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Methods

2.1 Study Design and Overview

This study employed a three-phase analytical pipeline to investigate molecular pathway heterogeneity in amyotrophic lateral sclerosis (ALS) using synthetic patient populations derived from clinically validated pathogenic variants (Figure 1). The methodology comprised: (1) synthetic patient generation with federated clustering to identify disease severity strata, (2) mechanistic pathway annotation based on curated gene-pathway relationships, and (3) comprehensive pathway co-occurrence and correlation analysis stratified by cluster assignment.

2.2 Data Sources

2.2.1 ClinVar Variant Database

Pathogenic ALS variants were extracted from the National Center for Biotechnology Information (NCBI) ClinVar database. The curated dataset (clinvar.cleaned.csv) was filtered using the following inclusion criteria:

Inclusion Criteria:

  • Clinical significance classified as "Pathogenic" or "Likely Pathogenic" per American College of Medical Genetics and Genomics (ACMG) guidelines
  • Disease association with amyotrophic lateral sclerosis or related motor neuron disease phenotypes
  • Minimum review status of "criteria provided, single submitter"

Resulting Dataset Characteristics:

Parameter Value
Total pathogenic variants ~450
Unique genes represented 34
Variant types included SNV, indel, repeat expansion

2.2.2 Variant Record Structure

Each ClinVar record provided the following biological ground truth for simulation:

Field Description Example
Gene Association HGNC-approved gene symbol SOD1, TARDBP, C9orf72
Clinical Significance ACMG/AMP pathogenicity classification Pathogenic, Likely pathogenic
Molecular Consequence Predicted functional impact Missense, nonsense, frameshift
Genomic Coordinates GRCh38 chromosome position chr21:31659666

2.3 Synthetic Patient Population Generation

2.3.1 Population Architecture

Synthetic patient cohorts were generated to represent five continental superpopulations, following the 1000 Genomes Project nomenclature:

Code Population Simulated n
AFR African/African American 3,000
AMR Admixed American 3,000
EAS East Asian 3,000
EUR European 3,000
SAS South Asian 3,000
Total 15,000

2.3.2 Variant Assignment Model

Pathogenic variants were assigned to synthetic patients using a stochastic model incorporating population-specific allele frequencies and gene-level penetrance estimates. For each patient i and variant v:

$$ P(\text{carries } v_j) = f_{v,pop} \times \pi_{gene(v)} $$

Where:

  • $f_{v,pop}$ = population-specific allele frequency from gnomAD v3.1
  • $\pi_{gene(v)}$ = penetrance coefficient for the variant's associated gene

2.3.3 Severity Score Computation

Each variant carrier was assigned a composite severity score reflecting the cumulative pathogenic burden. The severity score for patient i carrying variants ${v_1, v_2, \ldots, v_n}$ was computed as:

$$ S_i = \sum_{j=1}^{n_i} w_{gene(v_j)} \times w_{consequence(v_j)} \times w_{pathogenicity(v_j)} $$

Component Weights:

Gene Weight ($w_{gene}$): Literature-derived penetrance estimates

Gene Weight Justification
SOD1 1.0 High penetrance, well-characterized
C9orf72 1.0 Most common familial ALS cause
TARDBP 0.9 High penetrance
FUS 0.9 Aggressive juvenile-onset forms
Other genes 0.5–0.8 Variable penetrance

Molecular Consequence Weight ($w_{consequence}$):

$$ w_{consequence} = \begin{cases} 1.0 & \text{if loss-of-function (nonsense, frameshift)} \\ 0.9 & \text{if canonical splice site} \\ 0.7 & \text{if missense with CADD} \geq 25 \\ 0.5 & \text{if missense with } 15 \leq \text{CADD} < 25 \end{cases} $$

Pathogenicity Confidence Weight ($w_{pathogenicity}$):

$$ w_{pathogenicity} = \begin{cases} 1.0 & \text{if ClinVar = "Pathogenic"} \\ 0.8 & \text{if ClinVar = "Likely pathogenic"} \end{cases} $$

2.3.4 Severity Categorization

Continuous severity scores were discretized into clinical severity categories:

Category Severity Score Range Clinical Interpretation
Healthy $S = 0$ No pathogenic variants detected
Mild $0 &lt; S \leq 5.5$ Single low-penetrance variant
Moderate $5.5 &lt; S \leq 8.0$ Multiple variants or single high-impact
Severe $S &gt; 8.0$ Multiple high-impact variants

2.3.5 Predicted Progression Assignment

Disease progression rate was modeled as a probabilistic function of severity score:

$$ P(\text{progression} = k \mid S) = \text{softmax}\left(\beta_k \cdot S + \alpha_k\right) $$

Where $k \in {\text{Slow}, \text{Moderate}, \text{Fast}}$ and parameters were calibrated to clinical literature on ALS progression rates.

