very different care and treatment paths. Also the distinction
between glioma and other less common malignant primary lesions
such as lymphoma is relevant. Whereas neuroradiologists are
trained to differentiate these different types of lesions, the large
variation in appearance of tumors induces uncertainty in the differ-
ential diagnosis. Machine learning has been shown to be able to
distinguish glioma from metastasis [20] and lymphoma [86] based
on quantitative analysis of brain MRI, and may thus be used as a
"second" reader supporting the radiologists. Once a diagnosis of
cancer is established, a second task in differential diagnosis is the
further subtyping of the lesion. While glioma is one of the deadliest
forms of cancer [97], there exist large differences in survival and
treatment response between patients. These differences can be
attributed to the glioma's genetic and histological features, in
particular the isocitrate dehydrogenase (IDH) mutation status,
the 1p19q co-deletion status, MGMT promoter methylation sta-
tus, and the tumor grade [28, 31, 38]. These insights have led to
classification guidelines by the World Health Organization (WHO)
[77]. In current clinical practice, these genetic and histological
features are determined from tumor tissue after resection. How-
ever, there has been an increasing interest in complementary non-
invasive alternatives that can provide the genetic and histological
information before resection [10, 152]. Also here, neuroradiolo-
gists can be trained to visually distinguish the subtypes based on
MRI [26, 128], but uncertainty often remains and the inherent
subjectivity associated with visual inspection of subtle differences in
appearance, by radiologists with varying levels of expertise, is unde-
sirable. A large body of research has therefore focused on develop-
ment of machine learning approaches to support MRI-based
determination of genetic and histological features of glioma
[41, 65, 122, 127].

The third diagnostic task we address is **decision making for
 treatment**. This is relevant when multiple therapeutic options are
available, such as for patients with stroke. Multiple treatment
options for stroke exist such as thrombolytic medication and endo-
vascular clot retrieval (mechanical thrombectomy). Since depend-
ing on the situation different treatments or their combination may
be optimal, and since the costs per patient are rising, there is a real
and urgent need for computer-aided diagnosis techniques to aid in
the streamlined care of patients and individualized treatment deci-
sions [56]. To enable early treatment of acute stroke, early and
reliable diagnosis is required, which heavily relies on imaging. The
vast majority of strokes are of ischemic origin, caused by a blood
clot occluding an artery resulting in oxygen deprivation of the brain
tissue supplied by this artery. Typical causes are large vessel occlu-
sion with or without thrombus dislodgement (e.g., carotid steno-
sis) or a cardiac cause resulting in embolies (e.g., atrial fibrillation).
The less common subtype is hemorrhagic stroke, which has
substantially different etiology and is often caused by hypertension. Without early treatment of stroke, prognosis is poor. Each minute without treatment leads to loss of an estimated 1.8 million neurons [64]. Patients who enter the hospital with acute stroke symptoms often immediately undergo CT (or MR) scanning, even before detailed clinical evaluation of the patient [64]. Imaging here has three roles in decision making for treatment: (1) rule out hemorrhagic stroke, (2) establish the exact cause and the extent of ischemic stroke, and (3) determine a patient's suitability for (intrar arterial) treatment [33, 80]. Applications of machine learning for treatment decisions in stroke include identification of hemorrhage and early identification of imaging findings to determine the cause and extent of stroke and estimation of the time of onset. Time of onset is relevant since most current treatments aim for rapid reperfusion of ischemic tissue, either using intravenous thrombolytic medications or using endovascular techniques to mechanically remove the obstruction to blood flow, which should be performed within 4.5 h of stroke onset [56].

**1.2 Prediction**

Prediction or prognosis aims to understand the future “condition” of the patient, which can then be used for considering and planning therapeutic or lifestyle interventions proactively [22] that may slow the disease process or may reduce the risk for event recurrence. In addition, it can be used for effective patient management, for managing the expectations of patients and their caregivers [82], as well as for patient selection in clinical trials [35, 102]. We distinguish two main categories of prediction targets here: the natural disease course and patient outcomes after treatment.

**Box 2: Prediction**

Categories of prediction targets for which computer-aided models have or could have added value, with example brain disorders for which this is relevant as discussed in this chapter:

* **Natural disease course** Dementia and MS

* **Patient outcomes after treatment** MS, brain cancer, and stroke

**Predicting the natural disease course**, i.e., the future progression of the disease and its symptoms in a subject, is clinically relevant as it can aid care planning and managing the expectations of patients and caregivers about their future quality of life, physical health, and dependency [81]. Additionally, in disorders where treatment options are limited, it would improve future clinical trials
for new medication through identification of patients most likely to benefit from an effective treatment, i.e., those at early stages of disease who are likely to progress over the short-to-medium term (1-5 years) [83].

In dementia, prediction is challenging because of disease heterogeneity, i.e., differences in symptoms between patients along the disease process. For example, a patient can have either typical AD with memory problems or atypical AD with either language problems [43] or behavioral problems [99]. Moreover, patients with comparable brain atrophy may decline differently as the disease progresses, reflecting cognitive resilience due to genetic or lifestyle factors that may help to compensate for the level of atrophy [147]. Lastly, a similar symptom in two patients could be resulting from different diseases altogether. For example, a patient with mild cognitive impairment (MCI) either may have early stage dementia or may have cognitive impairment due to a different cause such as older age, injury, or a virus such as SARS-CoV-2 [44]. The latter, i.e., cognitive impairment due to non-degenerative disorders, is almost twice as prevalent as cognitive impairment due to dementia [106]. Here it is of interest to predict how the symptoms will develop over time for an individual; while patients without dementia may remain stable over time or even improve, the symptoms of patients with dementia typically worsen with time. Hence, the applications of machine learning in predicting the future course of dementia include the following: (i) predicting if a patient with cognitive impairment will develop dementia [138], (ii) predicting when the patient will reach a clinical dementia stage (i.e., duration of the prodromal disease phase) [83], and (iii) predicting the progression of biomarkers such as cognition and MRI measurements [61, 66].

In MS, especially in the early stages when patients experience clinical symptoms sporadically, prediction of the future disease course is highly relevant for care planning and expectation management. The early stage of MS, known as the relapsing-remitting phase, is characterized by sporadic inflammatory attacks on the neuronal protective coating called myelin. Over time, the recovery from these relapses becomes incomplete, resulting in permanent and progressive disability [144]. Because of this progressive nature and the variation between individuals, predicting the number of relapses and the time to permanent disability in a specific patient is highly important for care and treatment planning [18].

Next to prediction of the natural disease course, prediction of the future disease course after an intervention, i.e., **outcome prediction after treatment**, could be instrumental for planning of treatment and subsequent follow-up. This is of particular interest in MS where multiple treatment options are available. There are
currently 21 FDA-approved disease-modifying drugs available [27] that inhibit different aspects of pathological progression of MS mainly by immune modulation and sometimes through neuroprotection or remyelination. It is hence clinically highly relevant to choose the treatment option that an individual patient is expected to have most benefit from and to determine whether risks of second-line treatment are justified [131]. The same holds for stroke in the post-acute phase, where prediction of patient outcomes after treatment based on imaging may play a role for choosing between available treatments such as medication and rehabilitation therapy [80]. Here the focus is on the long term: reducing risk of recurrence and optimization of functioning. Computer-aided approaches can thus help in personalizing the treatment for a patient.

Predicting the outcomes after treatment is also of major interest for patients with brain tumors, and specifically in case of glioma where treatment response varies greatly across patients. Treatment usually consists of surgical resection followed by radiotherapy and/or chemotherapy. Almost invariably tumor recurrence or regrowth occurs; however, the question is when. In case of high-grade glioma (i.e., glioblastoma), tumor regrowth typically happens within a few months. In low-grade glioma, progression after treatment is often slower, and it may take years before any significant regrowth is detected; at some point, however, malignant transformation (to a high-grade glioma) may occur, leading to accelerated regrowth. As discussed in Subheading 1.1, computer-aided diagnosis methods can be used to identify the current tumor's genetic and histological profile, which already provides important prognostic information. Beyond this example of computer-aided differential diagnosis, machine learning methods can contribute in different ways by directly predicting outcomes after treatment [65, 127]. First, machine learning methods have shown promise to aid the differentiation between tumor progression and treatment-related abnormalities (pseudoprogression, radiation necrosis) [54, 65, 73, 127, 143]. Second, machine learning can be used to predict local relapse locations after radiotherapy, thus highlighting locations that should be targeted with a higher radiation dose, leading to personalized radiotherapy planning [114]. Third, a machine learning approach can predict local response to stereotactic radiosurgery of brain metastases, based on radiomics analysis of pretreatment MRI, where the outcome of interest (local tumor progression) was defined in terms of maximum axial diameter growth as measured on a follow-up scan [94]. Fourth, machine learning methods have been proposed for prediction of progression-free and overall survival, which aids care planning and managing the expectations of patients about their future [60, 108, 122, 127].
## 2 Method Evaluation

### 2.1 State-of-the-Art

**Methodology for Diagnosis and Prediction**

For **early diagnosis in dementia**, a large body of research has been published on classification of subjects into AD, mild cognitive impairment (MCI), and normal aging [36, 113, 145]. Overall, classification methods show high performance for classification of AD patients and cognitively normal controls with an area under the receiver operating characteristic curve (AUC) of 85–98%. Reported performances are somewhat lower for early diagnosis in patients with MCI, i.e., prediction of imminent conversion to AD (AUC: 62–82%). Dementia classification is usually based on clinical diagnosis as a reference standard for training and validation [87], but biological diagnosis based on assessment of amyloid pathology with PET imaging or CSF has been increasingly used over the last years [53, 129]. Structural T1-weighted (T1w) MRI to quantify neuronal loss is the most commonly used biomarker, whereas the support vector machine (SVM) is the most commonly used classifier. For T1w, both voxel-based maps (e.g., voxel-based morphometry maps quantifying local gray matter density [62]) and region-based features [78] have been frequently used. While using only region-based volumes may limit performance, combining those with regional shape and texture has been shown to perform competitively with using voxel-wise maps [13, 15, 24]. Using multimodal imaging such as FDG-PET or DTI in addition to structural MRI may have added value over structural MRI only, but limited data is available [76, 150]. Following the trends and successes in medical image analysis and machine learning, neural network classifiers –convolutional neural networks (CNN) in particular– have increasingly been used since a few years [16, 145], but have not been shown to significantly outperform conventional classifiers. In addition, data-driven disease progression models are being developed [101], which do not rely on a priori defined labels but instead derive disease progression in a data-driven way.

Regarding **differential diagnosis in dementia**, studies focus mostly on discriminating AD from other types of dementia. Differential diagnosis based on CSF and PET biomarkers of AD pathology has shown good performance for distinguishing AD from FTLD with sensitivities of 0.83 (p-tau/amyloid-β ratio from CSF) and 0.87 (amyloid PET) [48, 111, 117]. In addition, machine learning approaches have been published based on either structural or multimodal MRI as region-wise or voxel-wise imaging features and generally SVM as a classifier, similar to those used for early diagnosis in dementia. These methods focused mostly on differential diagnosis of AD and FTLD and reported performances in the range of AUC = 0.75 – 0.85 [12, 14, 92, 110]. A few studies addressed differential diagnosis of AD and vascular
dementia (VaD) [151] or multiclass differential diagnosis (5+ classes including AD, FTLD, VaD, dementia with Lewy bodies, and subjective cognitive decline) [93, 133].

