. Algorithmically-wise, as it happened and was explained before with the separated biomarkers’ datasets, linear algorithms usually obtained a higher score than non-linear algorithms in each of the datasets. Moreover, for each algorithm, the variant that only uses the first feature obtains a slightly higher SI score than the variant that uses all of the available features. This is explained for the reason that variants that only use the first feature have lower dimensionality in their datasets than the other variant, therefore clusters have lower intra-cluster distance. As for MRI, from an algorithmic perspective, all models obtained a very poor SI score when compared to the prior models. However, since we have introduced 6 new dimensions for our algorithm to work with, and where the Ventricles region has a different direction than the other regions in terms of increased neurodegeneration, it is logical that the distance between samples will increase considerably, difficulting the possibility of obtaining high scores. Nevertheless, models that use all of the available features obtain higher scores than the models that do not, as evidenced by Figure 3.5. Therefore, a plausible hypothesis could be that in multidimensional datasets, variants that use all features obtain higher scores as opposed to unidimensional datasets, where variants using only the baseline visit feature obtain better scores. Moreover, in both variants, the K-Means algorithm obtains higher scores than SOM, which supports the idea that linear models obtain better scores than 44 non-linear ones. In conclusion, for non-temporal models, we have seen that in the majority of cases, an algorithm that is based on linear regression obtains a higher SI score than non-linear algorithms. Moreover, unidimensional datasets seem to obtain better scores when only using the baseline visit whereas multidimensional datasets obtain higher scores when using all the available features, as evidenced by the MRI regions which obtained greater scores with the variants that make use of all features, unlike the separated biomarkers. Finally, we have seen how pairs of similar biomarkers generally obtained higher scores. We wanted to confirm further these results with temporal models. Among temporal models, we differentiate between those (a) including the temporality within the dataset through a polynomial regression transformation; and (b) those including the temporality within the algorithm therefore the dataset is built as a time series and the algorithm (DTW) works with that kind of data. Regarding polynomial regression models, when using individual biomarkers, it is clear that these models obtained a worse score (the majority falling under a SI score of 0.40) than the non-temporal models (SI score higher than 0.60). The main reason for this could be related with the polynomial transformation performed. This transformation works as a feature extraction technique: we change the features in which the data is represented. However polynomial regression could not accurately represent the original time series progression, therefore information is lost. This can be observed when applying the polynomial variant of SOM, where we firstly perform a feature extraction from 5 to 3 features, and a second feature extraction from 3 to 2 features. Regarding that last statement, linearity in models obtains a higher score than non-linear models, as evidenced by K-Means and Hierarchical clustering obtaining a higher SI score than SOM. Moreover, a key difference between these models and the non-temporal models is that AV45 no longer obtained the highest score, instead, TAU and PTAU, which previously obtained worse scores in non-temporal models, now give better results. Furthermore, regarding DTW models from the dataset perspective, we obtained uniform results for each dataset as they 45 all obtained a score over 0.50, except for FDG dataset. In order to calculate the SI score for these models, we have considered DTW distance instead of Euclidean distance since clusters will be made based on the former instead of the latter. From an algorithmic point of view, it seems that the combination of DTW and DBSCAN struggles with biomarkers such as TAU, where it does not obtain a result based on the filtering criteria, or PTAU, where it obtained a very low SI score. However, DTW+DBSCAN models obtained better results when using AV45 or ABETA datasets. Temporal models were also tested using pairs of biomarkers, as done with non-temporal models. Regarding the polynomial regression model, from a dataset point of view, all pairs that contained either AV45 or ABETA features performed worse compared to other datasets that contained either TAU or FDG. Therefore, when temporality is taken into account, it seems the AV45 dataset is no longer the dataset that obtains the best score, as it previously happened with non-temporal models. Moreover, from an algorithmic point of view, once again linear algorithms (KMeans and Hierarchical clustering) obtained considerably better results than the non-linear ones (SOM). Finally, regarding DTW models, we obtained uniform results between datasets, generally SI scores around 0.4 with a few exceptions. In the case of DTW, it makes sense for the SI score to be lower compared to the DTW models with biomarkers alone, as we have added dimensionality. Moreover we obtained the same results than one-biomarker models: pairs with AV45 obtained worse scores than those with TAU or PTAU, contrarily to the non-temporal models. Finally, combining DTW+DBSCAN generally returns better results than DTW+Hierarchical clustering. This is due to the fact that DBSCAN by definition is a clustering algorithm that creates clusters out of initial samples and builds around them, therefore favoring a better SI score. Regarding the MRI