2.4 Phase 1: Federated K-Means Clustering

2.4.1 Rationale

Federated learning was employed to simulate a privacy-preserving multi-institutional collaboration where patient-level data remains decentralized at each population node. This architecture enables identification of disease subgroups without sharing raw genetic data.

2.4.2 Feature Engineering

For each carrier patient, a feature vector $\mathbf{x}_i \in \mathbb{R}^d$ was constructed:

$$ \mathbf{x}_i = \left[ n_{variants}, S_i, g_1, g_2, \ldots, g_{34}, c_1, c_2, c_3, c_4 \right] $$

Feature Set Dimension Description
$n_{variants}$ 1 Total pathogenic variant count
$S_i$ 1 Composite severity score
$g_1, \ldots, g_{34}$ 34 Binary gene indicators (1 if patient carries variant in gene)
$c_1, \ldots, c_4$ 4 Consequence counts (missense, nonsense, frameshift, splice)
Total 40

2.4.3 Federated K-Means Algorithm

The clustering algorithm proceeded iteratively across $P = 5$ population nodes:

Algorithm: Federated K-Means

Input: K (number of clusters), ε (convergence threshold), T_max (max iterations)
Initialize: Global centroids μ₁⁽⁰⁾, μ₂⁽⁰⁾, ..., μ_K⁽⁰⁾ randomly

For t = 1 to T_max:
    For each population node p = 1 to P:
        # LOCAL STEP 1: Assign patients to nearest centroid
        For each patient i in population p:
            z_i = argmin_k ||x_i - μ_k⁽ᵗ⁻¹⁾||²
        
        # LOCAL STEP 2: Compute local cluster statistics
        For k = 1 to K:
            n_k⁽ᵖ⁾ = |{i : z_i = k}|                    # Local cluster size
            μ_k⁽ᵖ⁾ = (1/n_k⁽ᵖ⁾) Σ_{z_i=k} x_i          # Local centroid
        
        Send {n_k⁽ᵖ⁾, μ_k⁽ᵖ⁾} to central coordinator
    
    # GLOBAL AGGREGATION
    For k = 1 to K:
        μ_k⁽ᵗ⁾ = Σ_p (n_k⁽ᵖ⁾ × μ_k⁽ᵖ⁾) / Σ_p n_k⁽ᵖ⁾    # Weighted average
    
    # CONVERGENCE CHECK
    Δ = Σ_k ||μ_k⁽ᵗ⁾ - μ_k⁽ᵗ⁻¹⁾||²
    If Δ < ε: break

Output: Cluster assignments {z_i} and final centroids {μ_k}

Hyperparameters:

  • $K = 5$ (determined by elbow method and silhouette analysis)
  • $\epsilon = 10^{-6}$
  • $T_{max} = 100$
  • Distance metric: Euclidean

2.4.4 Cluster Number Selection

The optimal cluster count was determined using two complementary methods:

Elbow Method (Within-Cluster Sum of Squares):

$$ \text{WCSS}(K) = \sum_{k=1}^{K} \sum_{i \in C_k} |\mathbf{x}_i - \boldsymbol{\mu}_k|^2 $$

Silhouette Score:

For each patient i: $$ s(i) = \frac{b(i) - a(i)}{\max{a(i), b(i)}} $$

Where:

  • $a(i)$ = mean distance to other patients in same cluster
  • $b(i)$ = mean distance to patients in nearest other cluster

Mean silhouette score across patients indicated optimal separation at $K = 5$.

2.4.5 Cluster Interpretation

The resulting five clusters exhibited distinct severity and progression profiles:

Cluster n Mean Severity Score Modal Progression % Modal Interpretation
C0 287 5.00 Slow 74.2% (213/287) Mild
C1 3,287 7.27 Moderate 92.9% (3,055/3,287) Moderate-A
C2 1,999 9.30 Fast 96.5% (1,930/1,999) Severe
C3 8,957 0.00 N/A 100% Control (Healthy)
C4 845 6.32 Moderate 91.2% (771/845) Moderate-B

Key Finding: Clusters C1 and C4, while both classified as "Moderate" severity, emerged as distinct molecular subtypes, providing evidence for severity-stratified molecular heterogeneity within the moderate disease category.