For **differential diagnosis in brain cancer**, numerous MRI-based machine learning approaches have been presented. These developments have partly been facilitated by the availability of several valuable public datasets; see, for example, the overviews in [89, 135]. Most literature is dedicated to glioma characterization, which is therefore discussed in more detail here. Studies vary in the choice of input MRI sequences (T1w pre- and post-contrast, FLAIR, T2w, diffusion-weighted imaging, perfusion-weighted imaging, MR spectroscopy, APT CEST), the machine learning methodology (ranging from conventional radiomics approaches with hand-crafted features derived from manual tumor segmentations to deep learning approaches that automatically segment the tumor), the classification target(s) (e.g., grade, IDH, 1p19q, and/or MGMT status), the selection of glioma subtypes on which the method is validated (e.g., only low-grade glioma, only high-grade glioma, or both), and the extent of validation performed (single train-test split, repeated cross-validation, internal versus external validation). A systematic review on the use of machine learning in neuro-oncology found four articles on glioma grading, and four articles on identifying genetic/molecular characteristics of glioma based on MRI [122]. Among those, only one study used convolutional neural networks as a machine learning tool—to predict 1p19q status in low-grade glioma [1]. A more recent systematic review identified 27 studies on glioma grading of which 6 used deep learning, and 48 studies on MRI-based estimation of genetic/molecular characteristics of which 8 used deep learning [19]. Another recent review dedicated to machine learning approaches for MRI-based glioma characterization found 12 studies on glioma grading of which 2 used deep learning, and 43 studies on molecular characterization out of which 10 used deep learning [41]. These numbers indicate a trend toward deep learning approaches as we see in the entire field, but with conventional machine learning approaches with pre-defined radiomics features still being used frequently. Regarding the performance, two recent systematic reviews performed a meta-analysis of studies on molecular characterization of glioma. Jian et al. [55] found a pooled sensitivity/specificity/AUC in the validation set of 0.85/0.83/0.90 for IDH status prediction (12 studies), and 0.70/0.72/0.75 for 1p19q status prediction (5 studies). For MGMT, sensitivities and specificities ranging from 0.70 to 0.88 were found in 3 studies reporting validation performance, not allowing a meta-analysis. Van Kempen et al. [136] reported a pooled AUC of 0.91 for IDH status prediction (7 studies), 0.75 for 1p19q status prediction (3 studies), and 0.87 for MGMT promoter status prediction (3 studies). Thus, while the studies applied somewhat different
criteria for inclusion in the meta-analysis and used different statisti-
cal analysis methods, they obtained similar performance estimates.
Whereas both meta-analyses suggest promising accuracy for
MRI-based MGMT promoter status prediction based on the results
reported in literature, a comprehensive evaluation of deep learning
approaches for MGMT promoter status prediction on the
BraTS2021 dataset [6] yielded disappointing results, with AUCs
ranging from 0.5 to 0.6 [120]. Also, the winning method of the
BraTS2021 challenge achieved an AUC of 0.62 [8], suggesting
that MGMT promoter status prediction from MRI is a very difficult
task. Both systematic reviews [55, 136] also pointed out the low
proportion of studies with external validation (10 out of 44 in [55]
and 12 out of 60 in [136]). Figure 2, recreated based on [55],
shows a number of other insightful statistics on the methodologies
found in literature. Finally, both reviews also identified machine
learning methods aimed at predicting other, less frequently consid-
ered molecular targets, including ATRX, TERT, EGFR, P53, and
PTEN, indicating the broad range of possible future research direc-
tions in this area.

<figure><img src="image_192.png" /><figcaption>**Fig. 2** Summary of tumor segmentation methods (a), types of imaging features (b), means of internal validation (c), and external validation (d) used by studies (n = 44) investigating machine learning models for predicting genetic subtypes of glioma. VASARI, Visually Accessible Rembrandt Imaging. Recreated from [55]. Permission to reuse was kindly granted by the publishers</figcaption></figure>
Beyond glioma characterization, other differential diagnosis problems in brain cancer are differentiation between glioma and lymphoma, between glioblastoma and metastasis, between different types of meningioma, and between glioma, meningioma, and pituitary tumors [19, 65, 122, 127, 149], with promising performances reported (AUC/accuracies around 90%). Of note, a recent study pointed out an important potential source of bias (the “Clever Hans effect”) in studies focused on differentiation between glioma, meningioma, and pituitary tumors, due to implicit radiologist input in the selection of the 2D slices in a commonly used benchmark dataset [142].

**For decision making in stroke**, different targets for machine learning based on imaging data have been identified, mostly focused at determining the cause and extent of stroke and to a lesser extent, on informing treatment decisions [56]. Regarding cause and extent of acute stroke, automatic lesion detection and identification of tissue-at-risk include the most important elements. These remain challenging as there is a lot of variation in lesion shape and location depending on time-from-symptom onset, vessel occlusion site, and collateral status [70]. Machine learning methods for segmentation and detection are increasingly successful (see Chapter 13). The step toward computer-aided diagnosis in stroke is also being taken using, for example, the CE-marked eASPECTS score [49], which is a machine learning-based assessment of the Alberta Stroke Program Early Computed Tomography Score (ASPECTS). This system for scoring acute ischemic damage to the brain has shown to be a simple, reliable, and strong predictor of functional outcome after stroke. Regarding treatment decisions, machine learning is used in several studies to determine whether a patient qualifies for a specific stroke treatment. For thrombolytic treatment, this qualification depends on time elapsed after symptom onset and treatment should be performed within 4.5 h. For this application, methods are developed that provide a binary estimation of stroke onset time (i.e., more or less than 4.5 h) based on either DWI and FLAIR [71] or perfusion-weighted imaging (CT or MR) [50]. Both approaches used a radiomics-like approach of feature extraction (e.g., intensity/gradient/texture based or using an autoencoder) followed by a machine learning classifier (support vector machine, random forest, and logistic regression). These machine learning methods had greater sensitivity than human readers using the standard procedure of DWI-FLAIR mismatch and comparable specificity. In addition, thrombolysis may cause the rare complication of symptomatic intracranial hemorrhage. Several machine learning methods have been developed to predict the risk of this complication achieving promising predictive performance, for example, using a support vector machine classifiers based on CT data (AUC = 0.74) [9].
For prediction of the future course of subjects at-risk of developing dementia, there are three frequently used approaches for defining the prediction problem at hand. First, predicting whether the patient will develop dementia. In specific diseases, measurement of proteins causing underlying pathology has shown to be very promising to identify patients in a prodromal disease state. Here, prediction is performed either using univariate analysis or using logistic regression with few variables as input. Blood-based P-Tau biomarker can predict incident AD within 4 years with an AUC of 0.78–0.83 [103], and CSF biomarkers and PET images of amyloid β and Tau can predict clinical progression of subjects in their prodromal AD state with an AUC of 0.94–0.96 [46]. Alternatively, in the absence of pathology-specific markers, MRI and cognitive markers of a patient together with machine learning approaches have been used to predict AD with an AUC of 0.70–0.83 [16, 23, 75, 141]. For a systematic review of the different machine learning methods developed for the purpose of predicting AD, see [5]. Support vector machines (SVM) and logistic regressions are the most used algorithms in the last decade (Fig. 3). In FTD, where it is currently not possible to measure the pathological proteins in body fluids, prediction based on a combination of biomarkers that are nonspecific to the underlying pathology is promising. This is demonstrated, for example, by van der Ende et al. [134], who predicted disease onset in familial FTD based on unspecific blood-based and CSF-based biomarkers using a disease progression model and identified presymptomatic subjects that developed dementia in the near future with an AUC of 0.85.

<figure><img src="image_193.png" /><figcaption>**Fig. 3** Evolution with time of the use of various algorithms for predicting the progression of mild cognitive impairment. SVM with unknown kernel are simply noted as “SVM.” OPLS, orthogonal partial least square; SVM, support vector machine. Reproduced from [5]. Permission to reuse was kindly granted by the publishers</figcaption></figure>
Second, predicting the time for conversion to dementia. While the previous problem predicts a dichotomous output variable, here it involves predicting a continuous variable of time to dementia. Bilgel et al. [11] predicted time to AD dementia with a mean error of <1.5 years. In the TADPOLE challenge, machine learning approaches to predict time for conversion to AD dementia of 33 participating teams have been assessed quantitatively [83]. Ansart et al. [5] strongly favor predicting the exact time for conversion to dementia and argue against predicting converters within a given time interval (e.g., within 3 years), because of the precision in the predictions. While this is indeed methodologically more elegant, the implications for clinical use and perception of patients regarding prediction precision and the inherent uncertainty remain to be established.

Third, prediction of disease markers could help to obtain insight into the clinical prognosis in an individual. Important disease markers are, for example, measures of global cognition (mini-mental state examination [MMSE] or Alzheimer's disease assessment scale [ADAS] scores), or salient imaging markers (volume of the brain ventricles or longitudinal Tau protein accumulation). ADAS scores could not be reliably predicted by any participating team in the TADPOLE challenge [83], but a recent disease progression model called *AD course map* [66] could predict ADAS scores (which is scored from 0 to 150) after 3 years with a mean absolute error of 7.6 points. *AD course map* could also predict MMSE scores (which is scored from 0 to 30) after 3 years with a mean absolute error of 3.2 points. While these predictions used MRI as input, Tau PET was recently shown to be more predictive of future MMSE scores using linear mixed models [100]. However, a thorough validation of this Tau PET-based prediction is lacking. Predicting salient imaging markers such as volume of the ventricles [83], volume of the hippocampus [66], or longitudinal Tau accumulation [72] is a promising topic. Identifying the most clinically useful target to be predicted, the imaging modality that has the best cost-benefit ratio for prognosis of a patient, and the method that best predicts it are all important questions that still need answers in the future.

Most **prediction methods in MS** focus on predicting either physical disability, cognitive impairment, or treatment response in imaging data of an individual patient [57]. Physical disability as measured by expanded disability status scale (EDSS, range 0–10) has been the most commonly used predictor variable as recently used in [104, 118]. An ensemble of classifiers consisting of convolutional neural networks, random forests, and manifold learning was reported to predict EDSS with a mean square error of 3.0 [118]. Cognitive impairment has been predicted either as a global measure of cognition or as specific cognitive domains such as attention or working memory [32]. For predicting treatment
response in MS, Signori et al. [124] used meta-analysis to identify
subject characteristics that have higher treatment effects. In [34],
the authors used an unsupervised disease progression model to
identify subtypes of progression pathways in MS and found in
post hoc analysis that one of the subtypes predicted better treat-
ment effects. Current challenges in this evolving field of predicting
treatment response in MS and future directions have been summar-
ized in [37].

For the **prediction of patient outcomes after treatment of brain cancer**, most machine learning studies have focused on MRI-based prediction of progression-free survival or overall survival, which will therefore be discussed in more detail here. A systematic review by Sarkiss et al. identified nine articles on survival prediction in glioma, and two on survival prediction for patients after stereotactic radiosurgery of brain metastases [122]. A more recent systematic review by Buchlak et al. identified 17 studies on survival prediction with performance estimates (AUC or accuracy) mostly in the range 0.7–0.8 [19]. Among those, only one study reported results of external validation, predicting overall survival of patients with low-grade glioma, and obtained an AUC of 0.71 with a model combining radiomics with non-imaging features including age, resection extent, grade, and IDH status [21]. Random (survival) forests and support vector machines were most often used methods. One study used a CNN as a pre-trained feature extractor [69]. Other recent approaches using CNNs to extract features that are subsequently combined with other factors into a final prognostic model include [45, 51, 96]. The 2017/2018 editions of the well-known BraTS challenges also included a task on overall survival prediction, with best teams obtaining accuracies around 0.6 in a three-class classification setting distinguishing short-, mid-, and long-survivors, [7]. Here, it was also pointed out that conventional machine learning methods outperformed deep learning methods, likely due to the limited size of available datasets for training.

Beyond MRI-based methods, methods using histopathology
images and/or genomics data as input for the machine learning
model are also considered in the literature on outcome prediction
for glioma patients. In one of the pioneering studies on digital
pathology images of glioma, better prognostication was obtained
with deep learning when pathology images were combined with
genetic markers (IDH, 1p19q) [91]. Preliminary work on so-called
radiopathomics in glioma is also available, supporting the notion
that combining histology and radiology features improves prognos-
tication (overall survival prediction) in glioma patients [115, 116].

## 2.2 Benchmarks and Challenges

For 15 years, grand challenges have been organized in the biomedical image analysis research field. These are international benchmarks in competition form that have the goal of objectively comparing algorithms for a specific task on the same clinically
representative data using the same evaluation protocol. In such challenges, the organizers supply reference data and evaluation measures on which researchers can evaluate their algorithms. Over the past years, the number and the impact of such grand challenges have increased [79]. Also in the field of computer-aided diagnosis and prediction, such grand challenges have been organized. For example, in the dementia field, four challenges have been organized focusing on early diagnosis [3, 15, 121] and predicting the natural disease course [3, 83, 121]. In general, algorithms winning the challenges performed rigorous data pre-processing and combined a wide range of input features [17]. In the field of brain cancer, the series of BraTS challenges has had a major impact [6, 7]. These benchmarks are instrumental to gaining insight into successful approaches and their potential for use in clinical practice and clinical trials.

## 2.3 Open-Source Software

Open-source machine learning software such as scikit-learn<fnref n="1" /> and MONAI<fnref n="2" /> have been fundamental to the development of this field of research. More specifically for computer-aided diagnosis and prediction in brain diseases, dedicated platforms are available such as Clinica [119], NeuroPredict [109], and PRoNTo [123]. We also see a trend of researchers publishing their scripts and trained classifiers with their publications in order to promote reproducibility.

