Alzheimer's disease (AD) is a neurodegenerative disorder common in the elderly population [1]. Patients develop mild cognitive impairment, which progresses to dementia. AD is characterized by gradual loss of brain cells, also known as brain atrophy, which can be detected through structural magnetic resonance imaging (sMRI) [2]. Genetic factors also play a significant role in disease development [3] and progression [4]. Genetic risk factors, such as single nucleotide polymorphisms (SNPs), help pinpoint mutations in the DNA that influence the pathophysiology [5] of AD. Most research disentangles AD mechanisms by studying the neural influence and genetic factors separately. However, separating the data modalities may provide an incomplete picture of the underlying biological process [6].
Imaging-genetics studies integrate neuroimaging and genetic data to improve disease prediction [7]. Imaging features are often derived from structural and functional MRI *Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI provided data but did not participate in analysis or writing of this report.
(s/fMRI), and genetic variants are typically captured by SNPs. Data-driven imaging-genetics methods can be grouped into four main categories: simple regression, nonlinear methods, correlation methods, and deep learning approaches. The first category uses linear models like SVM [8], [9] and Logistic Regression [10] for AD classification. However, these methods typically train on single data modality and fail to discover interactions between modalities. The second category leverages gradient boosting [11], [12] and decision trees [13] for multi-class classification. These models can encode nonlinear interactions between the features, but they fail to disentangle the neuroimaging and genetic pathways linked to AD. The third category uses correlation analysis to identify associations between genetic variations and quantitative traits [14], [15], [16]. However, these models do not incorporate clinical diagnosis directly. Thus, the biomarkers obtained through such analysis may not align with the predictive group differences. The last category relies on deep learning architectures to combine high dimensional, structured data for imaging-genetic analysis [17]. Deep learning frameworks are highly complex, lacking model explainablility. Recent work such as the Genetic and Multimodal Imaging data using Neural-network Designs (G-MIND) framework can identify predictive biomarkers of a disease from imaging and genetic modalities [18]. However, G-MIND performs classification and cannot accommodate the progression of AD severity.
We introduce a novel framework to combine Genetic and Imaging data using Rank-consistent mUltimodal multiclaSs network (GIRUS-net) that identifies neuroimaging and genetics biomarkers for AD diagnosis [18]. This work extends the G-MIND model and uses a rank-consistent ordinal regression module [19] to track disease severity from imaging and genetics data. Thus, GIRUS-net can identify biomarkers that are associated with the progressive representation of disease severity. GIRUS-net consists of an autoencoder coupled with an ordinal regression module. The encoders combine the imaging and genetics features into latent space and pass it through the ordinal regression module for disease severity prediction. We introduce a binary mask with binary concrete prior [20] as feature selection layer for biomarker detection. On a population study of AD, GIRUS-net yields sparser and more consistent biomarkers than baselines methods, while maintaining competitive classification performance.
Figure 1 illustrates our GIRUS-net framework. The inputs are the genotype data g n ∈ R G×1 for each subject n and the corresponding imaging features i n ∈ R I×1 . The class labels y n ∈ {1, 2, 3, 4} corresponds to different severity of AD: cognitive normal (CN), early mild cognitive impairment (EMCI), late mild cognitive impairment (LMCI), and mild Alzheimer's disease (AD). The diagnosis (phenotype) y n is known during training but not during testing.
We jointly model the imaging and genetic data using an autoencoder, coupled with an ordinal regression module.
a) Bayesian Feature Selection: The first layer of the encoder incorporates Bayesian feature selection using a learnable dropout layer. Unlike Bernoulli dropout where the underlying probability is fixed a priori, here we parameterize the dropout layer using Gumbell-Softmax distribution. The reparameterization trick relaxes the standard binary dropout to a continuous representation, which allows us to learn the posterior probability of the binary vectors. Mathematically, the subject specific dropout masks z m n are generated as:
(1) where m indexes the data modality, p m represents the underlying importance map, t captures the extent of relaxation from Bernoulli dropout, and u i n is a random vector sampled from U nif orm(0, 1) for stochasticity. During each forward pass and for every subject n, the network randomly samples z i n for imaging and z g n for genetics, respectively. The continuous representation of the dropout masks allow us to learn the underlying importance maps during training. We also incorporate a KL divergence loss KL(Ber(q)∥Ber(p m )) to enforce sparsity in p m . As seen in Eq. ( 1), higher values in p m are representative of the most selected features and can be identified as potential biomarkers.
The imaging and genetic features are passed through the learnable dropout layers to two separate encoders to obtain latent embeddings. These embeddings are then fused to leverage the common structure shared between both modalities. Mathematically, the fusion operation is
where E i (•), E g (•) denote the encoding operations for imaging and genetics. After fusion, the latent vectors ℓ n are passed through the decoders D i (•) and D g (•) to reconstruct the imaging and genetic data, ensuring that information is preserved during encoding. The reconstruction loss is an L 2 loss between the input and the reconstructed outputs:
(3
where B is the batch size, and λ 1 , λ 2 capture relative contribution of the loss terms.