Severity Gradient Validation:

The cluster severity ordering (C0 < C4 < C1 < C2) was validated by:

  1. Monotonic increase in mean severity scores
  2. Concordant shift in predicted progression rates
  3. Distinct gene enrichment patterns (detailed in Section 2.6)

2.5 Phase 2: Mechanistic Pathway Annotation

2.5.1 Pathway Ontology Definition

Seven canonical ALS-associated molecular pathways were defined based on comprehensive literature review of motor neuron degeneration mechanisms:

Pathway Code Primary Biological Process
Proteostasis PROT Protein folding quality control, autophagy, ubiquitin-proteasome system
RNA Metabolism RNA Pre-mRNA splicing, stress granule dynamics, nucleocytoplasmic transport
Cytoskeletal/Axonal Transport CYTO Microtubule dynamics, motor protein function, neurofilament organization
Mitochondrial Dysfunction MITO Oxidative phosphorylation, reactive oxygen species homeostasis, apoptosis
Excitotoxicity EXCITO Glutamatergic neurotransmission, calcium homeostasis, AMPA/NMDA receptor function
Vesicle Trafficking VES Endosomal sorting, autophagosome-lysosome fusion, synaptic vesicle cycling
DNA Damage Response DNA Genome stability, DNA repair, R-loop resolution

2.5.2 Gene-Pathway Mapping

Each of the 34 ALS-associated genes was mapped to one or more pathways based on established molecular mechanisms. The mapping schema permitted pleiotropy, reflecting biological reality where single genes participate in multiple cellular processes.

Complete Gene-Pathway Assignment:

Gene Pathway(s) Mechanistic Basis
SOD1 PROT, MITO, EXCITO Misfolded aggregates disrupt proteostasis; mitochondrial localization impairs respiration; EAAT2 cleavage reduces glutamate clearance
C9orf72 PROT, RNA, EXCITO Dipeptide repeat proteins inhibit proteasome; RNA foci sequester splicing factors; AMPA receptor upregulation
TARDBP RNA, EXCITO TDP-43 mislocalization disrupts splicing; ADAR2 downregulation increases Ca²⁺-permeable AMPA receptors
FUS RNA, MITO Nuclear export defects; interaction with ATP synthase impairs mitochondrial function
VCP PROT Autophagosome maturation failure
UBQLN2 PROT Ubiquitin-proteasome dysfunction
OPTN PROT Autophagy receptor dysfunction
SQSTM1 PROT p62-mediated selective autophagy impairment
TBK1 PROT Autophagy initiation kinase deficiency
CCNF PROT E3 ubiquitin ligase dysfunction
MATR3 RNA mRNA nuclear export block
HNRNPA1 RNA Stress granule dysregulation
HNRNPA2B1 RNA Stress granule dysregulation
ANG RNA Ribosomal biogenesis impairment
ELP3 RNA tRNA modification defects
TUBA4A CYTO Microtubule destabilization
PFN1 CYTO Actin polymerization failure
NEFH CYTO Neurofilament accumulation
DCTN1 CYTO Retrograde axonal transport failure
KIF5A CYTO Anterograde axonal transport failure
CHCHD10 MITO Cristae disruption, mtDNA instability
SIGMAR1 MITO MAM calcium dysregulation
ATXN2 MITO NADPH oxidase activation, ROS surge
C19orf12 MITO Mitochondrial iron dysregulation
ALS2 VES Endosome-lysosome fusion failure
CHMP2B VES ESCRT-III dysfunction
VAPB VES ER-Golgi transport defects
FIG4 VES Lysosomal biogenesis failure
SPG11 VES, DNA Lysosome reformation failure; DNA repair defects
NEK1 DNA DNA damage checkpoint failure
C21orf2 DNA DDR defects via NEK1 interaction
SETX DNA R-loop accumulation, genomic instability
UNC13A EXCITO Synaptic vesicle release defects
DAO EXCITO D-serine metabolism, NMDA modulation

2.5.3 Pathway Scoring Algorithm

For each patient i, two complementary pathway metrics were computed:

Binary Pathway Indicator:

$$ B_{i,p} = \begin{cases} 1 & \text{if } \exists \text{ gene } g \in G_p \text{ such that patient } i \text{ carries variant in } g \\ 0 & \text{otherwise} \end{cases} $$

Where $G_p$ denotes the set of genes mapped to pathway $p$.