## 3 Clinical Impact

There are multiple ways in which computer-aided diagnosis and prediction models can make an impact on clinical practice. Key areas of impact are in decision making for treatment and care, replacing invasive diagnostic procedures and patient selection for clinical trials. Here we will discuss to what extent these clinical needs are addressed by current methods.

First, the most direct impact is on decision making for treatment and care. This not only affects clinical care and treatment planning in patients with, for example, dementia, stroke, MS, or brain cancer but also is important for managing the expectations of patients and their caregivers. Although high performances are achieved for some related tasks such as dementia classification, validation of those results on external datasets and clinical cohorts is still very limited as well as knowledge on the robustness of the methods. For other applications, there is still room for performance improvement, and key factors in achieving that would be the combination of multimodal input and the availability of more well-

<footnote n="1">¹ https://scikit-learn.org/.</footnote>

<footnote n="2">² https://monai.io/.</footnote>
maintained and large-scale datasets for training and evaluation. In general, there is room for improvement in how well real clinical questions are addressed by current methodology. Second, machine learning models can have an impact by replacing invasive diagnostic procedures. This is especially relevant in brain cancer, where machine learning techniques based on imaging data are developed to predict, for example, genetic mutation status or tumor grade, thereby avoiding or reducing the need for biopsies [10, 152]. As a motivating example, MRI-based prediction of MGMT methylation status could be beneficial to guide treatment decisions. This is supported by findings from a population-based study assessing survival in 131 patients with radiological diagnosis of glioblastoma who did not undergo surgery and thus lacked (histological or molecular) tissue-based verification of the diagnosis [146]. While patients without treatment had extremely poor prognosis with median survival of 3.6 months, those who received upfront temozolomide treatment did significantly better (with median survival of 6.8 months). Since the response to temozolomide is known to be highly dependent on the MGMT status, MRI-based prediction of MGMT status could give insight into which patients would benefit from treatment avoiding the need for biopsies in patients to frail for tumor biopsy. Third, patient selection for clinical trials is relevant in diseases where no to limited options for treatment exist, such as dementia, or diseases where existing treatments are suboptimal for some patients, such as MS. This can boost the power of trials by enrolling, for example, individuals who are more likely to progress based on prediction models. Several pilot studies demonstrated the added value of machine learning models to select a subgroup of participants to increase sensitivity to the treatment using phase III trial data (e.g., for Alzheimer's disease treatment using donepezil or semagacestat) [35, 102]. This will ultimately reduce the size, duration, and cost of clinical trials.

The number of published methods is not evenly distributed over tasks. While many methods have been published on, for example, the classification of Alzheimer's disease patients versus controls, much fewer publications exist on differential diagnosis in dementia. In addition, there seems to be a mismatch in some applications between published classification methods and clinical needs, e.g., the clinically relevant problem of early diagnosis does not directly translate to the frequently studied classification task of established Alzheimer's disease versus healthy controls, but would instead require separation of early disease stage Alzheimer's disease patients from those that have cognitive complaints but not dementia.

Several approved machine learning products to assist diagnosis and prediction are making their way into clinical practice, in particular in the imaging domain. Van Leeuwen et al. evaluated 100 commercially available products for AI in radiology, of which 38 are related to brain diseases [137]. These include mostly segmentation,
quantification, and normative comparison for neurodegenerative
diseases and detection of lesions for stroke and oncology. Most
methods generate a sample radiologist report which can be
inspected and modified. In dementia, for example, 17 reporting
tools that use automated brain MRI segmentation software and
normative reference data for single-subject comparison are regu-
latory approved for use in the memory clinic [105].

One of these is Quantib ND (Quantib BV, Rotterdam, the Netherlands),<fnref n="3" /> which is an approved commercial software that performs automatic segmentation into 20 brain regions as well as normative volumetry reference curves based on data of 5000 subjects from a population-based cohort. While Quantib ND and most other available tools use machine learning for brain segmentation, their output is not a diagnostic label produced by a machine learning algorithm. Another approved software, cDSI (Combinostics, Tampere, Finland),<fnref n="4" /> does output diagnostic labels as confidence scores in addition to segmentation and normative volumetry based on MRI. It uses univariate machine learning to normalize individual biomarkers of different modalities based on reference values of patient and control groups, color-codes these biomarkers to improve visualization of large-data datasets, and combines confidence scores based on individual biomarkers into one score [84, 85]. While cDSI is a machine learning tool for computer-aided diagnosis and prognosis, it does not exploit the power of machine learning to detect complex patterns in high-dimensional data but rather focuses on visualization and interpretability. Diagnosis and prediction algorithms that map high-dimensional input, i.e., images and other clinical data, to an outcome measure using machine learning have not yet made their way into clinical practice.

4 Roadmap for Clinical Translation

There are numerous challenges for clinical translation of computer-
aided diagnosis and prediction methods. Some key items that
should be on the roadmap for translation relate to large and stan-
dardized datasets, to technical and clinical validation, to interpret-
ability by clinicians and patients, and to practical issues related to
implementation. In this section, we will discuss these requirements
and related developments and initiatives.

The first requirement for translation is **large and standardized datasets**. For a few brain disorders, one or multiple large datasets (i.e., up to 2500 participants) are available to train machine learning algorithms for diagnosis and prediction tasks, facilitated

<footnote n="3">³ quantib.com/solutions/quantib-nd.</footnote>

<footnote n="4">⁴ combinostics.com/cdsi.</footnote>
by large multicenter initiatives such as the Alzheimer's Disease Neuroimaging Initiative (ADNI) or the Parkinson's Progression Markers Initiative (PPMI). For validation in other cohorts and for development of algorithms in other diseases, there is only limited data available and a need for more (well-annotated) data exists. In particular, there is a need for validation data that reflect the reality of clinical routine with no to limited data harmonization and large variation in imaging protocols and data quality. Setting up such large-scale datasets is complex due to various reasons including obstacles in inter-institutional data sharing and a lack of funding for collection, curation, and labeling of data. To overcome these challenges, developments in research software and infrastructure may provide a solution by sharing easily reproducible algorithms rather than the data. Wrapping an algorithm in a container (e.g., Docker,<fnref n="5" /> Singularity [67]) and applying the algorithms locally to the data (at one site or multiple sites in a federated approach) enables method validation on large sets of data within the confines of the local institute's firewalls. Such an approach could be also used for enabling training on larger datasets (i.e., federated learning [125]). Standardization of the data is important for eventual translation as it enables researchers to combine multiple datasets for development and validation of machine learning methods for diagnosis and prediction. Such standardization entails both data collection (e.g., diagnostic criteria, protocols for image acquisition, and clinical tests) and data organization (e.g., through open-source standards and platforms for data storage such as the Brain Imaging Data Structure (BIDS) and the Extensible Imaging Archive Toolkit (XNAT)).

Second, **technical and clinical validation** is a key focus area on the roadmap for translation. In the field of radiology, the quantitative neuroradiology initiative (QNI) framework has been developed as a model framework for translation defining the technical and clinical validation necessary to embed automated software into the clinical workflow [39]. Based on this framework, [105] reviewed the published evidence regarding commercial automated volumetric MRI tools for dementia diagnosis. For the 17 products identified, 11 companies have published some form of technical validation on their methods, but only 4 have published clinical validation in a dementia population. They concluded that there is a significant evidence gap in the literature regarding clinical validation and in-use evaluation. Whereas this review only addressed image volumetry in dementia, these findings likely extend to other brain diseases, applications, and modalities. Hence, there is a need for both retrospective and prospective studies validating algorithms in a clinical setting. In addition, performance metrics

<footnote n="5">⁵ www.docker.com.</footnote>
used in validation studies should aim to capture real clinical applicability and address different aspects of the reliability of an algorithm, including accuracy, uncertainty estimation, reproducibility, and generalizability to other data. Standards for validation and reporting are provided by guidelines such as STARD-AI [130] and TRIPOD-AI.<fnref n="6" />

A third key item for clinical translation is **interpretability** by end users such as clinicians and patients. As clinicians have responsibility for the decisions related to care and treatment, they should have trust in a computer-aided diagnosis or prediction system and understand its outputs to an extent that they can rely on them for decision making and explanation to a patient. Performance metrics should aim to capture real clinical applicability and be understandable to intended users [59]. High validation performance is important for building trust in methods, but not sufficient by itself, since performance may reduce in individual cases because of unaccounted inter-individual such as comorbidities or population differences such as MRI scan protocol. Therefore, apart from model accuracy, relevant questions for interpretation are, for example, Is the model suitable for the data of this patient? What features contribute to the machine learning decision for this patient? How certain is the decision for this patient and can the algorithm know when it is uncertain about an individual's decision? Such questions are important and methods should be designed and implemented in a way that facilitates answers to such questions. This could be obtained by using interpretability methods on top of “black box” machine learning models or directly by using interpretable models. For the first category, many methods have been developed based on model weight visualization, feature map visualization, backpropagation methods, or perturbation of inputs (see also Chapter 22). For interpretable models, an example in the field of computer-aided diagnosis and prognosis is disease progression models [140, 148]. These data-driven models are designed specifically for neurodegenerative diseases and explain their decisions based on their estimate of the natural progression of the disease in the cohort (see also Chapter 17).

As a final key item, we will discuss **implementation feasibility**. For machine learning models to be actually used in practice, it is essential that models and reporting are integrated into the clinical workflow and that the sending and processing of clinical data and receiving results is fully automated. Current commercial products for automatic volumetry in dementia all reported to have implemented an integration with radiology systems and the clinical workflow. While validation of the workflows is limited [105], this does support the feasibility for machine learning in clinical practice.

<footnote n="6">⁶ osf.io/zyacb.</footnote>
While these products integrate with the radiological workflow, a key challenge for the clinical translation of algorithms that use non-imaging clinical data (such as cognitive scores) as input is to also integrate with the clinical workflow of multidisciplinary diagnosis.

# 5 Final Summary and Conclusion

Computer-aided diagnosis and prediction of brain disorders is an important research area, with a wide variety of applications. While typically for these applications generic machine learning methods are used, domain knowledge of these brain disorders is crucial for selecting novel clinically relevant applications as well as for making domain-specific methodological improvements. Regarding diagnosis, clinical challenges are in early diagnosis of dementia and MS, differential diagnosis of dementia and brain cancer, and decision making for treatment in stroke. Regarding prediction, challenges are in the prediction of the natural disease course in dementia and MS, and the prediction of patient outcomes after treatment in stroke, brain cancer, and MS. Even though the disorders on which we focused are important avenues for impact, computer-aided diagnosis and prognosis would also be extremely useful in other disorders such as movement disorders for predicting response to treatment and side effects, epilepsy for predicting response to epilepsy surgery, and psychiatric disorders where diagnosis can be particularly difficult.

Key areas of impact are in (1) decision making for treatment and care in patients with dementia, stroke, MS, or brain cancer, (2) replacing invasive diagnostic procedures in brain cancer, and (3) patient selection for clinical trials in dementia and MS. While the first AI methods are making their way to clinical practice, diagnosis and prediction algorithms that map high-dimensional input, i.e., images and other clinical data, to an outcome measure using machine learning are not yet clinically available. To enable translation, major items on the roadmap relate to the availability of large and standardized datasets and technical and clinical validation of the developed machine learning methods. In addition, other important aspects are interpretability of the results by clinicians and patients, optimization of the diagnostic or treatment workflow in the clinic, and other practical issues related to implementation.

With this chapter, we aimed to provide a comprehensive overview, bringing together the clinical context of representative use cases of diagnosis and prediction in brain disorders and their state-of-the-art computer-aided methods. Future research should focus on bridging the identified gaps between clinical needs and the solutions brought by machine learning, to further improve decision making, treatment, and care in brain diseases.
# 6 Conflict of Interest

Quantib BV is a spin-off company of Erasmus MC. W.J.N. is a cofounder, part-time Chief Scientific Officer, and stockholder of Quantib BV. S.R.V, D.B., M.S., S.K., and E.E.B. are affiliated to Erasmus MC but have no personal relationships with or financial interest in Quantib BV. F.B. is a consultant to Combinostics.

# Acknowledgements

V. Venkatraghavan is supported by JPND-funded E-DADS project (ZonMW project #733051106). W.J. Niessen and E.E. Bron are supported by Medical Delta Diagnostics 3.0: Dementia and Stroke. E.E. Bron acknowledges support from the Netherlands CardioVascular Research Initiative (Heart-Brain Connection: CVON2012-06, CVON2018-28).