models from an algorithmic point of view, there is a clear difference between the scores obtained when using polynomial regression and those obtained using DTW, as the former score close to 0.1 whereas the latter score above 0.2. Similarly to the non-temporal models, the scores are lower when compared to separated biomarkers or 46 when combined by pairs as the dimensionality has increased greatly, distancing each sample further. Finally, as for the algorithms using the polynomial variant, once again linear models obtain better scores. Regarding algorithms that use DTW, DBSCAN obtains a better SI score because of its nature as explained above. In conclusion, for temporal models, the SI scores obtained are generally worse than the non-temporal models since we use feature selection like in DTW. Moreover, when considering temporality, more complex biomarkers such as TAU or PTAU obtained better scores than biomarkers like AV45 or ABETA. Finally, datasets with higher dimensionality, such as MRI datasets, will generally obtain lower scores. Although the results obtained with SI scores yielded interesting discussions about which biomarkers work better and what clustering algorithms are preferred from the point of view of SI score, we also wanted to see if the obtained clusters were making sense with the known diagnosis transitions and the sociodemographic information of the subjects. One of the greatest potentialities of clustering is the discovering of new knowledge, and therefore it is important to take into account clinical information, to properly label these new patients’ groups obtained. Therefore, we developed a metric based on accuracy score to measure the reliability of these new groups from a clinical point of view. We named this metric "progression accuracy" (see Section 2.5). This metric measures the overrepresentation of patients that progress worse in diagnosis (towards MCI or Dementia) against patients that did not progress, staying in their diagnosis. Therefore in the following lines we described what happened regarding the previously described models. When using separated biomarker datasets, from a dataset perspective, AV45 and ABETA obtained considerably better accuracies than the rest of the biomarkers regardless of the algorithm used, as all of their accuracy scores are over 0.60, contrarily to the rest of the datasets. Moreover, TAU and PTAU obtain similar accuracies as well as the worst ones between all the datasets. AV45 is a biomarker that is very considered when giving a patient 47 diagnosis16, as it measures amyloid burden in the brain, therefore it differentiates best between patients in the Alzheimer’s disease continuum. Algorithmically-wise, in general Self Organizing Maps seem to obtain higher accuracies than the other algorithms, specially in AV45. Moreover, in AV45 regarding the features used, considering all five features seems to obtain a higher accuracy, specially in linear algorithms as a correlation17 higher than 0.8 between features can be observed. However, Self Organizing Maps with only one feature obtains as high an accuracy as linear algorithms with all features, which suggests that nonlinear models are capable of inferring further than linear algorithms. Finally, as for the other datasets, using all features in a time series does not necessarily improve the accuracy. As for pairs of biomarkers, from a dataset standpoint, pairs that consider the AV45 biomarker always obtain a higher accuracy than other pairs, specially the combination of the AV45 and FDG datasets which obtains the highest result when used with Self Organizing Maps. Moreover, the FDG dataset, which obtains a very good accuracy with AV45, does not obtain as good a result when combined with other datasets, which indicates that the biomarkers in the pair have a considerable influence on the accuracy obtained. From an algorithmic perspective, generally the algorithm that works best is Self Organizing Maps. Moreover, linear algorithms obtain better accuracies either when using the first component or all of them, depending on the pair of biomarkers used. Regarding the MRI dataset, the accuracies obtained are low, as all of the models’ accuracies are lower than 0.6. However, as aforementioned, non-linear models such as SOM performed better than linear models. It is important to note that, while these models obtained poor results regarding the accuracies, they have an extremely high potential to describe the clusters formed, as SOM’s obtained clusters with MRI biomakers resulted in four significantly different sociodemographic variables between them (with very low p-values, in the order of e−49 for the MMSE score). This result proves that the amount of significant variables in a model does not depend of the progression accuracy obtained, but rather of the biomarker used: in this case the MRI regions. Furthermore, the AV45 biomarker is an 48 average of all the cerebral regions, and while the former usually obtains very high accuracies, the latter seems to describe clusters better. Therefore using biomarkers that make up the average of other biomarkers will eventually omit information about its patients and poorly describe the clusters. Therefore with non-temporal models we can surmise that, first and foremost, non-linear models work better than linear algorithms, contrary to the computational perspective described above. Moreover, the AV45 biomarker seems to favor a better accuracy than other datasets. Finally, the combination of biomarkers when used in multidimensional datasets influences the Progression Accuracy as well as the significant variables obtained for that model. From a clinical perspective in temporal models, when using separated biomarkers, and taking into account polynomial regression, from a dataset perspective we can find better accuracies