Abstract
Amyotrophic Lateral Sclerosis (ALS) is a complex and rare
neurodegenerative disorder characterized by significant genetic,
molecular, and clinical heterogeneity. Despite numerous endeavors to
discover the genetic factors underlying ALS, a significant number of
these factors remain unknown. This knowledge gap highlights the
necessity for personalized medicine approaches that can provide more
comprehensive information for the purposes of diagnosis, prognosis, and
treatment of ALS. This work utilizes an innovative approach by
employing a machine learning-facilitated, multi-omic model to develop a
more comprehensive knowledge of ALS. Through unsupervised clustering on
gene expression profiles, 9,847 genes associated with ALS pathways are
isolated and integrated with 7,699 genes containing rare, presumed
pathogenic genomic variants, leading to a comprehensive amalgamation of
17,546 genes. Subsequently, a Variational Autoencoder is applied to
distil complex biomedical information from these genes, culminating in
the creation of the proposed Multi-Omics for ALS (MOALS) model, which
has been designed to expose intricate genotype-phenotype
interconnections within the dataset. Our meticulous investigation
elucidates several pivotal ALS signaling pathways and demonstrates that
MOALS is a superior model, outclassing other machine learning models
based on single omic approaches such as SNV and RNA expression,
enhancing accuracy by 1.7 percent and 6.2 percent, respectively. The
findings of this study suggest that analyzing the relationships within
biological systems can provide heuristic insights into the biological
mechanisms that help to make highly accurate ALS diagnosis tools and
achieve more interpretable results.
Keywords: ALS diagnosis, Pathway level analysis, Variational
autoencoder, Multi-omic integration
Graphical abstract
graphic file with name gr001.jpg
[37]Open in a new tab
Highlights
* •
An advanced machine learning-based multi-omic model was developed
to enhance the understanding of ALS mechanisms.
* •
MOALS combined 9,847 ALS-related genes with 7,699 rare variant
genes, creating a comprehensive dataset for precise analysis.
* •
Findings showed that unsupervised clustering exposed critical ALS
pathways, validating MOALS performance in gene analysis.
* •
The proposed model outperformed existing ML methods, with accuracy
improvements ranging from 1.7% to 6.2% in ALS prediction.
Nomenclature
ALS
Amyotrophic Lateral Sclerosis
MND
Motor Neuron Disease
FDA
Food and Drug Administration
GWAS
Genome-Wide Association Studies
ML
Machine Learning
FALS
Familial Amyotrophic Lateral Sclerosis
SALS
Sporadic Amyotrophic Lateral Sclerosis
RNA-seq
RNA Sequencing
mRNA
Messenger RNA
WGS
Whole Genome Sequencing
SNV
Single Nucleotide Variant
SHAP
Shapley Additive Explanations
iPCS
Induced Pluripotent Stem Cells
ATAC-seq
Assay for Transposase-Accessible Chromatin using sequencing
ChIP-seq
Chromatin Immunoprecipitation Sequencing
Hi-C
A method to study the three-dimensional architecture of genomes
MOALS
Multi-Omics for ALS
VAE
Variational Autoencoder
GRCh38
Genome Reference Consortium Human Build 38
bwa-mem2
Burrows-Wheeler Aligner-Maximum Exact Matches 2
GATK
Genome Analysis Toolkit
VEP
Variant Effect Predictor
FASTQC
Fast Quality Control
FDR
False Discovery Rate
BQSR
Base Quality Score Recalibration
[38]CE
Cross Entropy
MSE
Mean Squared Error
DEM
Deep Embedding Module
BCE
Binary Cross Entropy
SVM
Support Vector Machine
UMAP
Uniform Manifold Approximation and Projection
PCA
Principal Component Analysis
MTLR
Multi-Task Logistic Regression
GradNorm
Gradient Normalization
KEGG
Kyoto Encyclopedia of Genes and Genomes
ER
Endoplasmic Reticulum
UPR
Unfolded Protein Response
UPS
Ubiquitin-Proteasome System
STRING-db
Search Tool for the Retrieval of Interacting Genes/Proteins
database
TF-IDF
Term Frequency-Inverse Document Frequency
ROC
Receiver Operating Characteristic
AUC
Area Under the Curve
FCNN
Fully Connected Neural Network
RFR
Random Forest Regression
SVR
Support Vector Regression
RMSE
Root Mean Square Error
MAE
Mean Absolute Error
MedAE
Median Absolute Error
[39]R2
Coefficient of Determination
C-index
Concordance Index
IBS
Integrated Brier Score
CoxPH
Cox Proportional Hazards
AI
Artificial Intelligence
RNA
Ribonucleic Acid
1. Introduction
Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease that
causes Motor Neuron (MN) loss in the spinal cord and the motor cortex.
ALS, also known as Lou Gehrig's disease, leads to progressive
paralysis, muscular atrophy, and death. According to the US Centers for
Disease Control and Prevention, 12,000 to 15,000 Americans are thought
to have ALS [40][1]. About 10 percent ALS cases are familial while the
rest 90 percent are sporadic. Some monogenic drivers of familial ALS
include mutations in the genes C9orf72, SOD1, TARDBP, and FUS [41][2].
However, the pathogenesis of sporadic ALS still has no known genetic or
environmental cause. Familial and sporadic ALS patients have few
treatment options. Despite 30 years of clinical trials, only Rilutek
(riluzole), Radicava (edaravone), Relyvrio (sodium phenylbutyrate and
taurursodiol), and Qalsody (tofersen) have been approved by the FDA as
symptomatic treatments for ALS (in 1995, 2017, 2022, and 2023
respectively). Unfortunately, drug neither stops the disease nor
restores motor function [42][3].
In understanding the genetic complexities of Amyotrophic Lateral
Sclerosis (ALS), it is crucial to consider that known causative genetic
variants manifest predominantly in later life and account for only 10
percent of ALS heritability, leaving a large “missing heritability”
component that may be polygenic or even omnigenic in nature [43][4].
Addressing these issues requires a systems biology perspective that
considers disease as a dysfunction in biological modules or pathways.
Our research addresses these gaps by focusing on the biological
pathways disrupted in ALS, employing a two-step approach for mapping
genotypes to disease prevalence. In the first stage, genes were
clustered based on their expression profiles in specific brain and
spinal cord regions of ALS patients, compared to healthy controls. In
the second stage, germline mutations and gene expression data were
integrated into a general classifier using a multi-omics approach. Our
methodology introduces a novel diagnostic process for ALS, addressing
critical methodological challenges such as the limitations of
genome-wide association studies (GWAS) in capturing non-additive
genetic effects like epistasis. These findings open up avenues for
further research, particularly in the exploration of machine learning
models to capture the complexity of gene-gene interactions and the
potentially omnigenic nature of ALS.
Machine learning (ML) as a data-driven platform has played a
significant role in making progress in the diagnosis of many diseases,
including ALS. However, particularly for ALS, mainly single-omic
approaches have been used in ML models for diagnoses [44][4], [45][7],
[46][9], prognosis [47][12], mutation [48][11], subtyping [49][6],
biomarkers [50][10], pathway [51][5], biological identification
[52][13], and gene discovery [53][8]. Another ML approach RefMap
[54][14] uses iPCS cells, ATAC-seq, Histone ChIP-seq, Hi-C, and RNA-seq
for gene discovery. Further details about the mentioned studies and
their specific features have been summarized in [55]Table 1 (top).
Table 1.
Literature review of ML based methods for ALS (top) and other diseases
(bottom).