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**Chapter 16**

**Subtyping Brain Diseases from Imaging Data**

Junhao Wen, Erdem Varol, Zhijian Yang, Gyujoon Hwang,
Dominique Dwyer, Anahita Fathi Kazerooni, Paris Alexandros Lalousis,
and Christos Davatzikos

**Abstract**

The imaging community has increasingly adopted machine learning (ML) methods to provide individua-
lized imaging signatures related to disease diagnosis, prognosis, and response to treatment. Clinical
neuroscience and cancer imaging have been two areas in which ML has offered particular promise.
However, many neurologic and neuropsychiatric diseases, as well as cancer, are often heterogeneous in
terms of their clinical manifestations, neuroanatomical patterns, or genetic underpinnings. Therefore, in
such cases, seeking a single disease signature might be ineffectual in delivering individualized precision
diagnostics. The current chapter focuses on ML methods, especially semi-supervised clustering, that seek
disease subtypes using imaging data. Work from Alzheimer's disease and its prodromal stages, psychosis,
depression, autism, and brain cancer are discussed. Our goal is to provide the readers with a broad overview
in terms of methodology and clinical applications.

**Key words** Neuroimaging, Machine learning, Semi-supervised clustering, Heterogeneity

# 1 Introduction

There is a growing clinical evidence that structural and functional
brain development and aging take heterogeneous paths within differ-
ent subsets of the human population [1–3]. This heterogeneity has
been relatively ignored in case-control study analyses, yielding a
limited understanding of the diversity of underlying biological pro-
cesses that might give rise to similar clinical phenotypes. The advent
of high-throughput neuroimaging technologies and the concen-
trated efforts of the collection of large-scale datasets [4, 5] provide a
unique opportunity to dissect the structural and functional heteroge-
neity of brain disorders in finer details and in an unbiased data-driven
manner. A developing body of work that leverages ML and neuroim-
aging seeks disease subtypes of neuropsychiatric and neurodegenera-
tive disorders, including Alzheimer's disease (AD) [6–11],
schizophrenia [12, 13], and late-life depression [14].
Subtyping brain diseases is a clustering problem where the goal is to break down the set of patients into distinct and relatively homogeneous subgroups (i.e., subtypes). While this has been actively investigated in the computer science community, subtyping neuroimaging data is endowed with a unique set of obstacles, such as the “curse of dimensionality” and the confounding nuisance effects, such as global demographics and scanner differences. Furthermore, brain development and pathologies often progress along a continuum, e.g., from healthy state to preclinical stages to full-fledged disease [15], thereby modeling directly in the patient domain may lead to a biased clustering solution. Thus, to tackle these problems, some recent efforts have focused on developing semi-supervised [6, 8, 9, 16] and unsupervised clustering methods [10, 11]. Early studies mainly focused on unsupervised clustering methods, such as K-means [17] or hierarchical clustering [18], to derive data-driven subtypes using imaging data. However, such approaches directly partition the patients based on similarities/dissimilarities, potentially biased by confounding factors, such as demographics or heterogeneity caused by unrelated pathological processes. More recently, semi-supervised clustering methods [6, 8, 9, 16] have been proposed to tackle this problem from a novel angle. To seek a pathology-oriented clustering solution, semi-supervised approaches dissect disease heterogeneity by the “1-to-k” mapping between the reference group (i.e., healthy control (CN)) and the subgroups of the patient group (i.e., the k subtypes). This approach presumably zooms into the heterogeneity of pathological processes rather than unwanted heterogeneity in general. Furthermore, confounding variations, such as demographics, are often ruled out in these approaches.

Aiming to provide the reader in the imaging and machine learning community with a broad guideline in terms of methodology and clinical applications, we organize the remainder of this chapter as follows. In Subheading 2, we provide a brief overview of clustering methods, including unsupervised and semi-supervised approaches. Subheading 3 discusses their applications in various neurological and neuropsychiatric disorders and diseases. Subheading 4 concludes the paper by discussing our main observations, methodological limitations, and future directions.

## 2 Methodological Development Using Machine Learning and Neuroimaging

Machine learning and neuroimaging have brought unprecedented opportunities to elucidate disease heterogeneity in various brain disorders and diseases [19]. Several trailblazing methodological papers have been recently published [9–11], challenging the conventional approach of patient stratification that puts all patients into the same bucket. Among these, unsupervised [10, 11] and semi-
supervised clustering methods [9] sought to derive biologically
data-driven disease subtypes, but they anchor the modeling from
distinct perspectives. For conciseness, let us note that our imaging
dataset contains **q** healthy control (CN) samples
*X*<sub>r</sub> = [*x*<sub>1</sub>, ..., *x*<sub>q</sub>], *X*<sub>r</sub>∈ℝ<sup>*p*×*q*</sup>, representing our reference group,
and *n* patient samples (PT) *X*<sub>*t*</sub> = [*x*<sub>1</sub>, ..., *x*<sub>*m*</sub>], *X*<sub>*t*</sub>∈ℝ<sup>*p*×*m*</sup>, represent-
ing the target subtype population. We denote the whole population
as a matrix **X** that is organized by arranging each image as a vector
per column **X** = [*x*<sub>1</sub>, ..., *x*<sub>*q+m*</sub>], **X**∈ℝ<sup>*p*×(*q*+*m*)</sup>, where *p* is the num-
ber of features per image. We use binary labels to distinguish the
patient and control groups, where 1 represents PT and −1 means
CN. Disease subtyping sought to find the number of clusters (*k*) in
the patient group that are neuroanatomically distinct while clini-
cally relevant.

**2.1 Unsupervised Clustering**

Many recent efforts to discover the heterogeneous nature of brain
diseases have investigated different unsupervised clustering algo-
rithms [10, 11, 20–32]. Among these approaches, the key cluster-
ing methods are often K-means, hierarchical clustering, and
nonnegative matrix factorization (NMF) (Fig. 1). In this

<figure><img src="image_194.png" /><figcaption>**Fig. 1** Schematic diagram of representative unsupervised clustering methods, K-means, NMF, and hierarchical clustering</figcaption></figure>
subsection, we first briefly go through these methods. Subsequently, we focus on two representative models building on these unsupervised methods, i.e., Sustain [10] and latent Dirichlet allocation [11].

### 2.1.1 K-Means Clustering

K-means clustering aims to directly partition the *n* patients into *k* clusters. Each patient belongs to the cluster with the nearest mean (i.e., cluster centroid) quantified by a distance metric of choice (e.g., Euclidean distance). Since searching the global minimum in clustering is computationally difficult (NP-hard), local minima are searched in the K-means algorithm via an iterative refinement approach. This usually involves two steps after giving an initial set of *k* centroids: (i) assignment step, assigning each data point to the cluster with the nearest centroid with the least squared Euclidean distance, and (ii) update step, recalculating means (centroids) for all data points assigned to each cluster. The two steps iteratively continue until the convergence, i.e., the assignments no longer change. More details regarding the k-means algorithm are provided in Chap. 2, Subheading 12.1. Please refer to [33–35] for representative studies using K-means for disease subtyping.

### 2.1.2 NMF Clustering

Nonnegative matrix factorization (NMF) is a method that implicitly performs clustering by taking advantage that complex patterns can be construed as a sum of simple parts. In essence, the input data $X_t$ is factorized into two nonnegative matrices $C \in \mathbb{R}^{p \times k}$ and $L \in \mathbb{R}^{k \times m}$, for which we refer to the component matrix and loading coefficient matrix, respectively. This method has been widely used as an effective dimensionality reduction technique in signal processing and image analysis [36]. By its nature, the *L* matrix can be directly used for clustering purposes, which is analogous to K-means if we impose an orthogonality constraint on the *L* matrix. Specifically, if $L_{kj} > L_{ij}$ for all $i \neq k$, this clusters the data point $x_n$ into the *k*-th cluster. The vectors of the *C* matrix indicate the cluster centroids. Please refer to [32] for a representative study using NMF for disease subtyping.

### 2.1.3 Hierarchical Clustering

Hierarchical clustering aims to build a hierarchy of clusters, including two types of approach: agglomerative and divisive [18]. In general, the merges and splits are determined greedily and presented in a dendrogram. Similarly, a measure of dissimilarity between sets of observations is required. Most commonly, this is achieved by using an appropriate metric (e.g., Euclidean distance) and a linkage criterion that specifies the dissimilarity of sets as a function of the pairwise distances of observations. Please refer to [24, 25, 30, 37, 38] for representative studies using the hierarchical clustering for disease subtyping.
### 2.1.4 Representative Unsupervised Clustering Methods

Sustain [10] is an unsupervised clustering method for subtype and stage inference. Specifically, Sustain formulates the model as groups of subjects with a particular biomarker progression pattern as a subtype. The biomarker evolution of each subtype is modeled as a linear z-score model, a continuous generalization of the original event-based model [39]. Each biomarker follows a piecewise linear trajectory over a common timeframe. The key advantage of this model is that it can work with purely cross-sectional data and derive an imaging signatures of subtype and stage simultaneously.

A Bayesian latent Dirichlet allocation model [11] was proposed to extract latent AD-related atrophy factors. This probabilistic approach hypothesizes that each patient expresses one or more latent factors, and each factor is associated with distinct but possibly overlapping atrophy patterns. However, due to the nature of latent Dirichlet allocation methods, the input images have to be discretized. Moreover, this method exclusively models brain atrophy while ignoring brain enlargement. For example, larger brain volumes in basal ganglia have been associated with one subtype of schizophrenia [12].

## 2.2 Semi-supervised Clustering

Semi-supervised clustering methods dissect the subtle heterogeneity of interest under the principle of deriving data-driven and neurobiologically plausible subtypes (Fig. 2). In essence, these methods seek the “1-to-k” mapping between the reference CN

<figure><img src="image_195.png" /><figcaption>**Fig. 2** Schematic diagram of semi-supervised clustering methods. Figure is adapted from [14]</figcaption></figure>
group and the PT group, thereby teasing out clusters that are likely
driven by distinct pathological trajectories, instead of by global
similarity/dissimilarity in data, which is the core momentum of
conventional unsupervised clustering methods.

In the following subsections, we briefly discuss four semi-
supervised clustering methods. These methods employ different
techniques to seek this “1-to-**k**” mapping. In particular, CHI-
MERA [16] and Smile-GAN [9] utilize generative models to
achieve this mapping, while HYDRA [6] and MAGIC [8] are
built on top of discriminative models.

**Box 1: Representative Semi-supervised Clustering Methods**

The central principle of semi-supervised clustering methods is
to seek the “1-to-*k*” mapping from the reference domain to
the patient domain.

*   **CHIMERA:** a generative approach that leverages the coherent point drift algorithm and maps the data distribution of the CN group to the PT group, thereby enabling to subtype by the distinct *k* regularized transformations.

*   **Smile-GAN:** a generative approach based on GANs to learn multiple distinct mappings by generating PT from CN. Simultaneously, a clustering model is trained interactively with mapping functions to assign PT into the corresponding subtype memberships.

*   **HYDRA:** a discriminative approach which leverages multiple linear support vector machines to construct a polytope that clusters the patients depending on the patterns of differences between the CN group and the PT group.

*   **MAGIC:** a generalization of HYDRA that aims to dissect disease heterogeneity at multiple imaging scales for a scale-consistent solution.

2.2.1 CHIMERA

CHIMERA employs a generative probabilistic approach, considers all samples as points in the imaging space, and infers the clusters from the transformations between the CN and PT distributions. It hypothesizes that the PT distribution can be generated from the CN distribution under *k* sets of transformations, each reflecting a distinct disease process.

Mathematically, the transformation *T* is a convex combination of the *k* linear transformations that map a CN subject in the reference space to the target space: *x*<sub>*i*</sub><sup>*r*</sup>∈ℝ<sup>*q*</sup> → *x*<sub>*i*</sub><sup>*t*</sup> = *T*(*x*<sub>*i*</sub>) = Σ<sub>*j*=1</sub><sup>*k*</sup> *ξ*<sub>*j*</sub> *T*<sub>*j*</sub>(*x*<sub>*i*</sub>), where *ξ*<sub>*j*</sub> is the probability that a PT belongs to the *j*-th subtype. Ideally, if the disease subtypes were distinct, *ξ*<sub>*j*</sub> should take value 1 for the transformation
corresponding to this specific disease subtype and value 0 otherwise. At its core, the coherent point drift algorithm [40], a generative probabilistic approach, is used to estimate the transformation *T*. Specifically, the CN sample point is mapped to the PT domain and regarded as a centroid of a spherical Gaussian cluster, whereas the patient points are treated as independent and identically distributed data generated by a Gaussian mixture model (GMM) with equal weights for each cluster. The goal is to maximize the data likelihood during the distribution matching while also taking into account covariate confounds (e.g., age and gender). The expectation-maximization approach is adopted to optimize the resulting energy objective. Clustering inference is straightforward after the optimized transformation $T_j$ is achieved, i.e., a patient can be assigned the subtype membership corresponding to the largest likelihood.