Our auto-encoder is coupled with an ordinal regression module to predict the level of disease severity. The regression module ensures that the latent embeddings and the dropout masks learn discriminative information from the data. a) Rank Consistent Prediction: Our regression module consists of a sequence of fully connected layers which predicts the disease severity level from the latent embeddings. Mathematically, the prediction probabilities are calculated as
where ŷn is the predicted class label, Y(•) is the fully connected layers parameterized by W, and b k are separate biases associated with each severity level. To ensure rank consistency among prediction probabilities (i.e., P (ŷ n = k) > P (ŷ n = K + 1)), we need to ensure that b k > b k+1 . Previously, the work of [19] has shown that rank consistency can be achieved using multi-label cross entropy loss:
where B is batch size, y
is a binary multi-class vector generated from y n , and ŷn is the predicted label.
Combining Eqs. (1-5), the GIRUS-net loss function is:
where λ 1 , λ 2 capture the contribution of the reconstruction losses, λ 3 controls the contribution of ordinal loss and θ m captures the relative contribution of the sparsity penalties.
b) Prediction on New Data: During testing, the imaging and genetic data are multiplied by the dropout probabilities and passed through the encoder. The latent encoding then pass through the ordinal regression module for disease severity prediction. Disease severity is predicted by
The model parameters, {λ 1 , λ 2 , λ 3 , λ 4 }, are selected so that individual loss terms lie within the same order of magnitude. This criterion is model agnostic and does not require us to optimize them. We weighted each sparsity penalty by θ m to adjust for difference in number of features: θ i = number of Genetic Features number of Imaging Features , and θ g = 1. The learning rate and batch size are fixed based on validation performance in a 10fold cross validation setting. We perform grid search over learning rate ∈ [0.00001, 0.001] and batch size ∈ [8,128]. For all experiments, we fixed the Bernoulli probability to q = 0.0001, temperature t = 0.1, and batch size = 32. Model parameters were set to λ 1 = 0.0001, λ 2 = 0.001, λ 3 = 0.5, and λ 4 = 0.0001, where λ 1 , λ 2 , λ 3 were scaled to be on the same scale as sparsity penalty. Learning rate is 0.001 for 2class and 0.0005 for 3-class and 4-class experiments. Fig. 1 shows additional architecture details.
We compare GIRUS-net with four standard baseline models that operate on the concatenated data modalities, i.e.
x = [i T , g T ]. Hyperparameters are fixed using a grid search approach in a 10-fold cross validation setting.
a) Random Forest Classifier (RF): Random Forest is an ensemble method that constructs decision trees and average their outputs to provide a robust and accurate prediction. Feature importance is calculated as mean decrease in information gain [21] associated with each feature.
b) Support Vector Machine (SVM): Support vector machines create a hyperplane that maximally separates the data belonging to two different classes. Here, we extend the linear SVM by building K(K-1) 2 separate binary ºone vs. oneº classifiers to perform multi-class prediction [22]. We construct the feature importance map by taking the mean of the absolute values of weights of the linear kernels.
We train an ANN to perform classification based on input x. ANNs can model complex patterns from the data, but usually lack feature explainability, particularly for deeper networks. Thus, the feature importance maps are calculated post hoc using Shapley Additive Explanations [23].
d) Ordered Logit Model (O-Logit): O-Logit is a generalized linear model that performs ordinal regression [24]. Here, we learn a linear layer of weights w and bias b 1 • • • b K-1 . Similar to the implementation of GIRUS-net, we extended each label y n to K-1 labels, y
The predicted probability for the severity level are given by
We train O-Logit with the multi-label cross entropy loss in Eq. ( 5). We use the learned weights w as feature importances. We evaluate all the models for classification performance and biomarkers explainability. The biomarkers are identified by assessing the feature importance maps. For GIRUS-net, imaging and genetic feature importance maps are calculated from p i , p g and the classification predictions are the output of the ordinal regression branch.
a) Model Prediction Evaluation: We perform 10 repeats of stratified 10 fold cross validation. We evaluate the classification performance based on accuracy, f1-score (F1), Cohen's kappa (Kappa) [25], recall, and precision.
b) Feature Importance Evaluation: The feature importance maps are evaluated based on sparsity and consistency across classification task. We re-scaled the feature importance maps to [0, 1]. For all baseline methods, we scale imaging and genetic features importance maps collectively because imaging and genetic data are concatenated during training. For GIRUS-net, we scale the two feature maps separately as they come from separate branches of the model.
Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database [26]. The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment and early Alzheimer's disease.
The subjects in this study are included from the ADNI2/GO database. The subjects are classified as cognitive normal (CN), early mild cognitive impairment (EMCI), late mild cognitive impairment (LMCI), or mild Alzheimer's disease (AD) based on ADNI2 protocol. Table 1 summarizes the demographics of the 934 subjects, which contains both MRI and genetic data. The data are pre-processed and provided as a part of the TADPOLE challenge [27].
The T1-weighted MRI imaging data are collected using a 3T scanner. The data are processed with gradient non-linearity, B1 non-uniformity correction and peak sharpening [28]. This study uses cross-sectional cortical thickness as imaging features, which are extracted via Freesurfer [29]. The imaging features consists of 68 brain regions of interest (ROIs), with 34 features from the right hemisphere and 34 from the left, based on the Desikan-Killiany atlas [30]. As an additional preprocessing step, we normalize all testing, validation, and training imaging data with the mean and standard deviation of the training data.
b) Genetics Data: In parallel, genotyping was done with GenomeStudio v2009.1 (Illumina). Quality control was performed using PLINK, resulting in 141912 Linkage Disequilibrium (LD) independent SNPs. We subselect 1165 SNPs by thresholding the p-value p ≤ 0.001 based on an auxiliary genome-wide associated study data (GWAS) [31].
Fig. 2 quantifies the classification performance of all the methods across the three experimental setups. Compared to the baselines, GIRUS-net is consistently showing better, or comparable performance across all the performance metrics. The confusion matrices in Fig. 3 further show that the baseline models fail to handle class imbalance. Especially in 3-class and 4-class scenarios, the baselines tend to predict all subjects as the majority class(es). In comparison, GIRUSnet can successfully distribute its predictions across class labels. The improved performance suggests that GIRUS-net can extract discriminative patterns of disease severity.
The imaging and genetics biomarkers are identified by the mean feature importance maps across 10 repeats of 10-fold cross validations. As shown in Fig. 4, the baseline models rely mainly on one modality for diagnosis: imaging for RF, SVM, and ANN; genetics for Ordered Logit. In comparison, GIRUS-net puts equal importance on both the data modalities and extract a sparse set of biomarkers.
Additionally, the low importance scores demonstrate that these baseline methods fail to jointly extract discriminative information from both the data modalities. The superior performance of GIRUS-net suggests that the learnable dropout layers can selectively find brain and genetics biomarkers that are crucial for the downstream severity prediction.
We average the imaging feature importance maps learned from GIRUS-net across the three classification experiments. In Fig. 5, we plot top 10 regions onto the brain with colors corresponding to the value of feature importance. Our model identifies brain regions including lateral ventricle, medial temporal lobe, inferior temporal lobe, and parahippocampal gyrus. Correspondingly, AD is characterized by enlarged ventricles [32] and loss of tissue in inferior parietal gyrus [33] and parahippocampal gyrus [34]. Functionally, the hippocampus is crucial for episodic and spatial memory [35] which is affected by AD. Overall, GIRUS-net identifies brain regions with high association to AD in the literature.
Fig. 6 shows the mean of the genetic feature selection maps identified by the learnable dropout layer across the three classification experiments. A higher value indicates genetic variants containing discriminative information about all the classification tasks and are potential AD risk loci. We annotate the top 10 SNPs and their overlapping or affected genes as listed in The Ensemble Variant Effect Predictor and the GWAS Catalog [36], [37]. Our model identifies well established Alzheimer's risk factors such as TOMM40 [38] and APOE [39] with high feature importance. Using the GTEx database, we identify the set of brain tissues where the set of genes show high expression levels. Aside from APOE and TOMM40, we identify NDUFA4, which plays a regulatory role in the expression of synaptophysin in the hippocampus, and gene mutation could potentially lead to AD [40]. Aside from already established genes, several intergenic and non-coding SNPs are also selected with high feature importance by GIRUS-net . Their association to AD is unknown. The explainability study demonstrated that the genetic biomarkers identified by GIRUS-net aligns with research findings and may assist in future genetic analysis.
In this paper, we introduce GIRUS-net, a deep learning framework for multi-modal fusion, biomarker extraction, and severity prediction for AD. As compared to prior work, we introduce a rank-consistent ordinal regression module that extracts discriminative features that have a progressive effect on disease severity. In a population study of AD, GIRUSnet successfully integrates imaging-genetic data for disease severity prediction. Compared to standard baselines, GIRUSnet extracts consistent, distinctive, and clinically relevant information from imaging and genetic features across various complex diagnosis tasks. In addition, GIRUS-net is not tied to any specific data modality; the flexible design allows the user to combine diverse data modalities and provide a comprehensive view of various diseases.
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