Ref Disease Omics Approach ML model Feature
[56][5] ALS mRNA expression Pathways Unsupervised hierarchical
clustering Classification SALS and control, Identification of common
pathogenic link between FALS and SALS
[57][6] ALS RNA-seq Subtyping Clustering Identification of
TARDBP/TDP-43 and retrotransposon expression two factors for ALS
[58][7] ALS Whole Genome Sequence Diagnosis Convolutional neural
network, Deep neural network Identification of ALS-associated promoter
regions, ALS classification
[59][8] ALS Protein–protein interaction data, gene function annotation,
known disease-gene associations Gene discovery knowledge-based machine
learning Gene prioritization for ALS
[60][9] ALS RNA expression Diagnosis Deep convolution neural networks
and Shapley Values ALS classification
[61][10] ALS Plasma samples Biomarker Random Forest Presenting very
high prediction rates for ALS diagnosis and prognosis
[62][11] ALS Whole Genome Sequence Mutation Unsupervised
machine-learning Identification of subset of common genetic variants
for ALS
[63][12] ALS Demographic, Family history, Genetic factor Prognosis
Probabilistic Causal Discovery Assess genetic factors association ALS
clinical progressions
[64][13] ALS Multichannel fluorescence microscopy data Biological
Identification Image-based deep learning Evaluation the impact of
stress on valosin-containing protein related to ALS
[65][14] ALS iPCS cells, ATAC-seq, Histone ChIP-seq, Hi-C, RNA-seq
Diagnosis Regional fine-mapping (RefMap) Identification of risk genes
related to ALS
[66][4] ALS Whole Genome Sequence Diagnosis capsule networks Disease
prediction from individual genotype profiles
__________________________________________________________________
[67][15] Cancer mRNA expression, DNA methylation, microRNA expression
Diagnosis Variational Autoencoder Implementation of multi-task platform
for cancer diagnosis
[68][16] Cancer, Alzheimer mRNA, DNA methylation, RNA expression
Biomarker Graph convolutional networks Identification of important
biomarkers
[69][17] Cancer mutations, copy number changes, DNA methylation, gene
expression Biomarker Graph convolutional networks Identification of new
cancer genes and their associated molecular mechanisms
[70][18] Cancer mRNA expression, DNA methylation, microRNA expression
Diagnosis Interpretable deep learning, Variational Autoencoder
Discovering of biomedical knowledge, cancer classification
[71][19] Cancer DNA methylation, gene expression Translation framework
Generative adversarial networks Omics-to-omics translation
[72]Open in a new tab
So far single-omic based approaches have led to significant progress in
ML-based diagnosis of ALS. For instance, [73][4] made a groundbreaking
advancement in ALS research by being the first to utilize capsule
networks on a whole-genome scale, achieving an unprecedented 86.9
percent predictive accuracy and illuminating ‘non-additive’ genes that
have previously remained obscured in linear models. On the other hand,
in an investigation developed by [74][9], the convolutional neural
networks and the Shapley Additive Explanations (SHAP) as a novel
paradigm shift by converting RNA expression values into pixel-based
images for analysis, yielding 80.7 percent accuracy and a level of
interpretability that allowed for the identification of
disease-critical genes. Moreover, a two-step deep convolutional neural
network approach utilized by [75][7] underscores the importance of
domain-specific architecture, offering a 77 percent accuracy rate in
ALS prediction and highlighting the value of incorporating prior
genomic knowledge into machine learning models. It should be mentioned
that single-omic techniques have their deficiency in terms of
integrating various methodologies, and they face challenges in
exploring genetic, biochemical, metabolic, proteomic, and epigenetic
mechanisms that are important underlying factors for ALS. To reach a
comprehensive presentation of various layers of regulation,
interconnected complexity and higher resolution picture in biological
systems, the multi-omic approach might be useful. To this end,
incorporation of multi-omic approaches within ML models provides a
powerful analytical option that is capable of finding patterns in dense
datasets for genomically heterogeneous and complex diseases [76][15],
[77][18], biomarker identification [78][16], [79][17], and other
applications [80][19].
In an interdisciplinary effort to address the prevailing challenges of
omics data analysis in the biomedical sector, we introduce a compendium
of state-of-the-art computational methods. For example, [81][18]
utilized the framework of XOmiVAE to address the pressing need for
explainability in deep learning applications, particularly in cancer
classification, by elucidating the contributions of individual genes
and latent dimensions. Complementing this, [82][17], introduced an
integrated EMOGI multi-omics pan-cancer data with protein–protein
interaction networks through graph convolutional networks, thereby
providing an accurate and interpretable model for predicting cancer
genes. In another study, [83][16], presented MOGONET offers
advancements in the realm of multi-omics integrative analysis,
excelling in both data classification and biomarker discovery across
disparate biomedical applications. To confront the challenges
associated with high-dimensional data and cross-omics translation
[84][15] and [85][19] implemented OmiEmbed and OmiTrans. This action
extended the boundaries of current computational capabilities. However,
all the mentioned efforts have been restricted to some specific ones to
cancers, and Alzheimer and ALS diagnosis by multi-omics approach still
has not been taken into account. Further details about the multi-omics
studies and their specific features in other diseases have been
reported in [86]Table 1 (bottom).
In this paper, for the first time, a multi-omics approach based on ML
for ALS diagnosis, first symptom and survival prediction is presented.
We use unsupervised clustering to provide an interpretable biological
processes on gene expression profiles to identify 9847 genes associated
with ALS pathways, which were then integrated with 7,699 genes that
include rare, predicted pathogenic genomic variants prioritized based
on biological knowledge. We use a variational autoencoder to capture
biomedical information in the integrated 17,546 genes. We named our
model Multi-Omics for ALS (MOALS). Our investigation detects several
ALS signaling pathways, and MOALS outperforms other existing ALS
classification models in accuracy.
In summary, the contributions of this paper are as follows:
* •
Acquiring and preprocessing whole genome sequencing (WGS) data to
extract and analyze single nucleotide variants (SNVs) based on
biological knowledge.
* •
Selecting features using a clustering algorithm for ALS
pathway-level analyses on mRNA transcriptomes.
* •
Combining the above two in a variational autoencoder learning
framework to predict ALS status, the age of first symptoms and
survival predictions.
2. Materials and methods
In this section, the followed methodology for feature selection, the ML
platform, and the pathways level analysis will be described. The
innovative platform named MOALS is designed for multi-omic data
processing activities. MOALS's workflow may be broken down into three
components: (1) Pre-processing and extraction of genes in ALS pathways
by clustering of gene expression profiles; To begin, transcriptome data
were pre-processed, and feature preselection was performed to identify
ALS pathway signaling and to eliminate noise in the expression data
which may degrade classification task performance. (2) Then, in the
variations extraction step, the single nucleotide variants (SNV) were
detected by the sequence alignment/map tools, and the variants were
prioritized based on the biological knowledge using bioinformatic
programs. Briefly, fastq raw data was aligned to human reference genome
(GRCh38) using bwa-mem2. SNVs, and small insertions and deletions
(indels) were then called using GATK (version 4.2.5.0). Next, SNVs and
small indels were annotated with gene information using VEP (Version
104.2). Finally, variants were filtered and ranked using custom
scripts. (3) Machine learning using Multi-omics data; The initial class
probability estimates from each single omic were used to compute
multi-omics integration using variational autoencoder based on
concatenating each omics layer. In the following sub-sections, detailed
explanations related to each part will be presented. The overview
scheme relating to each step has been depicted in [87]Fig. 1.
Figure 1.
[88]Figure 1
[89]Open in a new tab
The overview of the implemented method for ALS diagnosis.
2.1. Data acquisition and preprocessing
The sequencing (RNA and WGS) analyzed in this study from the Target ALS
cohort were obtained upon application to the New York Genome Center
with the data request. The selection of 672 cases, including 593 ALS
and 79 non-ALS cases, was based on the availability of high-quality
multi-omics data necessary for robust analysis. Due to the limited
availability of Control samples, we selected a robust model
specifically designed to effectively handle the non-balanced nature of
the data.
2.1.1. RNA-sequencing analysis
The raw RNA sequencing data was processed in-house according to the
following pipeline. We used FASTQC [90][20] to perform quality control
after obtaining the raw sequencing data in fastq format, with mean
quality value across each base location in the read and per-sequence
quality scores as the major criteria for data quality evaluation.
Kallisto [91][21] pseudo-aligned the sequences to the reference genome
of GRCh38 from Ensembl release 95 [92][22].
To conduct pathway analysis, GO annotations and homology information
was obtained from Ensembl BioMart database [93][23]. Enrichr [94][24]
was used to perform gene set enrichment analysis. For the pathway
analysis, we utilized the Kyoto Encyclopedia of Genes and Genomes
(KEGG), a comprehensive database resource that offers a systematic
understanding of biological functions and the interconnection of
various elements of the biological system. KEGG pathway annotations
were employed against the whole genome as a background reference to
identify statistically significant pathways. A false discovery rate
(FDR) cutoff 0.05 was used to select significantly enriched pathways.
2.1.2. Genomic variant extraction
Whole-genome sequencing (WGS) data, represented by raw fastq files,
were meticulously aligned to the GRCh38 reference genome, employing the
GATK best-practices workflow. This comprehensive workflow incorporated
BWA-MEM for alignment, Picard tools for annotating repetitive reads,
local realignment surrounding indels, and a base quality score
recalibration (BQSR) [95][25] to refine alignment accuracy.
Following the precise alignment, individual sample variant calling was
executed utilizing HaplotypeCaller. This was augmented by joint
genotyping and Variant Quality Score Recalibration to enhance the
reliability of variant identification. Subsequently, the generated
variants underwent rigorous annotation using Variant Effect Predictor
(VEP) [96][26] and bcftools [97][27] to delineate the variant's
potential impacts, focusing on those with predicted effects on
protein-coding sequences, as discerned through functional annotation.
Post annotation, a series of meticulous filtering steps were
instigated. This involved isolating variants associated with canonical
transcripts, recognized gene symbols, and variants demonstrating a
population allele frequency < 0.01 or those absent in large normal
populations [98][26]. With the acquired biological context from
extensive annotation, the variants were systematically scored and
ranked based on their predicted impacts, prioritizing variants such as
frameshift, stop gained, transcript ablation, stop lost, start lost,
transcript amplification, and splice donor and acceptor variants. These
were meticulously ranked with scores of 5, 3, and 2, to delineate their
relative significance. After evaluating all samples related to
patients, 7699 variants of interest were identified. The number of
repetitions for each variant in each individual were different. This
exhaustive and systematic approach ensured the meticulous
identification and evaluation of variants with profound functional
implications, enabling a holistic insight into the investigated genomic
landscapes.