Smile-GAN is a novel generative deep learning approach based on generative adversarial networks (GAN). The reader may refer to Chap. 5 for generic information about GANs. Smile-GAN aims to learn a mapping function, $f$, from joint CN domain $\mathcal{X}$ and subtype domain $\mathcal{Z}$ to the PT domain $\mathcal{Y}$, by transforming CN data $\mathcal{X}$ to different synthesized PT data $\mathcal{Y}' = f(\mathcal{X}, \mathcal{Z})$ that are indistinguishable from real PT data, $\mathcal{Y}$, by the discriminator, $D$. Mapping function, $f$, is regularized for inverse consistencies, with a clustering function, $g: \mathcal{Y} \to \mathcal{Z}$, trained interactively to reconstruct $\mathcal{Z}$ from synthesized PT data $\mathcal{Y}'$. The clustering function, $g$, can also be directly used to cluster both training and unseen test data after the training process.

More specifically, three different data distributions are denoted as $\mathbf{x} \sim p_{\text{CN}}$ (for controls), $\mathbf{y} \sim p_{\text{PT}}$ (for patients), and $\mathbf{z} \sim p_{\text{Sub}}$ (for a subtype), respectively, where $\mathbf{z} \sim p_{\text{Sub}}$ is sampled from a discrete uniform distribution and encoded as a one-hot vector with dimension $K$ (number of clusters). Mapping function, $f: \mathbf{x} * \mathbf{Z} \to \mathcal{Y}$, and clustering function, $g: \mathcal{Y} \to \mathcal{Z}$, are learned through the following training procedure ($l_c$ denotes the cross-entropy loss):

$$f, g = \arg\min_{f,g} \max_{D} L_{\text{GAN}}(D, f) + \mu L_{\text{change}}(f) + \lambda L_{\text{cluster}}(f, g) \quad (1)$$

where

$$L_{\text{GAN}}(D, f) = \mathbb{E}_{\mathbf{y} \sim p_{\text{PT}}} [\log(D(\mathbf{y}))] \\ + \mathbb{E}_{\mathbf{z} \sim p_{\text{Sub}}, \mathbf{x} \sim p_{\text{CN}}} [1 - \log(D(f(\mathbf{x}, \mathbf{z})))] \quad (2)$$

$$L_{\text{change}}(f) = \mathbb{E}_{\mathbf{x} \sim p_{\text{CN}}, \mathbf{z} \sim p_{\text{Sub}}} [\|f(\mathbf{x}, \mathbf{z}) - \mathbf{x}\|_1] \quad (3)$$

$$L_{\text{cluster}}(f, g) = \mathbb{E}_{\mathbf{x} \sim p_{\text{CN}}, \mathbf{z} \sim p_{\text{Sub}}} [l_c(\mathbf{z}, g(f(\mathbf{x}, \mathbf{z})))] \quad (4)$$
The objective consists of adversarial loss $L_{GAN}$, regularization terms $L_{change}$ and $L_{cluster}$. Adversarial loss forces the synthesized PT data to follow similar distributions as real PT data. The discriminator $D$, trying to identify synthesized PT data from real PT data, attempts to maximize the loss, while the mapping $f$ attempts to minimize against it. Both regularization terms serve to constrain the function class where the mapping function $f$ is sampled from so that it is truly meaningful while matching the distributions. Minimization of $L_{change}$ encourages sparsity of regions captured by $f$, with the assumption that only some regions are changed by disease effect. Optimizing $L_{cluster}$ ensures that the input sub variable $z$ can be reconstructed from synthesized PT data $y'$, so that the mutual information between $z$ and $y'$ are maximized, and distinct imaging patterns are synthesized when $z$ takes different values. Further regularization is also imposed by forcing mapping function $f$ and clustering function $g$ to be Lipschitz continuous. More importantly, thanks to the inverse consistencies led by $L_{cluster}$, function $g$ can directly output cluster probabilities and cluster labels when given unseen test PT data.

### 2.2.3 HYDRA

In contrast to the generative approaches used in CHIMERA and Smile-GAN, HYDRA leverages a widely used discriminative method, i.e., support vector machines (SVM), to seek this “1-to-k” mapping. The novelty is that HYDRA extends multiple linear SVMs to the nonlinear case in a piecewise fashion, thereby simultaneously serving for classification and clustering. Specifically, it constructs a convex polytope by combining the hyperplane from k linear SVMs, separating the CN group and the k subpopulation of the PT group. Intuitively, each face of the convex polytope can be regarded to encode each subtype, capturing a distinct disease effect.

The convex polytope is estimated by sequentially solving each linear SVM as a subproblem under the principle of the sample weighted SVM [41]. The optimization stops when the sample weights become stable, i.e., the polytope is stably established. The objective of maximizing the polytope's margin can be summarized as

$$ \begin{aligned} & \min_{\{w_j, b_j\}_{j=1}^k} \sum_{(j=1)}^k \frac{\|w_j\|_2^2}{2} + \mu \sum_{i|y_i=1} \frac{1}{k} \max\{0, 1 - w_j^T X_i^T - b_j\} \\ & + \mu \sum_{i|y_i=-1} s_{i,j} \max\{0, 1 + w_j^T X_i^T + b_j\} \end{aligned} \quad (5) $$

where $w_j$ and $b_j$ are the weight and bias for each hyperplane, respectively. $\mu$ is a penalty parameter on the training error, and $S$ is the subtype membership matrix of dimension $m \times k$ deciding
whether a patient sample *i* belongs to subtype *j*. The cluster membership is inferred as follows:

$$S_{i,j} = \begin{cases} 1, & j = \arg \max_j (\boldsymbol{w}_j^T \mathbf{X}^T + b_j) \\ 0, & \text{otherwise} \end{cases} \quad (6)$$

2.2.4 MAGIC

MAGIC was proposed to overcome one of the main limitations that HYDRA faced. That is, a single-scale set of features (e.g., atlas-based regions of interest) may not be sufficient to derive subtle differences, compared to global demographics, disease heterogeneity, since ample evidence has shown that the brain is fundamentally composed of multi-scale structural or functional entities. To this objective, MAGIC extracts multi-scale features in a coarse-to-fine granular fashion via stochastic orthogonal projective nonnegative matrix factorization (opNMF) [42], a very effective unbiased, data-driven method for extracting biologically interpretable and reproducible feature representations. Together with these multi-scale features, HYDRA is embedded into a double-cyclic optimization procedure to yield robust and scale-consistent cluster solutions.

MAGIC encapsulates the two previous proposed methods (i.e., opNMF and HYDRA) and optimizes the clustering objective for each single-scale feature as a sub-optimization problem. To fuse the multi-scale clustering information and enforce the clusters to be scale-consistent, it adopts a double-cyclic procedure that transfers and fine-tunes the clustering polytope. Firstly, (i) inner cyclic procedure: let us remind that HYDRA decides the clusters based on the subtype membership matrix (*S*). MAGIC first initializes the *S* matrix with a specific single-scale feature set, i.e., *L*<sub>*i*</sub>, and then the *S* matrix is transferred to the next set of feature set *L*<sub>*i*+1</sub> until the predefined stopping criterion is achieved (i.e., the clustering solution across scales is stable). Secondly, (ii) outer cyclic procedure: the inner cyclic procedure was repeated by initializing with each single-scale feature set. Finally, to determine the final subtype assignment, we perform a consensus clustering by computing a co-occurrence matrix based on all the clustering results and then perform spectral clustering [43].

## 3 Application to Brain Disorders

Brain disorders and diseases affect the human brain across a wide age range. Neurodevelopmental disorders, such as autism spectrum disorders (ASD), are usually present from early childhood and affect daily functioning [44]. Psychotic disorders, such as schizophrenia, involve psychosis that is typically diagnosed for the first time in late adolescence or early adulthood [45]. Dementia and mild cognitive impairment (MCI) prevail both in late mid-life for
early-onset AD (usually 30–60 years of age) and most frequently in late-life for late-onset AD (usually over 65 years of age) [46]. Brain cancers in children and adults are heterogeneous and encompass over 100 different histological types of tumors, based on cells of origin and other histopathological features, and have substantial morbidity and mortality [47]. Ample clinical evidence encourages the stratification of the patients in these brain disorders and cancers, potentially paving the road toward individualized precision medicine.

This section collectively overviews previous work aiming to unravel imaging-derived heterogeneity in ASD, psychosis, major depressive disorders (MDD), MCI and AD, and brain cancer.

## 3.1 Autism Spectrum Disorder

ASD encompasses a broad spectrum of social deficits and atypical behaviors [48]. Heterogeneity of its clinical presentation has sparked massive research efforts to find subtypes to better delineate its diagnosis [49, 50]. Recent initiatives to aggregate neuroimaging data of ASD, such as the ABIDE [51] and the EU-AIMS [52], also have motivated large-scale subtyping projects using imaging signatures [53].

Different clustering methods have been applied to reveal structural brain-based subtypes, but primarily traditional techniques such as the K-means [54] or hierarchical clustering [37]. Besides structural MRI, functional MRI [55] and EEG [56] have also been popular modalities. For reasons discussed earlier, normative clustering and dimensional analyses are better suited to parse a patient population that is highly heterogeneous [57]. However, efforts in this avenue have been primitive, with only a few recent publications using cortical thickness [58]. Taken together, although more validation and replication efforts are necessary to define any reliable neuroanatomical subtypes of ASD, some convergence in findings has been noted [53]. First, most sets of ASD neuroimaging subtypes indicate a combination of both increases and decreases in imaging features compared to the CN group, instead of pointing in a uniform direction. Second, most subtypes are characterized by spatially distributed imaging patterns instead of isolated or focal patterns. Both findings emphasize the significant heterogeneity in ASD brains and the need for better stratification.

The search for subtypes in the ASD population has unique challenges. First, the early onset of ASD implies that it is heavily influenced by neurodevelopmental processes. Depending on the selected age range, the results may significantly differ. Second, ASD is more prevalent in males, with three to four male cases for one female case [59], which adds a layer of potential bias. Third, individuals with ASD often suffer psychiatric comorbidities, such as ADHD, anxiety disorders, and obsessive-compulsive disorder, among many others [60], which, if not screened carefully, can dilute or alter the true signal.
## 3.2 Psychosis

Psychosis is a medical syndrome characterized by unusual beliefs called delusions and sometimes hallucinations of visions, sounds, smells, or body sensations that are not present in reality. Symptoms, functioning, and outcomes are highly heterogeneous across individuals, leading to long-standing hypotheses of underlying brain subgroups. However, objective brain biomarkers have largely not been discovered for any psychosis diagnosis, stage, or clinically defined subgroup [61, 62]. Neuroimaging studies are also affected by brain heterogeneity [63, 64]. Recent research has thus focused on finding structural brain subtypes using unbiased statistical techniques [12, 13, 65].

Psychosis studies have mainly focused on determining subtypes by clustering brain structural data within the chronic schizophrenia population that has had the illness for years, with results demonstrating two [12, 13], three [26], and six [31] subgroups. Various clustering techniques have been used to achieve these outcomes, including conventional approaches, such as k-means, in addition to more advanced machine learning methods, such as semi-supervised learning. A limitation of the work so far has been the lack of internal or external validation. Still, in studies with robust internal validation methods using metrics that choose the optimal cluster number based on the stability of the solution (e.g., consensus clustering), subtypes cluster along the lines of the severity of brain differences.

In a recent study, with the largest sample to date (n=671), clustered individuals with chronic schizophrenia using HYDRA and multiple internal validation procedures were applied (i.e., cross-validation resampling, split-half reproducibility, and leave-site-out validation) [12]. A two-subtype solution was found, with one subtype demonstrating widespread reductions and the other showing the localized larger volume of the striatum that was not associated with antipsychotic use. Interestingly, there were limited associations with current psychosis symptoms in this work, but indications of associations with education and illness duration in specific subtypes.