Pathway Burden Score:

$$ \text{Score}_{i,p} = \left| {g \in G_p : V_{i,g} &gt; 0} \right| $$

Where $V_{i,g}$ is the count of pathogenic variants in gene $g$ for patient $i$.

This scoring scheme quantifies the breadth of pathway disruption by counting unique genes affected, rather than total variant count, thereby avoiding inflation from multiple variants in a single gene.

2.5.4 Summary Metrics

Derived Variables per Patient:

Variable Computation Interpretation
n_pathways_affected $\sum_{p=1}^{7} B_{i,p}$ Number of distinct pathways with ≥1 affected gene
primary_pathway $\arg\max_p \text{Score}_{i,p}$ Pathway with highest gene burden
pathway_X_genes Concatenated gene list Genes contributing to pathway X

Cohort-Level Summary:

Metric Value
Total patients 15,000
Carriers (≥1 pathway affected) 6,043 (40.3%)
Mean pathways per carrier 2.1 ± 1.3
Patients with ≥3 pathways 1,847 (30.6% of carriers)

2.6 Phase 3: Statistical Analysis of Pathway Patterns

2.6.1 Pathway Prevalence by Cluster

Pathway prevalence was computed within each non-control cluster:

$$ \text{Prevalence}_{p,k} = \frac{\sum_{i \in C_k} B_{i,p}}{|C_k|} \times 100% $$

Where $C_k$ denotes the set of carrier patients assigned to cluster $k$.

2.6.2 Co-occurrence Analysis

2.6.2.1 Co-occurrence Matrix Construction

For each cluster, a symmetric $7 \times 7$ co-occurrence matrix $\mathbf{M}$ was constructed where:

$$ M_{p,q} = \sum_{i=1}^{n} \mathbb{1}\left[B_{i,p} = 1 \land B_{i,q} = 1\right] $$

Diagonal elements represent within-pathway counts: $M_{p,p} = \sum_{i} B_{i,p}$

2.6.2.2 Co-occurrence Percentage

To normalize for pathway prevalence asymmetry, co-occurrence percentage was computed relative to the smaller pathway:

$$ \text{Co-occ%}_{p,q} = \frac{M_{p,q}}{\min(M_{p,p}, M_{q,q})} \times 100% $$

This formulation ensures that if all patients with the less common pathway also have the more common pathway, Co-occ% = 100%.

2.6.2.3 Odds Ratio Calculation

For each pathway pair $(p, q)$, association strength was quantified using the odds ratio derived from the $2 \times 2$ contingency table:

Pathway $q$ = 1 Pathway $q$ = 0 Total
Pathway $p$ = 1 $a$ $b$ $a+b$
Pathway $p$ = 0 $c$ $d$ $c+d$
Total $a+c$ $b+d$ $n$

Odds Ratio: $$ \text{OR}_{p,q} = \frac{a \times d}{b \times c} $$

95% Confidence Interval (Woolf logit method): $$ \ln(\text{OR}) \pm 1.96 \times \sqrt{\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}} $$

$$ \text{CI}_{95%} = \left[ \exp\left(\ln(\text{OR}) - 1.96 \times \text{SE}\right), \exp\left(\ln(\text{OR}) + 1.96 \times \text{SE}\right) \right] $$

Effect Size Interpretation:

Odds Ratio Effect Size Classification
OR > 3.0 Large positive association
1.5 < OR ≤ 3.0 Medium positive association
0.67 ≤ OR ≤ 1.5 Negligible association
0.33 ≤ OR < 0.67 Medium negative association
OR < 0.33 Large negative association

2.6.2.4 Jaccard Similarity Index

To quantify pathway overlap independent of marginal frequencies:

$$ J_{p,q} = \frac{|A_p \cap A_q|}{|A_p \cup A_q|} = \frac{M_{p,q}}{M_{p,p} + M_{q,q} - M_{p,q}} $$

Where $A_p$ = set of patients with pathway $p$ affected.

Jaccard index ranges from 0 (no overlap) to 1 (complete overlap).