2.2. Feature selection based on pathway-level analyses
Fuzzy k-means clustering is utilized as a central technique for
grouping mRNA gene expression data to discern intricate patterns
associated with Amyotrophic Lateral Sclerosis (ALS). Unlike traditional
k-means clustering, which assigns each data point rigidly to a single
cluster, fuzzy k-means permits a data point to belong to multiple
clusters with varying degrees of membership. This fuzziness is crucial
in revealing complex patterns in gene expression data, particularly in
cases where the boundaries between different expression levels are not
distinctly defined.
The primary advantage of using fuzzy k-means for gene expression
analysis is its ability to handle the inherent uncertainty and
variability in gene expression levels. This provides a nuanced and
comprehensive understanding of the underlying biological phenomena,
enabling more biologically meaningful interpretations of the
heterogeneous nature of mRNA transcripts associated with ALS. The
flexibility of fuzzy k-means is particularly relevant in addressing the
complex nature of neurodegenerative disorders such as ALS, thereby
facilitating more refined and precise analyses compared to conventional
clustering methods.
To enhance the description and reproducibility of our clustering
process, we detail our methodology as follows:
* •
Mathematical Formulation: The fuzzy k-means algorithm assigns
membership degrees using the formula shown in Equation [99](1):
[MATH:
uij=1∑k=1c(‖xi−vj‖‖xi−vk‖)2
m−1, :MATH]
(1)
where
[MATH:
uij :MATH]
is the membership degree of the i-th data point in the j-th
cluster,
[MATH: xi
:MATH]
is the i-th data point,
[MATH: vj
:MATH]
is the centroid of the j-th cluster, c is the number of clusters,
and m is the fuzziness parameter.
* •
Cluster Initialization: We employed the fuzzy k-means algorithm
with a specified range of cluster counts (6 to 12 clusters) to
determine the optimal granularity for our data.
* •
Cluster Optimization: The algorithm iteratively adjusts the cluster
centers based on a weighted average of the data points, where
weights correspond to the degree of belonging of each point to a
particular cluster. The process continues until the changes in the
cluster centers are minimal, ensuring convergence.
* •
Membership Degree Evaluation: Each gene's membership degree to the
cluster centers was evaluated to score and rank the genes based on
their centrality. This scoring influenced their subsequent
selection for pathway analysis.
* •
Statistical Evaluation: Ranked genes were analyzed through
pathway-level enrichment tests to determine their biological
significance, enhancing our understanding of ALS-associated
pathways.
By providing these additional details, we aim to improve the
transparency of our analytical approach and allow for better
reproducibility of our results by other researchers in the field.
2.3. Network architecture
The MOALS platform integrates a multi-task deep learning framework to
analyze multi-omics data, which is crucial for applications like ALS
classification, predicting the age at first symptoms, and survival
prediction. Central to this framework is the Deep Embedding Module
(DEM), which employs a Variational Autoencoder (VAE) to transform
high-dimensional multi-omics data into a meaningful, low-dimensional
latent space.
2.3.1. Variational Autoencoder (VAE) overview
The VAE is a cornerstone of our DEM, offering a robust method for
learning deep representations of complex datasets. Unlike traditional
autoencoders, VAEs introduce a probabilistic approach to encode inputs
into a latent (hidden) space. This approach not only helps in
compressing the data but also in generating new data points, hence
facilitating the modeling of complex biological phenomena.
Mathematical framework of VAE
In the VAE, each high-dimensional input vector
[MATH: x(i)∈Rd
:MATH]
from the multi-omics dataset
[MATH: D :MATH]
is mapped to a latent vector
[MATH: z(i)∈Rp
:MATH]
, where
[MATH: p≪d :MATH]
. The mapping is done through a probabilistic encoding process defined
by a distribution
[MATH: qϕ(z|x) :MATH]
, typically assumed to be Gaussian, as shown in Equation [100](2):
[MATH: qϕ(z|x)=N(z;μ(x),σ(x)2I<
mo stretchy="false">) :MATH]
(2)
where
[MATH: μ(x) :MATH]
and
[MATH: σ(x) :MATH]
are outputs from the encoder network, parameterized by ϕ, representing
the mean and variance of the latent distribution.
The VAE optimizes the parameters by maximizing the Evidence Lower Bound
(ELBO) to the logarithm of the likelihood of the data, as shown in
Equation [101](3):
[MATH: L(ϕ,θ;x(i))=Eqϕ(z|x(i))[logpθ(x(i)|z)]−DKL(qϕ(z|x(i))||p(z)) :MATH]
(3)
where
[MATH: pθ(x|z) :MATH]
is the probability of reconstructing x given z, modeled by the decoder
network with parameters θ, and
[MATH:
DKL
:MATH]
represents the Kullback–Leibler divergence, encouraging the encoded
latent variables to approximate a prior distribution
[MATH: p(z) :MATH]
, typically a standard normal distribution.
This ELBO component ensures that the VAE not only reconstructs the data
efficiently but also regularizes the learning process to avoid
overfitting, making the model robust to unseen data.
Implementation details
In our implementation, the VAE's encoder and decoder networks consist
of fully connected layers, with non-linear activation functions like
ReLU to introduce non-linearities into the model, crucial for capturing
complex patterns in the data. The encoder compresses the input into the
latent variables μ and σ, and the decoder reconstructs the input from
the latent representation sampled using the reparameterization trick,
as shown in Equation [102](4):
[MATH: z=μ+σ⊙ϵ,ϵ∼N(0,I) :MATH]
(4)
This step ensures that gradients can be backpropagated through the
stochastic sampling process, making the network trainable via standard
backpropagation techniques used in deep learning.
The integrated VAE module within the MOALS framework is pivotal for
reducing dimensionality and uncovering latent structures in complex
multi-omics data, facilitating downstream tasks such as classification
and regression with enhanced interpretability and accuracy.
The end-to-end downstream network of MOALS is capable of
classification, regression, and survival prediction. Employing the
method of multi-task training described in the next sections, every
downstream task that fits is possible to train individuals according to
one of these categories or in conjunction with other downstream tasks.
To perform classification-related downstream tasks, like (Control &
Target) type categorization, and site of motor onset classification, a
multilayer completely linked network. The categorization downstream
network's output dimensionality was set to the number of categories. An
analogous network was linked to the DEM for regression, but just one
neuron was maintained in the outlet layer to forestall the desired
scalar amount. There is a more complex downstream network for
predicting survival, which will be covered in greater detail in the
next section. To make this low-dimensional latent representation even
more regular, the downstream networks use the DEM to discover the omics
embeddings associated with certain downstream activities and use that
information in the module. Using downstream modules, from omics data, a
single good-educated multi-task MOALS network can rebuild a complete
diagnostic, predictive, and demographic profile.
2.3.2. Learning strategy
The joint loss function, like the overall structure, has two key
elements: the losses of deep embedding plus tasks in the downstream
sector. For every omics profile type,
[MATH: xj
:MATH]
is used to signify the input profile, and
[MATH:
xj′
:MATH]
is used to denote the reconstructed profile matching that input
profile, where M is different sorts of omics and the index is j. In
order to calculate the deep embedding loss, we use the formula provided
in Equation [103](5):
[MATH: Lemb<
mi>ed=1M<
/mi>∑j=1MBCE(xj,xj<
/mrow>′)+DKL(N(μ,σ)||N(0,I)) :MATH]
(5)
For comparison, BCE is the binary cross-entropy, while KL divergence
measures the difference between a learnt distribution and a standard
Gaussian one. A classification task's loss function is shown in
Equation [104](6):
[MATH: Lcla<
mi>ssification=CE(y,y
′) :MATH]
(6)
Suppose that the predicted label
[MATH: y′ :MATH]
is equal to the cross-entropy loss (CE), and that the true label y
represents the anticipated label. The regression task's loss function
is the same as the classification task's loss function, as shown in
Equation [105](7):
[MATH: Lreg<
mi>ression=MSE(y,y
′) :MATH]
(7)
In this case, MSE stands for the average squared difference between the
actual and predicted values.
MOALS was used to construct three training stages that made use of the
aforementioned loss mechanisms. This was a period in which the deep
embedding module was the exclusive focus, hence it was unsupervised in
the beginning. This training phase solely used backpropagation to
improve the deep embedding loss and only made minor adjustments to
those parameters based on the gradients. While the downstream networks
were being trained, the previously trained embedding network was fixed.
Only the downstream networks were updated during this phase, and the
total downstream loss was backpropagated.