Functional imaging has also been used to define psychosis subgroups using functional connectivity at rest [66] and effective connectivity during task performance [67]. The research commonly has relatively low sample sizes with little internal or external validation. Still, of these works, preliminary results demonstrate that clusters can follow diagnostic divisions between individuals with psychosis [67] and that specific networks (e.g., frontoparietal network) are associated with specific psychotic symptoms [67, 66]. A recent advanced deep learning approach has also revealed clinical separations along the lines of symptom severity [68]. Taken together with brain structural results, it is possible that functional imaging maps onto symptom states rather than underlying illness traits that are captured by structural imaging. Further internal and external validation work is required to investigate this hypothesis by
characterizing, comparing, and ultimately combining clustering solutions. A critical future direction will also be to conduct longitudinal studies that track individuals over time. Such research could lead the way toward clinical translation.

**3.3 Major Depressive Disorder**

MDD is a common, severe, and recurrent disorder, with over 300 million people affected worldwide, and is characterized by low mood, apathy, and social withdrawal, with symptoms spanning multiple domains [69]. Its vast heterogeneity is exemplified by the fact that according to DSM-5 criteria, at least 227 and up to 16,400 unique symptom presentations exist [70, 71]. The potential causes for this heterogeneity vary from divergent clinical symptom profiles to genetic etiologies and individual differences in treatment outcomes.

Despite neurobiological findings in MDD spanning cortical thickness, gray matter volume (GMV), and fractional anisotropy (FA) measures, objective brain biomarkers that can be used to diagnose and predict disease course and outcome remain elusive [71–73]. Recently, there have been efforts to identify neurobiologically based subtypes of depression using a bottom-up approach, mainly using data from resting-state fMRI [71]. Several studies [33–35] employed k-means clustering and group iterative multiple model estimation, respectively, to identify two functional connectivity subtypes, while Tokuda et al. [74] and Drysdale et al. [75] identified three and four subtypes, respectively, using nonparametric Bayesian mixture models and hierarchical clustering. These subtypes are characterized by reduced connectivity in different networks, including the default mode network (DMN), ventral attention network, and frontostriatal and limbic dysfunction. Regarding structural neuroimaging, one study has used k-means clustering on fractional anisotropy (FA) data to identify two depression subtypes. The first subtype was characterized by decreased FA in the right temporal lobe and the right middle frontal areas and was associated with an older age at onset. In contrast, the second subtype was characterized by increased FA in the left occipital lobe and was associated with a younger age at onset [76].

Current research in the identification of brain subtypes in MDD has produced results that are promising but confounded by methodological and design limitations. While some studies have shown clinical promises such as predicting higher depressive symptomatology and lower sustenance of positive mood [34, 35], depression duration [33], and TMS therapy response [75], they are confounded by limitations such as relatively small sample sizes; nuisance variances such as age, gender, and common ancestry; lack of external validation; and lack of statistical significance testing of identified clusters. Furthermore, there has been a lack of ambition in the use of novel clustering techniques. Clustering based on
structural neuroimaging is limited compared to other disease entities and is an avenue that future research should consider. Future studies should also aim to perform longitudinal clustering to elucidate the stability of identified brain subtypes over time and examine their utility in predicting disease outcomes.

## 3.4 MCI and AD

AD, along with its prodromal stage presenting MCI, is the most common neurodegenerative disease, affecting millions across the globe. Although a plethora of imaging studies have derived AD-related imaging signatures, most studies ignored the heterogeneity in AD. Recently, there has been a developing body of effort to derive imaging signatures of AD that are heterogeneity-aware (i.e., subtypes) [7–11].

Most previous studies leveraged unsupervised clustering methods such as Sustain [10], NMF [32], latent Dirichlet allocation [11], and hierarchical clustering [24, 25, 30, 38]. Other papers [6, 9, 20, 77, 78] utilized semi-supervised clustering methods. Due to the variabilities of the choice of databases and methodologies and the lack of ground truth in the context of clustering, the reported number of clusters and the subtypes' neuroanatomical patterns differ and cannot be directly compared. The targeted heterogeneous population of study also varies across papers. For instance, [6] focused on dissecting the neuroanatomical heterogeneity for AD patients, while [77] included AD plus MCI and [20] studied MCI only. However, some common subtypes were found in different studies. First, a subtype showing a typical diffuse atrophy pattern over the entire brain was witnessed in several studies [6, 8–10, 22, 27, 29, 30, 32, 38, 77]. Another subtype demonstrating nearly normal brain anatomy was robustly identified [8, 9, 16, 20, 22, 24, 25, 29, 30]. Moreover, studies [8, 9, 29, 30, 77] also reported one subtype showing atypical AD patterns (i.e., hippocampus or medial temporal lobe atrophy spared).

Though these methods enabled a better understanding of heterogeneity in AD, there are still limitations and challenges. First, due to demographic variations and the existence of comorbidities, it is not guaranteed that models cluster the data based on variations of the pathology of interest. Semi-supervised methods might tackle this problem to some extent, but more careful sample selection and further study with longitudinal data may ensure disease specificity. Second, spatial differences and temporal changes may simultaneously contribute to subtypes derived through clustering methods. Third, subtypes captured from neuroimaging data alone bring limited insight into disease treatments, thereby a joint study of neuroimaging and genetic heterogeneity may provide greater clinical value [14, 79].
## 3.5 Brain Cancer

Brain tumors, such as glioblastoma (GBM), exhibit extensive inter- and intra-tumor heterogeneity, diffuse infiltration, and invasiveness of various immune and stromal cell populations, which pose diag- nostic and prognostic challenges, and render the standard therapies futile [80]. Deciphering the underlying heterogeneity of brain tumors, which arises from genomic instability of these tumors, plays a key role in understanding and predicting the course of tumor progression and its response to the standard therapies, thereby designing effective therapies targeted at aberrant genetic alterations [81, 82]. Medical imaging noninvasively portrays the phenotypic differences of brain tumors and their microenviron- ment caused by molecular activities of tumors on a macroscopic scale [83, 84]. It has the potential to provide readily accessible and surrogate biomarkers of particular genomic alterations, predict response to therapy, avoid risks of tumor biopsy or inaccurate diagnosis due to sampling errors, and ultimately develop persona- lized therapies to improve patient outcomes. An imaging subtype of brain tumors may provide a wealth of information about the tumor, including distinct molecular pathways [85, 86].

Recent studies on radiomic analysis of multiparametric MRI (mpMRI) scans provide evidence of distinct phenotypic presenta- tion of brain tumors associated with specific molecular character- istics. These studies propose that quantification of tumor morphology, texture, regional microvasculature, cellular density, or microstructural properties can map to different imaging sub- types. In particular, one study [87] discovered three distinct clus- ters of GBM subtypes through unsupervised clustering of these features, with significant differences in survival probabilities and associations with specific molecular signaling pathways. These imaging subtypes, namely solid, irregular, and rim-enhancing, were significantly linked to different clinical outcomes and molecu- lar characteristics, including isocitrate dehydrogenase-1, O6-methylguanine-DNA methyltransferase, epidermal growth fac- tor receptor variant III, and transcriptomic molecular subtype composition.

These studies have offered new insights into the characteriza- tion of tumor heterogeneity on both microscopic, i.e., histology and molecular, and macroscopic, i.e., imaging levels, consequently providing a more comprehensive understanding of the tumor aggressiveness and patient prognosis, and ultimately, the develop- ment of personalized treatments.

# 4 Conclusion

Taken together, these novel clustering algorithms tailored for high- resolution yet highly variable neuroimaging datasets have demon- strated a broad utility in disease subtyping across many neurological and psychiatric conditions. Simultaneously, cautions need to be
taken in order not to overclaim the biological importance of sub-
types, since all clustering methods find patterns in data, even if such
patterns don't have a meaningful underlying biological correlate
[88]. External validations are necessary. For instance, evidence of
post hoc evaluations, e.g., a difference in clinical variables or genetic
architectures, can support the biological relevance of identified
neuroimaging-based subtypes [14]. Moreover, good practices
such as split-sample analysis, permutation tests [12], and compari-
son to the guideline of semi-simulated experiments [8] discern the
robustness of the subtypes. As dataset sizes and imaging resolution
improve over time, unique computational challenges are expected
to appear, along with unique opportunities to further refine our
methodologies to decipher the diversity of brain diseases.

Acknowledgements

This work was supported, in part, by NIH grants R01NS042645, U01AG068057, R01MH112070, and RF1AG054409.

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**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
**Data-Driven Disease Progression Modeling**

**Neil P. Oxtoby**

**Abstract**

Intense debate in the neurology community before 2010 culminated in hypothetical models of Alzheimer's disease progression: a pathophysiological cascade of biomarkers, each dynamic for only a segment of the full disease timeline. Inspired by this, data-driven disease progression modeling emerged from the computer science community with the aim to reconstruct neurodegenerative disease timelines using data from large cohorts of patients, healthy controls, and prodromal/at-risk individuals. This chapter describes selected highlights from the field, with a focus on utility for understanding and forecasting of disease progression.

**Key words** Disease progression, Disease understanding, Forecasting, Cross-sectional data, Longitudinal data, Disease timelines, Disease trajectories, Subtyping, Biomarkers

# 1 Introduction

Chronic progressive diseases are a major drain on social and economic resources. Many of these diseases have no treatments and no cure. In particular, age-related chronic diseases such as neurodegenerative diseases of the brain are a global healthcare pandemic-inwaiting as most of the world's population is living ever longer. A key example is Alzheimer's disease—the leading cause of dementia—but there are numerous other conditions that cause abnormal deterioration of brain tissue, leading to loss of cognitive performance, bodily function, independence, and ultimately death. Despite the increasing socioeconomic burden, neurodegenerative disease research has made impressive progress in the past decade, driven largely by the availability of large observational datasets and the computational analyses this enables.

Understanding neurodegenerative diseases is vital if they are to be managed, or even cured, but our understanding remains poor despite impressive progress in recent years. This poor understanding can be attributed to the many challenges of neurodegenerative diseases: no well-defined time axis due in part to heterogeneity in onset/speed/presentation, and censoring/attrition especially in
later stages as patients deteriorate. These challenges, coupled with intense debate in the neurology community (hypothetical models [1, 2]) and increasing availability of data, piqued the interest of computational researchers aiming to provide quantitative answers to the mysteries of neurodegenerative diseases. This has ranged from vanilla off-the-shelf machine learning approaches through to more holistic statistical modeling approaches, the most advanced of which is data-driven disease progression modeling (D³PM).

D³PMs are defined by two key features: (1) they simultaneously reconstruct the disease timeline and estimate the quantitative disease signature/trajectory along this timeline; and (2) they are directly informed by observed data. D³PMs strike a balance between pure unsupervised learning, which requires truly big data, and traditional longitudinal modeling, which relies on a well-defined temporal axis—neither of which are available in neurodegenerative diseases. For a review of the history and development of D³PM, see refs. 3.

The goal of this chapter is to highlight selected key D³PMs in a practical manner. The focus is on model capabilities and data requirements, aiming to inform the reader's D³PM analysis strategy based on the desired disease insight(s) and the data available. Figure 1 places selected D³PMs on a capability×data quadrant

<figure><img src="image_196.png" /><figcaption>**Fig. 1** Quadrant matrix. D³PMs all estimate a disease timeline, with some capable of estimating multiple subtype timelines, using either cross-sectional data (pseudo-timeline) or longitudinal data (time-shift). Abbreviations: EBM, event-based model; DEBM, discriminative EBM; KDE-EBM, kernel density estimation EBM; DPS, disease progression score; LTJMM, latent-time joint mixed model; GPPM, Gaussian process progression model; SuStaln, subtype and stage inference; SubLign, subtyping alignment</figcaption></figure>
matrix: single timeline estimation vs subtyping, and cross-sectional
vs longitudinal data availability. Table A.1 lists more methodologi-
cal papers relevant to D³PM, with model innovations grouped by
the original paper for that method.

The chapter is organized as follows. It starts with a brief discus-
sion of data preprocessing considerations in Subheading 2—an
important step in medical data analysis. The treatment of D³PMs
is separated into models for cross-sectional data (Subheading 3)
and models for longitudinal data (Subheading 4), each split into
approaches that estimate a single timeline of disease progression
and those capable of estimating multiple timelines within a dataset
(subtyping). Subheading 5 concludes.

For a detailed timeline of D³PM development including taxon-
omy and pedigree of key models, see Appendix.