2.6.3 Correlation Analysis

2.6.3.1 Spearman Rank Correlation

Spearman's ρ was computed between pathway burden scores to assess monotonic (potentially non-linear) relationships:

$$ \rho_{p,q} = 1 - \frac{6 \sum_{i=1}^{n} d_i^2}{n(n^2 - 1)} $$

Where $d_i = R(\text{Score}{i,p}) - R(\text{Score}{i,q})$ is the difference in ranks for patient $i$.

2.6.3.2 Pearson Correlation

Pearson's $r$ was computed to specifically detect linear dose-response relationships:

$$ r_{p,q} = \frac{\sum_{i=1}^{n}(\text{Score}_{i,p} - \overline{\text{Score}_p})(\text{Score}_{i,q} - \overline{\text{Score}_q})}{\sqrt{\sum_{i=1}^{n}(\text{Score}_{i,p} - \overline{\text{Score}_p})^2} \sqrt{\sum_{i=1}^{n}(\text{Score}_{i,q} - \overline{\text{Score}_q})^2}} $$

Rationale for Dual Analysis:

Method Detects Use Case
Spearman ρ Monotonic relationships Robust to outliers, non-normal distributions
Pearson $r$ Linear relationships Tests dose-dependent biological hypothesis

Linearity Assessment:

The difference $|\rho - r|$ was computed for each pathway pair. Small differences indicate approximately linear relationships.

Observed in overall cohort:

  • Maximum $|\rho - r|$ = 0.034
  • Mean $|\rho - r|$ = 0.009

The close agreement (Δ < 0.05 for all pairs) confirmed that pathway relationships are approximately linear, supporting Pearson correlation for dose-dependent inference.

2.6.3.3 Correlation Strength Classification

Correlation Strength Biological Interpretation
$ r \geq 0.7$
$0.3 \leq r < 0.7$
$ r < 0.3$

2.6.4 Quadrant Classification of Pathway Relationships

Pathway pairs were categorized into biological relationship types based on the joint distribution of co-occurrence frequency and correlation strength:

Classification Criteria:

Category Criteria Biological Interpretation
Dose-dependent Co-occ% > 50% AND $r$ > 0.5 Cascading failure: when one pathway intensifies, the other scales proportionally
Threshold effect Co-occ% > 50% AND $ r
Distinct subtypes Co-occ% < 30% AND $r$ < −0.3 Mutually exclusive: suggests separate molecular subtypes
Other Not meeting above criteria Mixed or transitional patterns

Exemplar Classifications (Overall Cohort):

Pathway Pair Co-occ% Pearson $r$ Classification
Mitochondrial × Excitotoxicity 86.5% 0.687 Dose-dependent
RNA Metabolism × Mitochondrial 60.4% 0.214 Threshold effect
Proteostasis × Vesicle Trafficking 24.4% −0.408 Distinct subtypes

2.6.5 Cross-Cluster Statistical Comparison

2.6.5.1 Chi-Square Test for Prevalence Heterogeneity

For each pathway, a $4 \times 2$ contingency table (4 clusters × pathway present/absent) was analyzed:

$$ \chi^2 = \sum_{i=1}^{4} \sum_{j=1}^{2} \frac{(O_{ij} - E_{ij})^2}{E_{ij}} $$

Where:

  • $O_{ij}$ = observed count in cell $(i,j)$
  • $E_{ij} = \frac{R_i \times C_j}{N}$ = expected count under independence
  • Degrees of freedom: $df = (4-1)(2-1) = 3$

2.6.5.2 Kruskal-Wallis Test for Score Differences

For pathway burden scores across clusters:

$$ H = \frac{12}{N(N+1)} \sum_{k=1}^{K} \frac{R_k^2}{n_k} - 3(N+1) $$

Where:

  • $N$ = total sample size
  • $K$ = number of clusters
  • $R_k$ = sum of ranks in cluster $k$
  • $n_k$ = sample size of cluster $k$

Under $H_0$, $H$ approximately follows $\chi^2$ distribution with $df = K - 1$.

2.6.5.3 Effect Size Measures

Given the large sample size ($n = 6,043$ carriers), statistical significance was anticipated for most comparisons. Effect sizes were therefore prioritized for interpretation of clinical and biological relevance.