2.3.3. Survival function strategy
The survival function, is defined as shown in Equation [106](8):
[MATH: S(t)=P[T>t] :MATH]
(8)
where T denotes the time elapsed during sample acquisition and the time
of event happening. The survival function demonstrates the probability
that the death (as the failure event) has not happened by time t. The
mentioned function can be measured via Equation [107](9):
[MATH: h(t)=limdt→0P[t≤T<t+dt|T≥t]dt
:MATH]
(9)
This shows the instantaneous frequency with which the unsuccessful
event occurs. High hazard numbers denote a high risk of death at the
time t indicated by the number. It is rare to use the original hazard
function in its original form; instead, the risk score for each sample
x is calculated by the following formula, as shown in Equation
[108](10):
[MATH: r(x)=∑i=1mh(ti,x) :MATH]
(10)
It is not only necessary to use the omics data x, a survival predicting
downstream network, as well as the event time T and the event
indication E. When a failure happened during the study, the indicator
was set to 1, and when it didn't, it was set to 0, a procedure known as
censoring. Time T is the interval between sample collection and the
subject's last contact in the case of censorship.
2.3.4. Multi-task learning
For application in the downstream task of survival prediction, the
MOALS architecture was modified from the multi-task logistic regression
(MTLR) model. Firstly, the time axis was split into m time intervals
[MATH: {li}i=1m :MATH]
. Time was taken into account as
[MATH: li=[ti−1,ti) :MATH]
, with
[MATH: t0=0 :MATH]
being zero and
[MATH:
tm≥max(T)
:MATH]
being the maximum allowed value. The hyperparameter m denotes the
number of time periods that are included in the calculation. Increased
precision comes at the expense of processing resources. A multi-layer
fully connected network underpins our survival prediction system, and
the output layer has the dimension of the number of time intervals.
Consequently, we get an m-dimensional vector
[MATH: y′=[y1<
/mrow>′,y2′,
...,y<
/mrow>m′] :MATH]
from our survival prediction network. At time point
[MATH: ti
:MATH]
, the survival label for each subject was kept as an m-dimensional
vector
[MATH: y=[y1,y2,...,<
mi>ym] :MATH]
, with name
[MATH: yi
:MATH]
denoting the subject's survival status. Sample x has the following
conditions, and the probability of finding y with the network
parameters θ is formulated by Equation [109](11):
[MATH:
Pθ(y|x)=exp(∑i<
mo linebreak="badbreak"
linebreakstyle="after">=1myiyi′)∑j=0mexp(∑i<
mo linebreak="badbreak" linebreakstyle="after">=j+1myi′) :MATH]
(11)
The goal of this survival network is to find a set of variables θ that
maximizes log-likelihood; consequently, the loss function for the
survival prediction function is written as shown in Equation [110](12):
[MATH: Lsur<
mi>vival=−∑i=1myi<
msubsup>yi′<
/mrow>+log
∑j=0mexp(∑i=j+1myi′) :MATH]
(12)
It can be implemented straight to the survival component and is
incorporated into MOALS's joint loss function. As an alternative to
training each downstream network in MOALS separately, several
downstream networks in MOALS simultaneously trained using the joint
loss function of the downstream tasks. This resulted in an integrated
model capable of reconstructing a comprehensive phenotypic profile for
each individual, as shown in Equation [111](13):
[MATH: Ldow<
mi>n=1k<
/mi>∑k=1KWk<
mrow>Ldow<
msub>nk :MATH]
(13)
The loss associated with each function is denoted by the letter
[MATH: Ldownk :MATH]
, and the weight is indicated by the
[MATH: Wk :MATH]
that might be explicitly set as hyperparameters or utilized as
trainable parameters during the training procedure. The last step
required calculating and backpropagating the total loss function
defined in Equation after pre-training the embedded and downstream
networks independently [112](13). During this last training step, the
whole MOALS network, including the DEM and downstream task, was
fine-tuned to maximize performance.
The multi-task optimization approach gradient normalization (GradNorm)
is adjusted to presented MOALS architecture to balance the optimization
of varied workloads. The weights for each downstream loss are different
for each training iteration. When a task's gradients are either too
large or too little, GradNorm penalizes the network, ensuring that all
tasks learn at a consistent rate. For starters, the gradient norm of
each subsequent job is derived using the Equation [113](14):
[MATH: Gθ(k)=‖▽ΘWk<
mrow>Ldow<
msub>nk‖2 :MATH]
(14)
In witch θ is the parameters of the DEM of MOALS's last encoding layer
are. The mean gradient norm for all tasks can therefore be determined
as shown in Equation [114](15):
[MATH: Gθ¯=1k<
/mi>∑k=1KGθ(k) :MATH]
(15)
where K represents the number of subsequent tasks. The following
definition applies to each task's relative inverse training rate, as
shown in Equation [115](16):
[MATH: rk=L˜downk1k∑k=1KL˜downk :MATH]
(16)
where
[MATH: L˜downk=Ldow<
msub>nk/Ldow<
msub>nk<
/mrow>0 :MATH]
which it is the difference between the current loss and the loss the
downstream task k experienced initially. In that case, the GradNorm
loss is defined as follows in Equation [116](17):
[MATH: Lgra<
mi>d=∑k=1K|Gθ<
/mrow>(k)−Gθ¯×rkα|1 :MATH]
(17)
where α is the hyperparameter corresponding to the strength required to
reduce tasks to a common training rate. During each training iteration,
a separate backpropagation process was run on
[MATH: Lgrad :MATH]
, which was utilized only to update
[MATH: Wk :MATH]
.
2.4. Models' training and evaluating procedure
In this section, a brief description of the MOALS is presented as our
proposed algorithm. MOALS implements PyTorch's deep learning library
for a multi-omics ALS prediction. During the training and testing of
the presented platform, the separation was conducted in a stratified
manner to keep the proportion of each class; five-fold cross-validation
of the train-validate data optimized the developed architecture and
other hyperparameters for MOALS. Moreover, accuracy, precision, recall,
and f1-score were selected as three different metrics to evaluate the
performance of the proposed algorithm. It should be mentioned that the
network architecture is fully connected through all layers. Besides, in
this paper, shallow machine learning models also have been considered.
The findings prove that there is essential to implement a deep network
to obtain a significant recall. Also, the GradNorm algorithm is applied
to optimize the network parameters with an initial learning rate of
0.02 and a decay of 2e-4. In a batch size of 32 and in over 200 epochs,
the optimization process was conducted. The hyperparameters used to
train this model were listed in [117]Table 2.
Table 2.
Hyper-parameters used in the model.
Hyper-parameter Value
Latent dimension 128
Learning rate 1e-3
Batch size 32
Epoch number—unsupervised 50
Epoch number—supervised 100
[118]Open in a new tab
With respect to multi-omics approaches and for each omics individually,
the platform's network architecture is optimized. It should be noted
that as well as for multi-omics one, variables are optimized separately
for each omic. Next, MOLAS is applied to the test data to determine the
performance of our approach. However, it should be highlighted that,
for these samples, the authors utilize the candidate genes and the
whole gene expression data individually. Moreover, a GPU with a
12-gigabyte capacity was utilized in this paper to develop and test the
proposed algorithm.
2.5. A comprehensive comparison between different machine learning methods
By considering test data during the assessment of MOALS, its
functionality has been evaluated with other algorithms. Three different
algorithms (SVM, random forest, and fully connected neural network)
were taken into account for mentioned comparison. To conduct a
dimension reduction, UMAP and PCA have been utilized for each mentioned
algorithm. Then, a cross-validation method is implemented to optimize
hyperparameters, and finally, the performance of examined dataset is
presented. To explore a non-linear boundary and consequently maximize
the margin between two different clusters, SVM, as a well-known binary
classification method is implemented. Also, a radial basis function is
implemented as SVM kernel and its coefficient is equal to 0.001.
Moreover, it is useful to highlight some points related to features of
the random forest algorithm. This algorithm is so popular, too. It is
an applied machine learning method that generates multiple decision
trees and blends their individual categories to reach a final
classification. A higher accuracy has a tight relationship with the
number of decision trees. However, increasing the number of trees has a
negative impact on the training time and decreases the train speed. In
the current study, 100 trees are implemented with a maximum depth of 5
and at most 100 features.
The neural network that is one of the implemented algorithms that has
been selected to carry out a comparison between its performance with
our proposed algorithm includes a series of fully connected layers that
connect every neuron in one layer to another one in the other layer.
The structure agnostic is the most significant feature of this method.
In fact, in this method, no special perception is needed in the input
data. In the current study, three hidden layers with ‘relu’ activation
function apart from input and output layers are implemented.
With considering three different assumptions about the data in the
algorithm, a dimension reduction method (UMAP) that has been founded
based on them is implemented in this investigation. It should be
mentioned that the data is uniformly distributed on the Riemannian
manifold; The mentioned metric is approximately fixed and locally
connected with respect to its position. After considering all mentioned
points, it is possible to apply a fuzzy topological structure in order
to simulate the manifold. Searching for a low-dimensional projection of
the data that has the nearest direction equivalent to the fuzzy
topological structure. It should be emphasized that 10 and 0.05 are
defined for the values of the number of neighbors and the minimum
distance, respectively.