when using the AV45 dataset, as found in non-temporal models. However, the rest of the datasets obtain a very similar accuracy, especifically TAU and PTAU, which now obtain a very high accuracy. Regarding the algorithms employed, SOM obtained the best accuracies, specially when applied to AV45 dataset. Meanwhile, K-Means and Hierarchical clustering obtain similar results, due to how similarly they both function. Moreover, when considering the DTW models, from a dataset perspective, models that include AV45 no longer obtain as good an accuracy as with non-temporal models. Moreover, TAU and PTAU models improved their accuracies, reaching an accuracy higher than 0.60. Therefore, it seemed that temporality, specially algorithms that exploit temporality like DTW, favor better accuracy while also worsening it in datasets like AV45. From an algorithmic standpoint, both algorithms implementing DTW obtained similar results, although one overcomes the other depending on the dataset: Hierarchical clustering with DTW obtains better accuracies in AV45 and FDG datasets, meanwhile the DBSCAN variant obtains better results in PTAU and ABETA datasets, specially struggling in finding a suitable result in the TAU dataset. 49 As for pairs of biomarkers when using polynomial regression, regarding the datasets, the best accuracies are obtained from the pairs containing the AV45 biomarker, specially when it is paired with FDG. Models using other datasets have increased too, for example the pair TAU+PTAU. This pair now yields an accuracy closer to the other models, reducing the distance between them. An interpretation similar to the one we gave with non-temporal models can be made: certain combinations of biomarkers favor a higher accuracy. Moreover, temporality seems to increase the accuracy in datasets like TAU or PTAU. As for the algorithms, SOM models obtained the highest accuracy in AV45 datasets, specially in the pair AV45+FDG. While FDG on its own generally obtains low accuracies, when paired with other biomarkers, especifically AV45, the resulting accuracy is much higher. As for KMeans and Hierarchical clustering, they both obtained similar accuracies, but depending on the dataset one overcomes the other. Finally, DTW models combining biomarkers in pairs, from a dataset standpoint, worked best when using the pair AV45+PTAU. The majority of the scores obtained with DTW models in the case of pairs of biomarkers were close to 0.60. As for the algorithms used, both DTW+Hierarchical clustering DTW+DBSCAN obtained similar scores and overcame each other depending on the biomarkers. Regarding the MRI dataset, all models obtain an accuracy close to 0.6. However, when compared to the non-temporal models, it seems that these models perform better as a few go beyond 0.6. This might be explained by the fact that we are no longer using only AV45, which represents the average of all regions, but rather six complex biomarkers that do not necessarily follow the same direction and therefore, adding temporality to the model improves the accuracy. As for the algorithms used, the polynomial variant of K-Means seems to do better than its other polynomial counterparts, meanwhile Hierarchical clustering and DTW do better than DBSCAN combined with DTW. K-Means obtaining a better accuracy than Self Organizing Maps might be due to the possibility that due to the high temporality, the latter is not able to morph its grid of neurons to represent accurately the data, therefore obtaining a poor result. Finally, this model obtained three significant variables, and not 50 only is it a bigger amount than other models when used with their polynomial variants, but also the descriptive power of the MRI dataset returns very low p-values (MMSE, e−60). Therefore, temporal models seemed to work exceptionally well combining non-linear models with the AV45 biomarker. Moreover, increasing the temporality in the model increases the accuracies obtained in TAU and PTAU datasets, although it does not favor the AV45 biomarker. Lastly, as for the MRI dataset, while the accuracies obtained are low, it is more descriptive than other biomarkers. Finally, we have seen how SI scores and progression accuracies (PA) are not interrelated, since the SI score is ultimately based on outerand intra-cluster distance while the PA considers diagnosis transitions. The Alzheimer’s Disease continuum does not follow a linear progression for a patient to be placed in one of the three stages therefore the clusters obtained in a perfect PA setting will inevitably overlap eachother. Lastly, we evaluated the differences between clusters regarding the sociodemographic variables of the patients on the models that obtained the best progression accuracies. We observed that a significant difference in one of these variables between clusters is not necessarily linked to the Progression Accuracy obtained. For instance, the temporal model that obtained an accuracy of 0.778 when using SOM and the pair of biomarkers AV45 and FDG only had two significant variables: the APOE4 genotype and MMSE score. Meanwhile, in the non-temporal model that obtained an accuracy of 0.7083 using SOM and the AV45 dataset, there were a total of four significant variables: APOE4 genotype, MMSE score, the patients’ age at baseline visit, and the education years of the patient. Additionally, the pair AV45+PTAU obtained a total of three out of five significant variables. Therefore the significant difference between clusters regarding a sociodemographic variable could be linked to the biomarkers in question: AV45 -it being an average of the volume of six brain regionsis more descriptive of Dementia, and when combined with other biomarkers, said descriptive potential is lost. Moreover, from a clinical perspective and for the sake of interpretability, we can gather 51