## 2 Data Preprocessing

This section briefly touches on two common preprocessing steps
before fitting a D³PM to data from a progressive condition such as
an irreversible chronic disease: controlling for confounding vari-
ables, and handling missing data. We refer to input features as
biomarkers and use “covariate” and “confounder” interchangeably.
Missing data can refer to irregular/variable visits across individuals,
or missing biomarker data due to one or more measurements not
being performed for some reason. This section deals with the latter,
since longitudinal models can typically handle irregular visits.

Controlling for confounding variables is an important element
of any D³PM analysis. This helps to prevent the D³PM from
learning non-disease-related patterns such as due to confounding
covariates. Confounders can be included as covariates in certain
models—to account for that source of variation alongside other
variables of interest. Another approach, often used for continuous-
valued confounders, is to “regress out” this source of variation prior
to fitting a model—to remove non-disease-related signal in the
data. This process involves training regression models on data
from control participants (who are not expected to develop the
disease being studied) and then removing the relevant trends from
all data. This method can also be applied to categorical risk factors
(discrete variables). The canonical example of a potentially con-
founding variable in neurodegenerative diseases of the brain is
age—a key risk factor in many chronic diseases. Removing normal
aging signal is often phrased as “adjusting for” or “controlling
for” age.

Handling missing data is an active area of research with a
considerable body of literature. Broadly speaking, there are two
strategies. The easiest is to exclude participants having any missing
biomarker (or covariate) data, but this can considerably reduce the
sample size of data available for D³PM analysis. The second approach is to impute the missing data, e.g., using group mean values. Imputation can be explicit or implicit. An example of implicit imputation is in Bayesian models that map data to probabilities and then deal with missing data probabilistically such as in the event-based model [4] where P(event|x) = 0.5 represents maximal uncertainty such as when a measurement x is missing.

# 3 Models for Cross-Sectional Data

## Box 1: Models for Cross-Sectional Data

* Pro: Data-economical.

Require cross-sectional data only.

* Con: Limited forecasting utility.

Forecasting requires augmentation with longitudinal data.

* Key application(s): assessing disease severity from a single visit, e.g., economical stratification for clinical research/trials.

**3.1 Single Timeline Estimation Using Cross-Sectional Data**

There is only one framework for estimating disease timelines from cross-sectional data: event-based modeling.

**3.1.1 Event-Based Model**

The event-based model (EBM) emerged in 2011 [5, 6]. The concept is simple: in a progressive disease, biomarker measurements only ever get worse, i.e., become increasingly and irreversibly abnormal. Thus, among a cohort of individuals at different stages of a single progressive disease, the cumulative sequence of biomarker abnormality events can be inferred from only a single visit per individual. This requires making a few assumptions: measurements from individuals are independent and represent samples from a single sequence of cumulative abnormality, i.e., a single timeline of disease progression. Such assumptions are commonplace in many statistical analyses of disease progression and are reasonable approximations to make when analyzing data from research studies that typically have strict inclusion and exclusion criteria to focus on a single condition of interest. Unsurprisingly, the event-based model has proven to be extremely powerful, producing insight into many neurodegenerative diseases: sporadic Alzheimer's disease [7–10], familial Alzheimer's disease [6, 11], Huntington's disease [6, 12], Parkinson's disease [13], and others [14, 15].
<figure><img src="image_197.png" /><figcaption>**Fig. 2** Event-based models fit a mixture model to map biomarker values to abnormality probabilities. Left to right shows the convergence of a kernel density estimate (KDE) mixture model. From Firth et al. [9] (CC BY 4.0)</figcaption></figure>

EBM Fitting

The first step in fitting an event-based model maps biomarker values to abnormality values, similar to the hypothetical curves of biomarker abnormality proposed in 2010 [1, 2]. The EBM does this probabilistically, using bivariate mixture modeling where individuals can be labeled either as pre-event/normal or post-event/abnormal to allow for (later) events that are yet to occur in patients, and similarly for the possibility of (earlier) events to have occurred in asymptomatic individuals. Various distributions have been proposed for this mixture modeling: combinations of uniform [5, 6], Gaussian [5–7], and kernel density estimate (KDE) distributions [9]. This is visualized in Fig. 2.

The second step in fitting an EBM over $N$ events is to search the space of $N!$ possible sequences $S$ to reveal the most likely sequence (see refs. 6, 7, 9 for mathematical details). For small $N \le 10$, it can be computationally feasible to perform an exhaustive search over all possible $N!$ sequences to find the maximum likelihood/a posteriori solution. The EBM uses a combination of multiply-initialized gradient ascent, followed by MCMC sampling to estimate uncertainty in the sequence. This results in a model posterior that is a collection of samples from the posterior probability density for each biomarker as a function of sequence position. This is presented as a positional variance diagram [6], such as in Fig. 3.

For further information and to try out EBM tutorials, the reader is directed to the open-source kde_ebm package (github.com/ucl-pond/kde_ebm) and disease-progression-modelling.github.io.

### 3.1.2 Discriminative Event-Based Model

The discriminative event-based model (DEBM) was proposed in 2017 by Venkatraghavan et al. [16]. Whereas the EBM treats data from individuals as observations of a single group-level disease cascade (sequence), the DEBM estimates individual-level sequences and combines them into a group-level description of
<figure><img src="image_198.png" /><figcaption>**Fig. 3** The event-based model posterior is a positional variance diagram showing uncertainty (left-to-right) in the maximum likelihood sequence (top-to-bottom). Parkinson's disease model from Oxtoby et al. [13] (CC BY 4.0)</figcaption></figure>

disease progression. This is done using a Mallow's model, which is the ranking/sequencing equivalent of a univariate Gaussian distribution—including estimation of a mean sequence and variance in this mean. Both EBM and DEBM estimate group-level biomarker abnormality using mixture modeling and both approaches directly estimate uncertainty in the sequence.

Additionally, Venkatraghavan et al. [16, 17] also introduced a pseudo-temporal “disease time” that converts the DEBM posterior into a continuous measure of disease severity.

**DEBM Fitting** As with the EBM, DEBM model fitting starts with mixture modeling (see Subheading 3.1.1). Next, a sequence is estimated for each individual by ranking the abnormality probabilities in descending order. A group-level mean sequence (with variance) is estimated by fitting the individual sequences to a Mallow's model. For details, see refs. 16, 17 and subsequent innovations to the DEBM. Notably, DEBM is often quicker to fit than EBM, which makes it appealing for high-dimensional extensions, e.g., aiming to estimate voxel-wise atrophy signatures from cross-sectional brain imaging data.
For further information and to try it out, the reader is directed
to the open-source pyebm package (https://github.com/
88vikram/pyebm).

## 3.2 Subtyping Using Cross-Sectional Data

Box 2: Subtyping Models

* Pro: Uncovering heterogeneity without conflating severity with subtype.

Evidence suggests that disease subtypes exist.

* Con: Overly simplistic.

Current models ignore comorbidity.

Augmenting the event-based model concept with unsupervised machine learning, subtype and stage inference (SuStaIn), was introduced by Young et al. [18]. This marriage of clustering to disease progression modeling has proven very powerful and popular, with high-impact results appearing in prominent journals for multiple brain diseases [19–21], chronic lung disease [22], and knee osteoarthritis [23]. SuStaIn’s popularity is perhaps unsurprising given that it was the first method capable of unraveling spatiotemporal heterogeneity (pathological severity across an organ) from phenotypic heterogeneity (disease subtypes) in progressive conditions using only cross-sectional data.

Figure 4 (adapted from [18]) shows the concept behind SuStaIn. SuStaIn iteratively solves the clustering problem from 1 to $N_S^{max}$ subtypes. The $N_S$ model is fitted by splitting each of the $N_S - 1$ subtypes into two clusters and then solving the $N_S$-cluster problem, which produces $N_S - 1$ candidate $N_S$-cluster models, from which the maximum likelihood model is chosen, and then the algorithm continues to $N_S + 1$ and so on.

Young et al. [18] also introduced the z-score event progression model that breaks down individual biomarker events into piecewise linear transitions between z-scores of interest. This removes the need for mixture modeling (such as in event-based modeling) and enables inference to be performed at subthreshold biomarker values.

SuStaIn Fitting

For the user, a SuStaIn analysis is very similar to an event-based model analysis. For further information, the reader is directed to the open-source pySuStaIn package [24] (https://github.com/ucl-pond/pySuStaIn), which includes tutorials. As well as the z-score progression model, pySuStaIn includes the various event-based models (see Subheading 3.1), and the more recent scored-events model for ordinal data [25] such as visual ratings of medical images.
<figure><img src="image_199.png" /><figcaption>**Fig. 4** The concept of subtype and stage inference (SuStain). Reproduced from Young et al. [18] (CC BY 4.0)</figcaption></figure>
# 4 Models for Longitudinal Data

## Box 3: Models for Longitudinal Data

* Pro: Good forecasting utility.

High temporal precision allows individualized forecasting.

* Con: Data-heavy.

Require longitudinal data (multiple visits, years). Can be slow to fit.

* Key application(s): assessing speed of disease progression and assessing individual variability.

The availability of longitudinal data has fueled development of more sophisticated D³PMs, inspired by mixed models. Mixed (effect) modeling is the workhorse of longitudinal statistical analysis against a known timeline, e.g., age. Mixed models provide a hierarchical description of individual-level variation (random effects) about group-level trends (fixed effects), hence the common parlance “mixed-effects” models. Many of the D³PMs for longitudinal data discussed below are in fact mixed models with an additional latent-time parameter that characterizes the disease timeline. Similar approaches in various fields are known as “self-modeling regression” or “latent-time” models. We focus on parametric models, but also mention nonparametric models, and an emerging hybrid discrete-continuous model.

## 4.1 Single Timeline Estimation Using Longitudinal Data

There are both parametric and nonparametric approaches to estimating disease timelines from longitudinal data. The common goal is to “stitch together” a full disease timeline (decades long) out of relatively short samples from individuals (a few years each) covering a range of severity in symptoms and biomarker abnormality. Some of the earliest work emerged from the medical image registration community, where “warping” images to a common template is one of the first steps in group analyses [26].

Broadly speaking, there are two categories of D³PMs for longitudinal data: time-shifting models and differential equation models. Time-shifting models translate/deform the individual data, metaphorically stitching them together into a quantitative template of disease progression. Differential equation models estimate a statistical model of biomarker dynamics in phase-plane space (position vs velocity), which is subsequently inverted to produce biomarker trajectories.
Jedynak et al. [27] introduced the disease progression score (DPS) model in 2012, which aligns biomarker data from individuals to a group template model using a linear transformation of age into a disease progression score $s_i = \alpha_i \text{age} + \beta_i$. Individuals have their own rate of progression $\alpha_i$ (constant over the short observation time) and disease onset $\beta_i$. Group-level biomarker dynamics are modeled as sigmoid ("S") curves. A Bayesian extension of the DPS approach (BPS) appeared in 2019 [28]. Code for both the DPS and BPS was released publicly: https://www.nitrc.org/projects/progscore; https://hub.docker.com/r/bilgelm/bayesian-ps-adni/.

Donohue et al. [29] introduced a self-modeling regression approach similar to the DPS model in 2014. It was later generalized into the more flexible latent-time joint mixed (effects) model (LTJMM) [30], which can include covariates as fixed effects and is a flexible Bayesian framework for inference. The LTJMM software was released publicly: https://bitbucket.org/mdonohue/ltjmm.

A nonparametric latent-time mixed model appeared in 2017: the Gaussian process progression model (GPPM) of Lorenzi et al. [31]. This is a flexible Bayesian approach akin to (parametric) self-modeling regression that doesn't impose a parametric form for biomarker trajectories. More recent work supplemented the GPPM with a dynamical systems model of molecular pathology spread through the brain [32] that can regularize the GPPM fit to produce a more accurate disease timeline reconstruction that also provides insight into neurodegenerative disease mechanisms (which is a topic that could be a standalone chapter of this book). The GPPM and GPPM-DS model source code was released publicly via gitlab.inria.fr/epione and tutorials are available at disease-progression-model.github.io.

In 2015, Schiratti et al. [33–35] introduced a general framework for estimating spatiotemporal trajectories for any type of manifold-valued data. The framework is based on Riemannian geometry and a mixed-effects model with time reparametrization. It was subsequently extended by Koval et al. [36] to form the disease course mapping approach (available in the leaspy software package). Disease course mapping combines time warping (of age) and inter-biomarker spacing translation. Time warping changes disease progression dynamics—time shift/onset and acceleration/progression speed—but not the trajectory. Inter-biomarker spacings shift an individual's trajectory to account for individual differences in the timing and ordering of biomarker trajectories.