PCA can significantly capture the variation present in the data with
fewer parameters and provides information on the whole structure of the
evaluated dataset. This action is conducted by the mentioned algorithm
using linear combinations of parameters to synthase orthogonal axes. In
the current manuscript, four components are considered as variables for
generating the orthogonal axes.
3. Results and discussion
3.1. Identification of ALS pathway correlated genes
We performed unsupervised clustering on the RNA expression profiles to
discover groups of genes with similar expression patterns in ALS
samples relative to healthy controls. The main objective of this
clustering was not solely to pinpoint genes directly associated with
ALS but to explore a broader spectrum of biological pathways
potentially contributing to ALS pathogenesis. This comprehensive
approach aids in understanding the complex network of interactions and
the potential overlapping pathways that could influence ALS and other
neurodegenerative diseases.
For each cluster of genes identified by the algorithm, we conducted a
pathway enrichment analysis. This analysis crucially allows us to
identify not just the direct pathways like ALS but also other
significant pathways that might be mechanistically linked. These
include pathways related to neurodegeneration, cellular stress
responses, and protein homeostasis, which are vital for understanding
the broader biological context of ALS.
We tested different numbers of clusters (6-12) for clustering of gene
expression, finding that irrespective of the number of clusters, at
least one cluster was consistently associated with ALS. This not only
demonstrates the robustness of our clustering approach but also
supports the hypothesis that molecular signatures of ALS are strongly
represented in the dataset. To visually represent this, we extracted
genes that appeared in any detected ALS KEGG pathways enriched clusters
and identified 9847 genes for downstream analysis.
It is important to note that our clustering approach also highlighted
other pathways with even more significant p-values, such as
Endocytosis. This finding underscores the multi-faceted nature of
neurodegenerative diseases where multiple biological processes are
often interconnected. The identification of pathways like Endocytosis
with better p-values than ALS itself suggests potential upstream or
parallel processes that could influence or be influenced by ALS
pathology.
The Endocytosis pathway plays a crucial role in cellular homeostasis by
mediating the internalization and recycling of cell surface receptors,
lipids, and other molecules. Dysregulation in endocytosis has been
implicated in the pathogenesis of neurodegenerative diseases, including
ALS [119][28]. In ALS, defective endocytosis could lead to impaired
clearance of misfolded proteins and other cellular debris, contributing
to neuronal damage. This pathway's significance in ALS is underscored
by its strong association with other neurodegenerative processes,
suggesting that alterations in endocytic trafficking may be a common
mechanism in ALS and other neurodegenerative disorders.
The endoplasmic reticulum (ER) is critical for proper protein folding
and processing. In ALS, mutations in proteins involved in ER stress
response, such as VAPB, have been shown to disrupt ER homeostasis,
leading to the accumulation of misfolded proteins and triggering the
unfolded protein response (UPR) [120][29]. Persistent UPR activation
can lead to neuronal apoptosis, contributing to the progressive loss of
motor neurons observed in ALS patients. The identification of this
pathway emphasizes the importance of protein homeostasis in ALS and
highlights potential therapeutic targets aimed at modulating ER stress
responses.
Ubiquitin-mediated proteolysis is essential for the degradation of
damaged or misfolded proteins via the ubiquitin-proteasome system
(UPS). In ALS, disruptions in UPS have been reported, leading to the
accumulation of ubiquitinated protein aggregates in motor neurons, a
hallmark of the disease. This pathway's involvement in ALS is supported
by the frequent observation of ubiquitin-positive inclusions in
post-mortem ALS tissues. Understanding how ubiquitin-mediated
proteolysis is compromised in ALS could provide insights into disease
mechanisms and inform strategies to enhance protein clearance in
affected neurons [121][30].
Autophagy is a cellular process involved in the degradation and
recycling of damaged organelles and proteins. In ALS, autophagy
dysfunction is believed to contribute to the accumulation of toxic
proteins and organelles in motor neurons. Enhancing autophagy has been
proposed as a potential therapeutic strategy for ALS, aimed at reducing
the burden of protein aggregates and promoting neuronal survival. The
identification of the autophagy pathway in our analysis reinforces its
critical role in ALS and provides a rationale for exploring autophagy
modulators as potential treatments [122][31].
The overlap between ALS and other neurodegenerative diseases, such as
Huntington's, Parkinson's, and Alzheimer's, suggests shared pathogenic
mechanisms. Common features include the accumulation of misfolded
proteins, mitochondrial dysfunction, and oxidative stress. The
identification of these pathways in ALS patients supports the
hypothesis that ALS may share molecular pathways with other
neurodegenerative conditions. This cross-disease perspective could lead
to the development of broad-spectrum therapeutics targeting these
shared mechanisms [123][32].
Moreover, the implications of these pathways extend beyond ALS,
potentially illuminating common mechanisms underlying other
neurodegenerative diseases such as Alzheimer's, Parkinson's, and
Huntington's diseases. The disruption of cellular trafficking in the
Endocytosis pathway, the imbalance in protein processing, and the
failure of protein clearance mechanisms observed in ubiquitin mediated
proteolysis are not only pivotal to ALS but are also critical
components in the pathology of these other diseases [124][33]. This
suggests a shared pathological framework, where targeting these
pathways could lead to broad-spectrum therapeutic strategies for
multiple neurodegenerative disorders. By identifying and understanding
these interconnected pathways, our study contributes to a holistic view
of neurodegeneration, offering insights that could inform cross-disease
therapeutic approaches.
[125]Table 3 delineates the Enrichr-derived analyses results,
illustrating a substantial association between the submitted gene list
and the ALS pathway, underscored by a highly significant p-value of
[MATH: 1.27×10−21 :MATH]
and an adjusted p-value of
[MATH: 2.02×10−19 :MATH]
. This statistical significance minimizes the likelihood of the
association emerging by random chance, reinforcing the credibility of
the biological linkage inferred. Additionally, the Odds Ratio of 2.94
elucidates that the genes within our investigated list are
approximately three times more probable to align with the ALS pathway
than expected by chance, with the combined score of 141.56 further
attesting to the robustness and overall significance of this
association.
Table 3.
The results of ALS signaling pathways obtained by MOALS.
Name P-value Adjusted p-value Odds Ratio Combined score
Endocytosis 2.35E-24 7.48E-22 4.28 232.93
Amyotrophic lateral sclerosis 1.27E-21 2.02E-19 2.94 141.56
Protein processing in endoplasmic reticulum 9.79E-21 1.04E-18 5.35
246.54
Ubiquitin mediated proteolysis 1.38E-19 1.10E-17 6.38 277.09
Huntington disease 4.26E-17 2.72E-15 2.79 105.35
Pathways of neurodegeneration 6.55E-17 3.48E-15 2.23 83.14
Parkinson disease 1.63E-15 7.41E-14 2.96 100.94
Autophagy 3.14E-15 1.17E-13 4.71 157.32
Spinocerebellar ataxia 3.30E-15 1.17E-13 4.5 150.16
Prion disease 8.63E-12 2.48E-10 2.38 60.55
Thermogenesis 9.34E-12 2.48E-10 2.57 65.37
Alzheimer disease 8.40E-11 2.06E-09 2.01 46.59
[126]Open in a new tab
Conversely, [127]Table 4 encapsulates the insights gained from
STRING-db, revealing that 96 out of the 352 genes analyzed are
implicated in ALS, with a significant association strength of 1.73.
This table corroborates the insights from Enrichr by demonstrating a
significant association, further emphasized by an exceptionally minimal
false discovery rate (FDR) of
[MATH: 5.52×10−154 :MATH]
, ensuring an exceptionally high level of confidence in the accuracy
and relevance of this association. The extraordinary significance of
the FDR consolidates the validity of the biological connection inferred
between the analyzed gene network and ALS.
Table 4.
The results of ALS signaling pathways for first hundred candidates'
genes obtained by MOALS.
Pathway Description Count in Network Strength False discovery rate
hsa03050 Proteasome 20 of 43 1.96 9.63e-30
hsa05014 Amyotrophic lateral sclerosis 96 of 352 1.73 5.52e-154
hsa04136 Autophagy - other 7 of 29 1.67 1.18e-08
hsa05017 Spinocerebellar ataxia 31 of 135 1.65 6.29E-39
hsa05012 Parkinson disease 45 of 240 1.56 1.02E-54
hsa05020 Prion disease 48 of 265 1.55 4.51E-58
hsa05016 Huntington disease 52 of 298 1.53 1.05E-62
hsa05010 Alzheimer disease 56 of 355 1.49 6.77E-66
[128]Open in a new tab
In consolidating the insights from [129]Table 3, [130]Table 4, it is
apparent that both Enrichr and STRING-db analyses converge on a similar
conclusion, highlighting a significant association between the examined
gene entities and the ALS pathway. Enrichr provides a comprehensive
perspective on the statistical and biological significance of the gene
list in the context of ALS, while STRING-db accentuates the interactive
networks among the genes, reinforcing the biological relevance of the
findings. The convergence of these analyses not only strengthens the
inferred association between the analyzed entities and ALS but also
propels our understanding forward, opening avenues for exploring the
intricate molecular mechanisms underlying ALS.