Epsilon-Squared ($\varepsilon^2$) for Kruskal-Wallis:

$$ \varepsilon^2 = \frac{H}{N - 1} $$

$\varepsilon^2$ Effect Size
≥ 0.14 Large
0.06 – 0.14 Medium
0.01 – 0.06 Small
< 0.01 Negligible

Cohen's $h$ for pairwise prevalence differences:

$$ h = 2 \arcsin\left(\sqrt{p_1}\right) - 2 \arcsin\left(\sqrt{p_2}\right) $$

Where $p_1$ and $p_2$ are prevalence proportions in the two clusters being compared.

| $|h|$ | Effect Size | |-------|-------------| | ≥ 0.80 | Large | | 0.50 – 0.80 | Medium | | 0.20 – 0.50 | Small | | < 0.20 | Negligible |

2.6.6 Multiple Testing Correction

For the correlation matrix (21 unique pairwise comparisons among 7 pathways), Bonferroni correction was applied:

$$ \alpha_{adjusted} = \frac{0.05}{21} = 0.0024 $$

Correlations with $p &lt; 0.0024$ were considered statistically significant.

2.7 Network Analysis

2.7.1 Network Construction

Pathway relationships were represented as an undirected weighted graph $G = (V, E, W)$ where:

  • Vertices ($V$): Seven molecular pathways
  • Edges ($E$): Pathway pairs with co-occurrence count > 0
  • Weights ($W$): Co-occurrence counts

2.7.2 Visual Encoding

Element Encoding Formula
Node size Pathway prevalence $r = \frac{\sqrt{n_{pathway}}}{5} + 15$ pixels
Node color Pathway identity Fixed color palette
Edge width Co-occurrence strength $w = \ln(\text{count} + 1) \times 2$
Edge color Effect size Red (large), Orange (medium), Gray (negligible)

2.7.3 Network Layout

Nodes were arranged in circular layout with angular position:

$$ \theta_p = \frac{2\pi \times \text{index}(p)}{7} - \frac{\pi}{2} $$

Coordinates: $$ x_p = x_{center} + R \cos(\theta_p) $$ $$ y_p = y_{center} + R \sin(\theta_p) $$

Where $R = 200$ pixels (layout radius).

2.8 Software Environment

2.8.1 Computational Stack

Component Version Purpose
Python 3.10.12 Primary analysis environment
pandas 2.0.3 Data manipulation
NumPy 1.24.3 Numerical computation
SciPy 1.11.1 Statistical tests
scikit-learn 1.3.0 K-means clustering
D3.js 7.8.5 Interactive visualization

2.8.2 Analysis Pipeline

The complete pipeline comprised three executable modules:

  1. phase1_federated_clustering.py — Federated K-means implementation with cross-population aggregation
  2. phase2_pathway_annotation_all.py — Gene-pathway mapping and patient scoring
  3. stage4_pathway_analysis_clusters.py — Statistical analysis, correlation matrices, and network generation

2.8.3 Code and Data Availability

All analysis scripts and intermediate datasets are available at [repository URL to be inserted]. The ClinVar source data is publicly accessible through NCBI (https://www.ncbi.nlm.nih.gov/clinvar/).

2.9 Methodological Considerations

2.9.1 Sample Size Justification

With $n = 6,043$ carriers, statistical power exceeded 99% for detecting:

  • Small correlations ($r = 0.10$) at $\alpha = 0.05$
  • Small prevalence differences (Cohen's $h = 0.20$) between clusters

Consequently, effect sizes rather than $p$-values were emphasized for interpretation.

2.9.2 Limitations

  1. Synthetic Data: Patients were computationally simulated based on variant-level characteristics; clinical phenotype heterogeneity and environmental factors were not modeled.

  2. Pathway Boundary Definitions: Gene-pathway assignments were based on primary literature and may not capture context-dependent or tissue-specific pathway involvement.

  3. Epistatic Effects: Complex genetic interactions between variants were not explicitly modeled in the severity score.

  4. Population Structure: While five superpopulations were represented, within-population stratification (e.g., ancestry-informative markers) was not addressed.

  5. Temporal Dynamics: The analysis represents a cross-sectional snapshot; longitudinal pathway evolution was not modeled.

2.10 Ethical Considerations

This study utilized exclusively synthetic data generated from publicly available ClinVar variant annotations. No human subjects were enrolled, and no identifiable patient information was used. Institutional review board approval was not required.

Statistical analyses were performed in Python 3.10 using scipy.stats for inferential tests. Interactive visualizations were developed using D3.js v7.8.5. All analyses were conducted between January and February 2026.