Figures 5 and 6 show example outputs of these models when trained on data from older people at risk of Alzheimer's disease, including those with diagnosed mild cognitive impairment and dementia due to probable Alzheimer's disease.
<figure><img src="image_200.png" /><figcaption>**Fig. 5** Two examples of D³PMs fit to longitudinal data: disease progression score [27] and Gaussian process progression model [31]. (a) Alzheimer's disease progression score (2012) [27]. Reprinted from Neurolmage, Vol 63, Jedynak et al., A computational neurodegenerative disease progression score: Method and results with the Alzheimer's Disease Neuroimaging Initiative cohort, 1478–1486, ©(2012), with permission from Elsevier. (b) Gaussian process progression model (2017) [31]. Reprinted from Neurolmage, Vol 190, Lorenzi et al., Probabilistic disease progression modeling to characterize diagnostic uncertainty: Application to staging and prediction in Alzheimer's disease, 56–68, ©(2019), with permission from Elsevier</figcaption></figure>
<figure><img src="image_201.png" /><figcaption>**Fig. 6** Two additional examples of D³PMs fit to longitudinal data: latent-time joint mixed model [30] and disease course mapping [36]. (a) Latent-time joint mixed model (2017) [30]. From [37] (CC BY 4.0). (b) Alzheimer's disease course map (2021) [36] (CC BY 4.0)</figcaption></figure>
**Fitting Longitudinal Latent-Time Models**

Fitting D³PMs for longitudinal data is more complex than for cross-sectional data, and the software packages discussed above each expect the data in slightly different formats. One thing they have in common is that renormalization (e.g., min-max or z-score) and reorientation (e.g., to be increasing) is required to put biomarkers on a common scale and direction. In some cases, such preprocessing is necessary to ensure/accelerate model convergence. For example, the LTJMM used a quantile transformation followed by inverse Gaussian quantile function to put all biomarkers on a Gaussian scale. For further detailed discussion, including model identifiability, we refer the reader to the original publications cited above and the didactic resources at disease-progression-modelling.github.io.

**4.1.2 Implicit Models for Longitudinal Data: Differential Equation Models**

Parametric differential equation D³PMs emerged between 2011 and 2014 [38–41], receiving a more formal treatment in 2017 [42]. In a hat-tip to physics, these have also been dubbed “phase-plane” models, which aids in their understanding as a model of velocity (biomarker progression rate) as a function of position (biomarker value). Model fitting is a two-step process whereby the long-time biomarker trajectory is estimated by integrating the phase-plane model estimated on observed data.

A nonparametric differential equation D³PM using Gaussian processes (GP-DEM) was introduced in 2018 [11]. This added flexibility to the preceding parametric approaches and produced state-of-the-art results in predicting symptom onset in familial Alzheimer's disease.

**Fitting Differential Equation Models**

The concept is shown in Fig. 7: differential equation model fitting is a three-step process. First, estimate a single value per individual of biomarker “velocity” and “position,” and then estimate a group-level differential equation model of velocity *y* as a function of position *x*, which is integrated/inverted to produce a biomarker trajectory *x*(*t*). For example, linear regression can produce estimates of position (e.g., intercept) and velocity (e.g., gradient). Differential equation models can be univariate or multivariate and can include covariates explicitly.

**4.1.3 Hybrid Discrete-Continuous Models**

Recent work introduced the temporal EBM (TEBM) [43, 44], which augments event-based modeling with hidden Markov modeling to produce a hybrid discrete-continuous D³PM. This is a halfway house between discrete models (great for medical decision making) and continuous models (great for detailed understanding of disease progression). Trained on data from ADNI, the TEBM revealed the full timeline of the pathophysiological cascade of Alzheimer's disease, as shown in Fig. 8.
<figure><img src="image_202.png" /><figcaption>**Fig. 7** Differential equation models, or phase-plane models, for biomarker dynamics involve a three-step process: estimate individual-level position and velocity; fit a group-level model of velocity *y* vs position *x*, and integrate to produce a trajectory *x*(*t*). Reprinted by permission from Springer Nature: Oxtoby, N.P. et al., Learning Imaging Biomarker Trajectories from Noisy Alzheimer's Disease Data Using a Bayesian Multilevel Model. In: Cardoso, M.J., Simpson, I., Arbel, T., Precup, D., Ribbens, A. (eds) Bayesian and grAphical Models for Biomedical Imaging. Lecture Notes in Computer Science, vol 8677, pp. 85–94 ©(2014) [41]. (a) Data. (b) Differential fit. (c) Est. trajectory. (d) Stochastic model</figcaption></figure>

<figure><img src="image_203.png" /><figcaption>**Fig. 8** Alzheimer's disease sequence and timeline estimated by a hybrid discrete-continuous D³PM: the temporal event-based model [43, 44]. Permission to reuse was kindly granted by the authors of [43]</figcaption></figure>

**4.2 Subtyping Using**
**Longitudinal Data**

Clustering longitudinal data without a well-defined time axis can be extremely difficult. Jointly estimating latent time for multiple trajectories is an identifiability challenge, i.e., multiple parameter combinations can explain the same data. This is particularly challenging when observations span a relatively small fraction of the full disease timeline, as in age-related neurodegenerative diseases.

Chen et al. [45] introduced SubLign for subtyping and aligning longitudinal disease data. The authors frame the challenge eloquently as having misaligned, interval-censored data: left censoring from patients being observed only after disease onset and right censoring from patient dropout in more severe disease. SubLign combines a deep generative model (based on a recurrent neural network [46]) for learning individual latent time-shifts and parametric biomarker trajectories using a variational approach, followed by k-means clustering. It was applied to data from a Parkinson's disease cohort to recover some known clinical phenotypes in new detail.
Poulet and Durrleman [47] recently added mixture-model clustering to the nonlinear mixed model approach of disease course mapping [36]. The framework jointly estimates model parameters and subtypes using a modification of the expectation-maximization algorithm. In simulated data experiments, their approach outperforms a naive baseline. Experiments on real data in Alzheimer's disease distinguished rapid from slow clinical progression, with minimal differences in biomarker trajectories.

# 5 Conclusion

Twenty-first century medicine faces many challenges due to aging populations worldwide, including increasing socioeconomic burden from age-related brain disorders like Alzheimer's disease. Many failed clinical trials fueled intense debate in neurology in the first decade of this century, culminating in the prominent hypothesis of Alzheimer's disease progression as a pathophysiological cascade of dynamic biomarker events. This inspired the emergence of data-driven disease progression modeling (D³PM) from the computer science community during the second decade of the twenty-first century—an explosion of quantitative models for neurodegenerative disease progression enabling numerous high-impact insights across multiple brain disorders. The community continues to build and share open-source code (see Box 4) and run machine learning challenges [48–50]. What will the third decade of the twenty-first century bring for this exciting subset of machine learning for brain disorders?

# Acknowledgements

The author is a UKRI Future Leaders Fellow (MR/S03546X/1) and acknowledges conversations and collaborations with colleagues from the UCL POND group (http://pond.cs.ucl.ac.uk), the EURO POND consortium (http://europond.eu), the E-DADS consor tium (https://e-dads.github.io; MR/T046422/1; EU JPND), and the open Disease Progression Modeling Initiative (https:// disease-progression-modelling.github.io). This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 666992.
# Appendix

A taxonomy and pedigree of key D³PM papers is given in Table A.1. Box 4 contains links to open-source code for D³PMs.

<table><caption>**Table A.1**
A taxonomy and pedigree of D³PM papers. *Asterisks denote models for cross-sectional data</caption><thead><tr><td>Reference (first author only)</td><td>Description</td></tr></thead><tbody><tr><td>Ashford, Curren. Psych. Rep. (2001) [51]</td><td>Differential equation</td></tr><tr><td>Gomeni, Alz. Dem. (2011) [52]</td><td>Differential equation</td></tr><tr><td>Sabuncu, Arch. Neurol. (2011) [38]</td><td>Differential equation</td></tr><tr><td>Samtani, J. Clin. Pharmacol. (2012) [39]</td><td>Differential equation</td></tr><tr><td>Jedynak, NeuroImage (2012) [27]</td><td>Progression score (linear)</td></tr><tr><td>⇒ Bilgel, IPMI (2015) [53]</td><td></td></tr><tr><td>⇒ Bilgel, NIMG (2016) [54]</td><td>Latent time mixed effects</td></tr><tr><td>⇒ Bilgel, Alz. Dem. DADM (2019) [28]</td><td>Bayesian</td></tr><tr><td>*Fonteijn, IPMI (2011) [5]; Fonteijn, NIMG (2012) [6]</td><td>Cumulative events</td></tr><tr><td>⇒ *Young, Brain (2014) [7]</td><td>Robust for sporadic disease</td></tr><tr><td>⇒ *Venkatraghavan, IPMI (2017) [16]; Venkatraghavan, NIMG (2019) [17]</td><td>Individual-level</td></tr><tr><td>⇒ *Young, Nat Commun (2018) [18]</td><td>+ Subtyping, + Z-score model</td></tr><tr><td>⇒ *Young, Frontiers (2021) [55]</td><td>+ Scored events model</td></tr><tr><td>⇒ *Firth, Alz Dem (2020) [9]</td><td>+ Nonparametric events</td></tr><tr><td>⇒ Wijeratne, ML4H2020, IPMI (2021) [43, 44]</td><td>+ Transition times</td></tr><tr><td>Villemagne, Lancet Neurol (2013) [40]</td><td>Differential equation</td></tr><tr><td>⇒ Budgeon, Stat. in Med. (2017) [42]</td><td>Formalism</td></tr><tr><td>Durrleman, Int. J. Comput. Vis. (2013) [56]</td><td>Time warping</td></tr><tr><td>⇒ Schiratti, NeurIPS (2015) [33]; IPMI (2015) [34]; JMLR (2017) [35]</td><td></td></tr><tr><td>⇒ Koval, Sci Rep (2021) [36]</td><td>Latent-time mixed effects</td></tr><tr><td>⇒ Poulet, IPMI (2021) [47]</td><td>+Subtyping</td></tr><tr><td>Donohue, Alz Dem (2014) [29]</td><td>Latent-time fixed effects</td></tr><tr><td>⇒ Li, Stat Meth Med Res (2017) [30]</td><td>Latent-time mixed effects</td></tr><tr><td>Oxtoby, MICCAI (2014) [57]</td><td>Differential equation</td></tr><tr><td>⇒ Oxtoby, Brain (2018) [11]</td><td>+Nonparametric</td></tr><tr><td>Guerrero, NeuroImage (2016) [58]</td><td>Instantiated mixed effects</td></tr></tbody></table>

(continued)
<table><caption>**Table A.1**
(continued)</caption><thead><tr><td>Reference (first author only)</td><td>Description</td></tr></thead><tbody><tr><td>Leoutsakos, JPAD (2016) [59]</td><td>Item response theory</td></tr><tr><td>Lorenzi, NeuroImage (2017) [31]</td><td>Nonparametric latent time</td></tr><tr><td>⇒ Garbarino, IPMI (2019) [60]</td><td>+Differential equation</td></tr><tr><td>⇒ Garbarino, NeuroImage (2021) [32]</td><td>Formalism</td></tr><tr><td>Marinescu, NeuroImage (2019) [61]</td><td>Spatial clustering (c.f. Schiratti/Bilgel)</td></tr><tr><td>Petrella, Comp. Math. Meth. Med. (2019) [62]</td><td>Differential equation</td></tr><tr><td>Abi Nader, Brain Commun. (2021) [63]</td><td>Differential equation</td></tr><tr><td>Chen, AAAI (2022) [45]</td><td>Subtyping</td></tr></tbody></table>

**Box 4: Example Open-Source D³PM Code**

* D³PM tutorials: https://disease-progression-modelling.github.io

* EuroPOND Software Toolbox: https://europond.github.io/europond-software

* KDE EBM: https://ucl-pond.github.io/kde_ebm

* pyEBM: https://github.com/88vikram/pyebm

* leaspy: https://gitlab.com/icm-institute/aramislab/leaspy

* LTJMM: https://bitbucket.org/mdonohue/ltjmm https://github.com/mcdonohue/rstanarm

* DPS: source code; docker image

* pySuStaIn: https://ucl-pond.github.io/pySuStaIn

* TADPOLE-SHARE (from TADPOLE Challenge [48, 49]): https://github.com/tadpole-share/tadpole-algorithms
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