[131]Fig. 2 displays a UMAP-based scatter plot visualizing terms from
the KEGG 2021 Human gene set library extracted from the fuzzy k-means
clustering algorithm. Terms, represented by points, are plotted on the
first two UMAP dimensions, clustered by the Leiden algorithm based on
computed TF-IDF values, allowing similar gene sets to be grouped
together. Larger, black-outlined points signify terms significantly
enriched, particularly relating to ALS, Parkinson's, Alzheimer's, and
neurodegeneration pathways.
Figure 2.
[132]Figure 2
[133]Open in a new tab
The scatter plot to demonstrate disease classification based on KEGG
conducted by MOALS.
Next, genes were ranked according to their degree of interconnection
(STRINGdb), and their association with ALS. STRINGdb detects
statistically significant associations between a list of input genes
and known biological pathways, and for this analysis, KEGG pathways
with adjusted p-values less than 0.05 were selected.
Based on current literature relating to the molecular pathways of ALS,
these pathways demonstrate a remarkable degree of association. The
input genes selected during the first phase of our analysis have more
interconnection among each other than what normally would be expected
for a random set of genes of the same size. This enrichment depicts
that the mentioned parameters are at least tendentiously biologically
interconnected as a group. Also, to show all the interconnection
between ranked genes and argue on it, [134]Fig. 3 has been illustrated.
As can be seen in the mentioned figure, five different clusters have
been detected related to ALS and other neurodegenerative diseases. The
figure shows the first 100 ranked genes (as nodes) that have been
connected by 604 edges. Between every two nodes, one or several edges
have been recognized which are classified by some colors. Besides,
co-expression that has been colored in black identifies which genes
have a tendency to show a coordinated expression pattern across a group
of genes.
Figure 3.
[135]Figure 3
[136]Open in a new tab
The clustering illustration of the first hundred candidates' genes by
MOALS. Image 1 , Image 2 , Image 3 , Image 4 , Image 5 , Image 6 ,
Image 7 , Image 8 , Image 9 , Image 10 .
3.2. Explaining multi-omics integration results
An in-depth analysis was conducted to distinguish between ALS and
healthy cases using single and multi-omic data, focusing explicitly on
either RNA expression data or SNV data. To evaluate the stability and
performance consistency of the classification models, a comprehensive
five-fold cross-validation analysis was performed. The results,
illustrated in [137]Fig. 4, include boxplots for accuracy, precision,
recall, and F1-score across the validation folds, stratified by the
classification methods and omic data types—Gene Expression, SNV, and
their combination. Additionally, 95% confidence intervals were
calculated for each performance metric, providing a more accurate
representation of variability across folds. The effect sizes (Cohen's
d) were also computed to assess the practical significance of the
observed differences between ALS and control groups, with values
ranging between 0.87 and 1.16. This range indicates a medium to large
effect size, underscoring the practical relevance and robustness of the
classification models in effectively distinguishing between ALS and
healthy cases.
Figure 4.
[138]Figure 4
[139]Open in a new tab
5-Fold cross-validation results for multiple classification methods on
omics data.
Key observations from the boxplots include notable fluctuations in
model performance metrics which may indicate variability in model
robustness or adaptive responses to the integration of multi-omic data.
These detailed distributions provide deeper insights into the
predictive stability of each method beyond the mean performance metrics
typically reported. Notably, the MOALS method consistently demonstrated
superior performance across all metrics, particularly in the Gene
Expression + SNV category, where it achieved the highest median scores
and showed relatively tight interquartile ranges, indicating less
variability and higher reliability in comparison to other methods.
Relating these insights to the consolidated results presented in
[140]Table 5, it is evident that the tabulated data encapsulates the
average performance metrics from the cross-validation exercise. While
the table effectively compares the methodological efficacies, the
boxplots enrich this comparison by detailing the range and consistency
of performance across multiple experimental runs, thus offering a
holistic view of each method's efficacy and reliability. The standout
performance of MOALS, as highlighted in the cross-validation plots,
underscores its robustness and underscores its potential as a highly
effective tool for integrating multi-omic data in the classification of
ALS.
Table 5.
Classification results based on six classification methods applied by
single omic and multi-omics approaches.
Gene Expression
__________________________________________________________________
SNV
__________________________________________________________________
Gene Expression + SNV
__________________________________________________________________
Accuracy Precision Recall F1-score Accuracy Precision Recall F1-score
Accuracy Precision Recall F1-score
UMAP+SVM 0.7564 0.7663 0.7438 0.7573 0.7367 0.7415 0.7273 0.7368 0.7846
0.7938 0.7743 0.7847
PCA+SVM 0.7406 0.7562 0.7305 0.7497 0.7252 0.7369 0.7161 0.7234 0.7796
0.7816 0.7653 0.7713
UMAP+RF 0.7761 0.7812 0.761 0.7704 0.7589 0.7612 0.7414 0.7598 0.801
0.8116 0.792 0.8002
PCA+RF 0.7656 0.7729 0.759 0.7645 0.7414 0.7599 0.7371 0.7486 0.79
0.8019 0.7809 0.7971
UMAP+FCNN 0.7824 0.7979 0.7702 0.7864 0.7628 0.7749 0.7561 0.7618
0.8183 0.823 0.8076 0.8176
PCA+FCNN 0.7564 0.7663 0.7438 0.7573 0.7367 0.7415 0.7273 0.7368 0.7846
0.7938 0.7743 0.7847
VAE+ FCNN 0.8048 0.8176 0.7965 0.8035 0.7706 0.7826 0.7638 0.7762
0.8505 0.8476 0.8255 0.8371
MOALS 0.8485 0.8374 0.8566 0.8214 0.9206 0.9186 0.9148 0.9211
[141]Open in a new tab
The comparative analysis delineates the performance of various
dimensionality reduction techniques when coupled with machine learning
classifiers, specifically in the context of Gene Expression data, SNV
data, and their integration. Performance is quantified via accuracy,
precision, recall, and F1-score, offering a comprehensive evaluation of
each method's efficacy.
Upon examining the performance of UMAP with SVM (UMAP+SVM), one
observes a moderate level of accuracy at 0.7564 for Gene Expression
data, precision at 0.7663, recall at 0.7438, and an F1-score of 0.7573.
This suggests a balanced classification capability. However, the
application of this combination to the integrated dataset yields
improved results, with the accuracy and F1-score elevating to 0.7846
and 0.7847, respectively. However, an intriguing enhancement in
performance is observed when SVM is applied to the integrated Gene
Expression and SNV dataset, suggesting that SVM classifiers benefit
from a richer feature space that encapsulates a more diverse biological
signal.
The PCA+SVM combination, while similar in approach to UMAP+SVM, records
a slightly reduced accuracy of 0.7406 and an F1-score of 0.7497 for
Gene Expression data. The metrics for the combined dataset are
marginally lower than those for UMAP+SVM, with an accuracy of 0.7796
and an F1-score of 0.7713, reaffirming UMAP's superior feature
extraction capability for SVM classifiers.
Moving to ensemble methods, UMAP paired with Random Forest (UMAP+RF)
shows an appreciable accuracy of 0.7761 and an F1-score of 0.7704 for
Gene Expression data, which is a marked improvement over SVM-based
methods. The amalgamation of Gene Expression and SNV data under UMAP+RF
further improves accuracy to 0.8010 and the F1-score to 0.8002,
suggesting an efficient harnessing of combined data features.
For neural network-based classifiers, UMAP+FCNN displays notable
efficacy, particularly in the integrated dataset, where the accuracy
reaches 0.8183 and the F1-score climbs to 0.8176. This combination
outperforms all other non-neural network classifiers, indicating FCNN's
superior ability in modeling complex data interactions. A substantial
leap in performance is evident with VAE+FCNN, especially for the
integrated dataset, where the accuracy surges to 0.8505 and the
F1-score to 0.8371. This indicates the VAE's powerful feature
extraction capability in conjunction with FCNN's classification
strength.
The standout performer, MOALS, which incorporates a clustering
algorithm for feature selection followed by VAE+FCNN for
classification, achieves the highest accuracy of 0.9206 and an F1-score
of 0.9211 in the integrated dataset. These metrics are considerably
higher than those of other methods, underscoring the profound impact of
feature selection through clustering in enhancing classifier
performance. The Multi-Omics Analysis with Latent Structures (MOALS)
approach, integrating the clustering algorithm with VAE+FCNN, showcases
the pinnacle of classification performance. This technique's robustness
is evidenced by the top-tier metrics across all evaluated categories in
the combined dataset. MOALS effectively narrows down the feature space
to the most discriminative gene sets, which evidently facilitates a
more refined and targeted classification process.
[142]Fig. 5 illustrates the Receiver Operating Characteristic (ROC)
curves for various classification methods, with a focus on the
integrated Gene Expression and SNV dataset. The Area Under the Curve
(AUC) is a critical metric for evaluating the performance of
classifiers, as it provides a single scalar value to compare models.
Among the methods evaluated, MOALS achieved the highest AUC of 0.91,
indicating superior discriminatory power in distinguishing between ALS
and control cases. This performance further solidifies the MOALS
approach as the most effective model in our study, outperforming other
deep learning and traditional machine learning models. The VAE+FCNN
model, while performing well, recorded a lower AUC of 0.84, followed by
UMAP+FCNN at 0.82, reinforcing the advantages of multi-omics data
integration combined with the MOALS methodology. The remaining models
exhibited moderate performance, with AUC values ranging from 0.78 to
0.80, highlighting the impact of model selection and data integration
strategies on predictive accuracy.
Figure 5.
[143]Figure 5
[144]Open in a new tab
AUC-ROC curve for ALS classification using multi-omics (Gene Expression
+ SNV).
[145]Fig. 6 presents a comparison of ROC curves between the MOALS model
using single-omic data (Gene Expression) and the MOALS model using
integrated multi-omic data (Gene Expression + SNV). The results clearly
indicate that the multi-omic approach significantly outperforms the
single-omic approach, as evidenced by the higher AUC value (0.91 for
multi-omic vs. 0.83 for single-omic). This highlights the substantial
improvement in classification accuracy that can be achieved by
incorporating diverse data types, thus providing a more comprehensive
understanding of the underlying biology in ALS.
Figure 6.
[146]Figure 6
[147]Open in a new tab
ROC curve comparison for ALS classification using MOALS with
single-omic (Gene Expression) and multi-omic (Gene Expression + SNV)
data.
In conclusion, the study underscores the crucial role of integrating
multi-omic data with dimensionality reduction and machine learning
techniques in analyzing complex biological data. The findings highlight
how deep learning, when combined with advanced dimensionality reduction
strategies and multi-omic integration, can effectively reveal the
subtle biological dynamics underlying complex diseases like ALS, paving
the way for breakthroughs in precision medicine.
An in-depth analysis was conducted to distinguish between ALS and
healthy cases using single and multi-omic data, focusing explicitly on
either RNA expression data or SNV data. To elucidate the superiority of
MOALS, a comprehensive comparison with existing models such as
PCA+FCNN, UMAP+FCNN, and other commonly utilized models in ALS research
is provided. This comparison extends beyond performance metrics to
include methodological differences, highlighting how MOALS's
integrative approach to multi-omics data provides a more robust and
accurate prediction model. Specifically, the integration of clustering
algorithms and VAE+FCNN allows MOALS to effectively handle the
heterogeneity and complexity of multi-omic data, leading to improved
prediction accuracy and reliability.
The use of advanced dimensionality reduction techniques combined with
deep learning architectures differentiates MOALS from traditional
models that may not fully exploit the potential of integrated
multi-omic datasets. Furthermore, the implementation of
cross-validation in MOALS is detailed, explaining how this was adapted
to manage the complexities of multi-omic data, including the
stratification of data across different omic types to ensure that the
validation process is robust and reflects the true predictive power of
the model.
These methodological advancements are crucial for understanding why
MOALS performs better than other models, as it not only leverages
genetic information but also incorporates epigenetic, transcriptomic,
and proteomic data, providing a holistic view of the disease pathology.
In summary, the innovative approach of MOALS sets a new standard in the
field by not just incrementally improving over existing models but by
redefining what is possible in the prediction and understanding of
complex diseases like ALS.
Our findings suggest that the MOALS model, with its superior diagnostic
accuracy and robustness in integrating multi-omic data, could be
effectively incorporated into existing clinical diagnostic pathways for
ALS. Specifically, we propose that the model be used as a complementary
tool alongside traditional clinical tests, such as neuroimaging and
electrophysiological studies, to enhance diagnostic precision. By
incorporating MOALS into the diagnostic workflow, clinicians may
achieve faster and more accurate identification of ALS, enabling
earlier intervention and potentially improving patient outcomes. This
integration could also lead to more efficient utilization of healthcare
resources by reducing the need for multiple confirmatory tests, thereby
streamlining the diagnostic process. Furthermore, the predictive power
of MOALS extends beyond diagnosis; it also demonstrates a significant
capability in related predictive tasks, such as estimating the onset
age of ALS symptoms and survival prediction.
[148]Fig. 7 provides a comprehensive display of regression lines and
diagnostic accuracy for various models. In the regression plots, the
MOALS model is distinguished by achieving the highest
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value of 0.78, indicating a strong linear correlation and capturing
about 78% of the variance in age data. This high
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value highlights MOALS' superior capability in integrating complex
multi-omic data, which significantly surpasses other models like
VAE+FCNN with an
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of 0.71, and models like UMAP+RFR and PCA+RFR, which show moderate fits
with
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values of 0.49 and 0.57, respectively. The confidence intervals around
the regression lines in MOALS' plot are notably narrower, pointing to
its higher precision in age predictions. This contrast is evident when
compared to PCA+FCNN and UMAP+FCNN, where broader intervals suggest
greater prediction variability.
Figure 7.
[149]Figure 7
[150]Open in a new tab
Comparison of different models for age prediction and diagnostic
accuracy.
In addition to regression analysis, the box plots in [151]Fig. 7
highlight the diagnostic accuracy between ALS and Control groups. Here,
statistical analysis, particularly t-tests, shows significant
differences in the means of ALS and Control groups, underscoring the
diagnostic reliability of the models. Despite the unbalanced sample
sizes between the ALS and control groups, the diagnostic accuracy
distributions depicted in [152]Fig. 7 demonstrate a remarkable
consistency across both groups. The box plots reveal that the median
accuracy levels for ALS and Control are closely aligned within the
context of each model, particularly for the MOALS model. This suggests
that despite the variability in group sizes, the model's performance in
distinguishing between ALS and Control remains robust, ensuring
reliable diagnostic outcomes.
This finding is particularly significant as it underscores the model's
capability to generalize well across different group sizes without a
loss in predictive accuracy. It highlights the efficacy of the model in
handling imbalanced datasets, which is a common challenge in medical
diagnostics. Such resilience in performance, evidenced by the narrow
interquartile ranges and similar medians in the box plots, supports the
utility of the model in clinical settings where the proportion of cases
to controls may not always be balanced. The statistical robustness of
MOALS, corroborated by the t-tests indicating significant differences
between the ALS and Control groups, further enhances the credibility of
the model. This statistical rigor, combined with the consistent
accuracy across diverse group sizes, provides compelling evidence of
the model's suitability for real-world applications, promising enhanced
diagnostic precision in the clinical diagnosis of ALS.
[153]Table 6 corroborates these findings by quantifying the relative
error indices—RMSE, MAE, and MedAE—across the models. MOALS' remarkable
reduction in all error metrics, especially in a multi-omics
environment, is clearly delineated, reaffirming its efficacy in the
predictive analytics realm. This detailed examination accentuates the
critical role of leveraging diverse omic data to enhance the accuracy
and reliability of biomedical predictions, firmly establishing MOALS as
a groundbreaking tool in predictive methodologies.
Table 6.
The first symptom age prediction results based on six prediction
methods applied by single omic and multi-omics approaches.
Gene Expression
__________________________________________________________________
SNV
__________________________________________________________________
Gene Expression + SNV
__________________________________________________________________
MedAE MAE RMSE R^2 MedAE MAE RMSE R^2 MedAE MAE RMSE R^2
UMAP+SVR 8.839 11.492 14.830 0.41 10.482 11.592 14.482 0.41 9.953
10.884 13.861 0.43
PCA+SVR 8.919 10.592 14.005 0.40 9.963 10.836 13.936 0.42 9.829 10.563
13.685 0.43
UMAP+RFR 8.899 9.971 12.991 0.45 8.928 9.949 13.002 0.48 8.936 9.925
12.893 0.49
PCA+RFR 8.850 9.283 12.629 0.54 8.994 9.385 12.693 0.52 8.317 9.623
12.317 0.57
UMAP+FCNN 8.965 10.037 13.199 0.51 8.842 9.513 12.839 0.50 8.629 9.666
12.582 0.52
PCA+FCNN 8.482 9.472 11.973 0.55 8.328 8.873 11.284 0.61 8.094 9.434
11.119 0.56
VAE+FCNN 8.194 8.548 10.913 0.64 7.893 8.361 9.952 0.68 6.625 8.242
10.619 0.71
MOALS 7.683 8.192 9.837 0.69 6.015 7.158 9.609 0.78
[154]Open in a new tab
A meticulous examination of the table reveals that the MOALS model, a
proposed multi-omics approach, notably outperforms the other models,
showcasing the least error across all the enlisted metrics—MedAE, MAE,
RMSE, and achieving the highest
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of 0.78 in the Gene Expression + SNV approach. It demonstrates superior
analytical accuracy and reliability, with errors reduced by 10.14
percent, 15.14 percent, and 10.51 percent in MedAE, MAE, and RMSE
respectively, when compared to the best-performing multi-omics approach
developed using alternative algorithms.
Delving deeper into the specifics, the MOALS model exhibits unambiguous
supremacy, attaining the lowest MedAE of 6.015, MAE of 7.158, and RMSE
of 9.609, underscoring its enhanced predictive precision and
reliability in estimating the first symptom age in ALS. When juxtaposed
with the single omic approaches, the superior analytical finesse of the
MOALS model becomes increasingly evident, especially in the context of
Gene Expression and SNV data.
In contrast, while the VAE model demonstrated considerable prowess,
especially in the single omic approaches, it was discernibly
overshadowed by the enhanced accuracy and reduced error rates
manifested by the MOALS model in the multi-omics approach, specifically
in the integrated Gene Expression + SNV method. This reinforces the
pivotal role of integrated multi-omic methodologies in achieving
heightened precision and reliability in predictive analytics,
surpassing the capabilities of singular omic data analyses.
Furthermore, the PCA+FCNN and UMAP+FCNN models, despite their
commendable performance in both single and multi-omic approaches, were
unable to match the elevated levels of analytical accuracy and reduced
error margins achieved by the MOALS model, thereby reiterating the
superior diagnostic capabilities of the latter.
In conclusion, the results derived from the comparison accentuate the
paramount importance and enhanced diagnostic proficiency of the
developed multi-omics model, MOALS, in predicting the onset of ALS
symptoms with refined precision and minimized error, validating its
significant potential as a groundbreaking tool in biomedical research.
The holistic integration of diverse omic data in the MOALS model
unequivocally contributes to its augmented reliability and precision,
setting a new benchmark in the contemporary spectrum of predictive
methodologies.
[155]Table 7 illustrates a meticulous comparative evaluation focusing
on survival prediction, employing various methods applied by both
single omic and multi-omics approaches. The evaluated models are
juxtaposed based on two pivotal metrics: the Concordance index
(C-index) and Integrated Brier Score (IBS), both quintessential for
appraising survival prediction tasks. A C-index value of 1 represents
the epitome of prediction accuracy, signifying an excellent model,
while a value of 0.5 symbolizes a model performing no better than
random. Concurrently, the accuracy of a predicted survival function at
specific time points, represented by IBS, ranges between 0 and 1, with
lower scores depicting higher levels of model accuracy.
Table 7.
The survival prediction results in different methods applied by single
omic and multi-omics approaches.
Gene Expression
__________________________________________________________________
SNV
__________________________________________________________________
Gene Expression+SNV
__________________________________________________________________
C-Index IBS C-Index IBS C-Index IBS
UMAP+CoxPH 0.617 0.209 0.627 0.208 0.693 0.201
PCA+CoxPH 0.592 0.224 0.616 0.220 0.671 0.216
UMAP+random survival forest 0.614 0.220 0.629 0.219 0.655 0.217
PCA+random survival forest 0.659 0.211 0.673 0.199 0.685 0.204
VAE(Selected Gene) 0.697 0.200 0.719 0.195 0.745 0.188
MOALS 0.777 0.180 0.837 0.121
[156]Open in a new tab
From a detailed viewpoint, the MOALS model conspicuously stands out,
showcasing an unparalleled C-index value of 0.837, the highest across
all examined models and approaches, coupled with the most optimal IBS
value of 0.121, reinforcing the enhanced predictive accuracy and
reliability of the proposed multi-omics model. These figures not only
accentuate the formidable precision of MOALS in predicting survival but
also illuminate its superior analytical reliability in comparison to
the other enlisted models, especially within the realm of integrated
Gene Expression + SNV approach.
Delving deeper, VAE(A) also demonstrated commendable prowess,
reflecting a substantial C-index of 0.719 and an impressive IBS of
0.195 within the SNV method, marking it as a noteworthy contender in
the landscape of survival prediction models. However, even with its
significant precision, it doesn't overshadow the supremacy of the MOALS
model in the multi-omics context, further validating the extensive
capabilities of MOALS in offering a more nuanced and comprehensive
analytical perspective.
Analyzing the results within the confines of single omic approaches, it
is unequivocal that the models exhibit varying degrees of accuracy and
reliability, with MOALS achieving a pioneering C-index of 0.777 and the
most favorable IBS of 0.180 in Gene Expression. This underscores
MOALS's superior predictive capabilities and higher levels of accuracy,
even in singular omic data analyses, bolstering its standing as a
multifaceted analytical tool.
In light of the above elucidation, the enhanced functionality and the
groundbreaking precision of the proposed multi-omics model, MOALS, are
conspicuously ratified. It sets a novel paradigm in the domain of
survival prediction, offering a more refined, holistic, and
high-resolution insight into survival prediction methodologies. The
enhanced C-index and optimized IBS values exhibited by MOALS emphasize
its unparalleled capability to provide more nuanced, reliable, and
precise survival predictions, solidifying its potential as an
innovative and pioneering instrument in advanced biomedical research
and analytics.
4. Limitations of the study and proposed framework for future research
The insights from this study highlight the significant potential of the
MOALS model in unraveling the complex molecular landscapes and gene
interrelationships associated with Amyotrophic Lateral Sclerosis (ALS).
Through the integration of multi-omics data and advanced machine
learning techniques like Variational Autoencoders (VAEs), this research
has made considerable progress in identifying key pathways that may
contribute to ALS pathogenesis. However, several limitations should be
addressed, and future research directions considered to enhance the
model's robustness, generalizability, and clinical applicability.
A primary challenge is the dependency on large-scale, high-quality
multi-omic datasets, which are not always accessible. This limitation
could lead to biased findings, as genetic and environmental factors
influencing ALS can vary widely across populations. Future research
should prioritize the inclusion of geographically and ethnically
diverse datasets to improve the model's generalizability and relevance
across different clinical settings. The current study's datasets may
not fully capture global genetic diversity, limiting the assessment of
the MOALS model's applicability across varied populations. To enhance
generalizability, validating and refining the model using more diverse
datasets is crucial. The computational complexity of the MOALS model,
especially with VAEs, poses another significant limitation. The high
demands for computational resources and expertise may challenge broader
applications, particularly in clinical settings. Future research should
focus on optimizing computational efficiency and enhancing the model's
interpretability, potentially by incorporating explainable AI
techniques.
While the study successfully integrates gene expression and genomic
variant data, the MOALS model's full potential could be realized by
adding additional omics layers, such as proteomics and metabolomics.
These layers would offer a more comprehensive understanding of ALS,
although integrating such diverse data types presents challenges.
Addressing these could lead to even more robust models and the
identification of novel biomarkers. Finally, the translational impact
of the MOALS model depends on rigorous validation in clinical settings.
This includes independent validation, clinical trials, and assessing
the model's ability to predict clinical outcomes. Ethical and data
privacy considerations must also be addressed, particularly concerning
the use of sensitive genomic data. Ensuring data privacy and navigating
ethical concerns are essential for the equitable application of models
like MOALS in clinical practice.
5. Conclusion
This study developed a novel multi-omics approach to understanding the
genetic underpinnings of Amyotrophic Lateral Sclerosis (ALS) using
machine learning techniques. By integrating gene expression profiles
and rare pathogenic genomic variants, the study identified 17,546 genes
associated with ALS pathways. The Multi-Omics for ALS (MOALS) model,
utilizing unsupervised clustering and a Variational Autoencoder (VAE),
revealed intricate genotype-phenotype correlations within the dataset.
The MOALS model significantly outperformed traditional single-omic
models, improving diagnostic accuracy by 1.7% and 6.2% compared to SNV
and RNA expression-based models, respectively. These findings highlight
the superiority of a multi-omic approach in capturing the complex
biological interactions underlying ALS, offering a more nuanced
understanding of the disease's molecular architecture.
Given its performance, the MOALS model holds potential for enhancing
diagnostic precision, informing prognosis, and guiding personalized
therapeutic strategies. This study underscores the importance of
integrating multi-omic data in Amyotrophic Lateral Sclerosis research
and contributes to uncovering the molecular mechanisms driving ALS and
other complex disorders.
CRediT authorship contribution statement
Hima Nikafshan Rad: Writing – review & editing, Writing – original
draft, Visualization, Validation, Methodology, Formal analysis,
Conceptualization. Zheng Su: Conceptualization. Anne Trinh: Writing –
review & editing. M.A. Hakim Newton: Writing – review & editing. Jannah
Shamsani: Formal analysis. NYGC ALS Consortium: Data curation. Abdul
Karim: Investigation. Abdul Sattar: Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgements