Unsupervised clustering of common human diseases based on GWAS and WGS data, with a focus on Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS)

Abstract

CompareME is an R-based pipeline that constructs protein–protein interaction (PPI) networks for 28 common diseases (including neurological, psychiatric, metabolic, cardiovascular, inflammatory, and autoimmune conditions) and compares them using three metrics: gene-level overlap (Jaccard index), functional enrichment correlation (ORA correlation), and network separation. A composite similarity score is then generated by similarity network fusion (SNF) and used as a distance in hierarchical clustering using several linkages. The Adjusted Rand Index was calculated against the ICD-10 disease classifications for each unsupervised clustering to select the best linkage.

For each disease, candidate genes are retrieved from GWAS credible sets (via the Open Targets platform, Locus-to-Gene scoring) and rare-variant studies (ClinGen curated genes and gene-burden tests). For ME/CFS specifically, a custom gene module is constructed by merging gene lists from two recent papers, one based on permutation analysis of DecodeME data (15,000 cases), the other on WGS-based rare variant prioritisation on 400 ME/CFS patients.

This machine learning algorithm classifies ME/CFS in the same cluster as Obesity, Alzheimer's disease, Sleep Disorders, and Diabetes Mellitus. It also suggests that ME/CFS does not belong to the cluster of psychiatric diseases, nor is it an inflammatory/autoimmune condition.

Methods

Data source

I selected 28 common diseases, including neurological, psychiatric, metabolic, cardiovascular, inflammatory, and autoimmune conditions. The complete list, with full names, abbreviations, and identifiers (EFO or MONDO codes), is in Table 1. The list of diseases is passed to the script through mydiseases.yml. ME/CFS is handled separately (see below). The classification according to ICD-10 v.2019 was manually retrieved from the official website (ICD-10 2019).

Disease Full Name	Abbreviation	ID	ICD-10 Code	ICD-10 Category
Alzheimer disease	AD	MONDO_0004975	G30	Diseases of the nervous system
Anxiety disorder	ANX	EFO_0006788	F41	Mental and behavioural disorders
Arteriosclerosis disorder	AS	MONDO_0002277	I70	Diseases of the circulatory system
Asthma	ASMA	MONDO_0004979	J45	Diseases of the respiratory system
Attention deficit hyperactivity disorder	ADHD	EFO_0003888	F90	Mental and behavioural disorders
Bipolar Disorder	BD	MONDO_0004985	F31	Mental and behavioural disorders
Blood coagulation disease	BCD	EFO_0009314	D65	Diseases of the blood and blood-forming organs
Chronic Fatigue Syndrome	CFS	EFO_0004540	G93.3	Diseases of the nervous system
Chronic obstructive pulmonary disease	COPD	EFO_0000341	J44	Diseases of the respiratory system
Crohn disease	CD	EFO_0000384	K50	Diseases of the digestive system
Depressive Disorder	DD	MONDO_0002050	F32	Mental and behavioural disorders
Diabetes Mellitus	DM	EFO_0000400	E11	Endocrine, nutritional and metabolic diseases
Epilepsy	EPI	EFO_0000474	G40	Diseases of the nervous system
Heart failure	HF	EFO_0003144	I50	Diseases of the circulatory system
Hypercholesterolemia	HC	HP_0003124	E78	Endocrine, nutritional and metabolic diseases
Hypertension	HTN	EFO_0000537	I10	Diseases of the circulatory system
Lupus erythematosus	SLE	MONDO_0004670	M32	Diseases of the musculoskeletal system and connective tissue
Metabolic syndrome	MetS	EFO_0000195	E88.8	Endocrine, nutritional and metabolic diseases
Multiple Sclerosis	MS	MONDO_0005301	G35	Diseases of the nervous system
Obesity	OB	EFO_0001073	E66	Endocrine, nutritional and metabolic diseases
Parkinson	PD	MONDO_0005180	G20	Diseases of the nervous system
Psoriasis	PSO	EFO_0000676	L40	Diseases of the skin and subcutaneous tissue
Post-traumatic stress disorder	PTSD	EFO_0001358	F43.1	Mental and behavioural disorders
Rheumatoid arthritis	RA	EFO_0000685	M05	Diseases of the musculoskeletal system and connective tissue
Schizophrenia	SCZ	MONDO_0005090	F20	Mental and behavioural disorders
Sleep Disorder	SD	EFO_0008568	G47	Diseases of the nervous system
Ulcerative colitis	UlCo	EFO_0000729	K51	Diseases of the digestive system
Vasculitis	VAS	EFO_0006803	M30	Diseases of the musculoskeletal system and connective tissue

Table 1. Diseases included in the present study, in alphabetical order, with ICD-10 classification and codes.

For each disease except ME/CFS, the function Targets4Disease() queries the Open Targets GraphQL API (v4). Gene–disease associations are collected from multiple evidence sources, including genome-wide association studies (GWAS), ClinGen curated rare-variant evidence, and gene burden studies from sequencing data. Only genes meeting predefined evidence thresholds are retained. The default filtering parameters include:

Parameter	Description	Default
L2G cutoff	minimum locus-to-gene score	0.5
ClinGen cutoff	minimum ClinGen evidence score	0.5
GeneBurden cutoff	minimum gene-burden score	0.5
Sample cutoff	minimum GWAS sample size	0

Table 2. Sources of the genes used to build the disease module of ME/CFS.

For each disease, the pipeline retrieves associated genes using a programmatic query to the Open Targets platform. Each gene is assigned a list label (GWAS, Rare, or GWAS/Rare) and annotated with its STRING preferred name (via the STRING API) and its NCBI Entrez ID (via a local copy of gene_info.gz). For myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS), I built a custom disease module based on the results of the studies in Table 3.

Number of cases	Sequencing Method	Gene-Mapping Method	Genes	Criteria	Reference
464	WGS	Deep Learning	115	ICC-IOM	(Zhang S 2025)
14767	Axiom UKB array	Combinatorial analysis	259	CCC-IOM	(Sardell JM 2025)

Table 3. Sources of the genes used to build the disease module of ME/CFS.

PPI network construction

The STRING v12.0 human PPI database (9606.protein.links.v12.0) is downloaded automatically on first run and filtered to interactions with a combined score ≥ 0.4 (configurable via STRING.co). For each disease, GeneMatrix() builds a weighted, symmetric adjacency matrix restricted to the disease gene set. The full union of all disease genes is also assembled into a background network used for inter-disease distance calculations. All matrices are stored as .rds files under Modules/.

Random disease modules

For each real disease module of size N, 1,000 random modules are generated by sampling N genes uniformly at random from the pool of all disease genes (myDiseaseGenes). These random modules serve as the null distribution for separation (see below). Another 1,000 random diseases with size given by the average size of disease modules are generated using disease genes; they serve as a null distribution for the similarity metric based on correlation between Z scores of over-representation analysis (see below). These modules are stored in the folder Random/ and a zipped copy of it is available (here).

Module characterisation

For every disease module, the following network properties are computed and compared against the corresponding random null (Tables 4 and 5). Empirical p-values are derived from the right tail (P_upper) or left tail (P_lower) of the random distribution. Results are saved to Modules/Modules_analysis.csv.

Property	Description
Module size	Number of nodes in the largest connected component
Mean shortest distance	Average weighted geodesic within the module (Dijkstra algorithm)
Mean degree	Average number of PPI edges per gene
Mean strength	Average weighted degree (sum of PPI scores per gene)
Relative strength	Mean strength / mean degree

Table 4. For each disease, we evaluate the network properties indicated in this table. We compare the results to distributions obtained from random diseases. See Table 5.

Over-representation analysis (ORA)

For each disease module, ORA.fun() runs hypergeometric over-representation tests against KEGG, Reactome, and Gene Ontology (GO) gene sets using the clusterProfiler and ReactomePA packages. Separately, Tissue.ORA() computes tissue enrichment z-scores using TissueEnrich. Both analyses are also run on each of the 1,000 random modules of the same size to build a pathway-level null distribution.

Pairwise disease similarity

All pairwise comparisons are stored under Comparisons/.

Jaccard Index (gene overlap). It is a standard measure of genetic overlap between two diseases, and it is calculated as:

$$J(A,B) = \frac{|A \cap B|}{|A \cup B|}$$

Statistical significance is assessed by a hypergeometric test against the universe of all disease genes. Results in Comparisons/Jaccard/.

ORA correlation (functional similarity). The Spearman correlation between the z-score vectors of two disease modules across all pathway and tissue terms is computed as a functional similarity score. For both disease modules, a comparison against all 1,000 random modules is performed to build a null correlation distribution of 2,000 correlation coefficients. An upper-tail T-test on fitted normal density is used to test for significance (custom function P_upper()).

Network separation SAB (topological similarity). I used the definition of separation between two gene networks proposed in (Menche J et al. 2015):

$$S_{AB} = \langle d_{AB} \rangle - \frac{\langle d_{AA} \rangle + \langle d_{BB} \rangle}{2}$$

where $\langle d_{AB} \rangle$ is the mean shortest path between genes of disease A and genes of disease B in the full disease interactome, computed with Dijkstra's algorithm, using the function distances() of the package igraph. Negative SAB indicates module overlap; positive $S_{AB}$ indicates topological separation. The null distribution is built in two steps: first, we calculate $S_{AB}$ between disease A and each one of the 1,000 random diseases of the same size as disease B; next, we perform the same calculations for disease B. This algorithm generates a distribution of 2,000 random separations. An empirical upper-tail p-value is used to test for significance (custom function P_upper).

Similarity Network Fusion. The three pairwise similarity scores (Jaccard index, ORA correlation, and network separation SAB) were integrated into a single composite score using Similarity Network Fusion (SNF) (Wang et al 2014). Prior to fusion, each score was normalised to [0,1]. The resulting distance matrices were converted to similarity matrices by W=1−D and their diagonals set to one. SNF was then applied with K = 5 nearest neighbours and t = 20 iterations, iteratively diffusing information across the three networks until convergence (function SNF of package SNFtool).

Cross-metric comparison

Pairwise regression (linear, quadratic, and cubic) is performed across all three similarity metrics to quantify their mutual consistency.

Hierarchical Clustering, Dendrograms, and Rand Index

Each similarity metric (Jaccard index, ORA Correlation, Network Separation, and composite score SNF) is transformed into a distance, such that the lower the value, the greater the similarity. Pairwise distances are then used to perform hierarchical clustering with the function hclust of the package stats, using all the available linkages, namely "ward.D", "ward.D2", "single", "complete", "average", "mcquitty", "median", and "centroid". For each clustering, a dendrogram is plotted, and an adjusted Rand Index is calculated against the disease classifications reported in Table 1, using adjustedRandIndex() from the package mclust. For each adjusted Rand Index, an empirical upper-tail p-value is calculated using 20,000 permutations to generate a null distribution. The adjusted Rand Index has a mean of zero in the case of random partition, and its maximum value is one (perfect agreement between two classifications) (Hubert et Arabie 1985). As a reminder of the meaning of each linkage used in hierarchical clustering, see the following table.

Method	Links clusters by
single	minimum distance between any two members
complete	maximum distance between any two members
average	mean distance between all pairs of members
mcquitty	average of the distances used to form previous clusters
median	median distance between all pairs of members
centroid	distance between cluster centroids
ward.D	minimises total within-cluster variance (Ward 1963)
ward.D2	minimises total within-cluster variance on squared distances

Gene-level network properties

For each gene in each module, the within-module degree and total STRING interaction count are retrieved. A linear model of within-module degree ~ STRING degree is fitted. This analysis was performed to study the level of connectivity in the complete interactome of those genes that appear isolated in disease modules. Are they isolated because fewer interactions are known for them, overall?

Results

Network properties of disease modules

Each disease network has been analysed in terms of its main network properties and compared with 1,000 random diseases of the same size, used to build the null distributions. Empirical one-tailed p-values have been used to test for significance, then a Benjamini-Hochberg correction was applied (Table 5). In particular, we used upper-tail p-values for all the variables but Mean Shortest Distance, in which case we used a lower-tailed p-value. Table 5 is available in CSV format in Modules_analysis.csv. We note that most diseases have a largest component significantly bigger than the corresponding null. But this is not true for ME/CFS, along with Bipolar Disorder, Hypertension, PTSD, and Sleep Disorder. Also, ME/CFS does not show a mean shortest distance smaller than what is expected by chance, even though its genes display a significantly higher mean degree, mean strength, and mean relative strength than what is seen in random diseases.

Disease	Vertices	Size	Size_%	p-val	Short_Dist	p-val	Degree	p-val	Strength	p-val	Rel_Strength	p-val
Alzheimer disease	134	79	0.59	0.0042	1.68	0.14	5.21	0.0014	3.29	0.0015	0.63	0.28
Anxiety disorder	95	63	0.66	0.0019	1.75	0.54	2.42	0.0014	1.28	0.0042	0.53	1
Arteriosclerosis disorder	170	116	0.68	0.0031	1.60	0.0056	5.15	0.0014	3.15	0.0015	0.61	0.57
Asthma	273	213	0.78	0.0019	1.72	0.0056	9.04	0.0014	5.59	0.0015	0.62	0.20
Attention deficit hyperactivity disorder	162	109	0.67	0.0031	1.95	0.22	2.89	0.0064	1.68	0.0089	0.58	1
Bipolar Disorder	107	50	0.47	0.056	1.65	0.31	2.00	0.0053	1.06	0.022	0.53	1
Blood coagulation disease	95	64	0.67	0.0019	1.92	0.66	9.47	0.0014	6.96	0.0015	0.73	0.014
Chronic Fatigue Syndrome	369	276	0.75	0.14	2.05	0.31	4.92	0.016	3.20	0.0053	0.65	0.014
Chronic obstructive pulmonary disease	120	82	0.68	0.0019	1.77	0.27	3.18	0.0014	1.89	0.0015	0.59	0.95
Crohn disease	177	141	0.80	0.0019	1.35	0.0056	10.53	0.0014	6.43	0.0015	0.61	0.54
Depressive Disorder	205	139	0.68	0.015	2.02	0.18	2.92	0.033	1.61	0.063	0.55	1
Diabetes Mellitus	789	712	0.90	0.0042	1.59	0.0056	11.92	0.0014	7.02	0.0015	0.59	1
Epilepsy	78	60	0.77	0.0019	1.46	0.52	7.18	0.0014	4.39	0.0015	0.61	0.59
Heart failure	118	88	0.75	0.0019	1.72	0.24	4.34	0.0014	2.66	0.0015	0.61	0.57
Hypercholesterolemia	136	89	0.65	0.0019	1.63	0.066	6.97	0.0014	4.58	0.0015	0.66	0.037
Hypertension	703	597	0.85	0.43	1.88	0.52	6.96	0.49	4.14	0.48	0.59	1
Lupus erythematosus	143	100	0.70	0.0019	1.83	0.16	5.93	0.0014	3.59	0.0015	0.61	0.57
Metabolic syndrome	121	82	0.68	0.0019	1.42	0.066	7.09	0.0014	4.62	0.0015	0.65	0.10
Multiple Sclerosis	93	63	0.68	0.0019	1.45	0.31	5.05	0.0014	3.03	0.0015	0.60	0.77
Obesity	295	235	0.80	0.0019	1.93	0.066	4.90	0.0014	2.82	0.0015	0.58	1
Parkinson	67	42	0.63	0.0019	1.41	0.65	5.22	0.0014	3.45	0.0015	0.66	0.28
Post-traumatic stress disorder	36	8	0.22	0.13	1.19	0.88	0.67	0.084	0.40	0.068	0.61	0.64
Psoriasis	142	112	0.79	0.0019	1.38	0.020	9.08	0.0014	5.61	0.0015	0.62	0.39
Rheumatoid arthritis	244	178	0.73	0.0031	1.68	0.0056	8.69	0.0014	5.27	0.0015	0.61	0.50
Schizophrenia	255	180	0.71	0.017	2.06	0.22	3.33	0.046	1.90	0.091	0.57	1
Sleep Disorder	257	176	0.68	0.068	1.91	0.056	3.35	0.038	1.88	0.093	0.56	1
Ulcerative colitis	146	89	0.61	0.0053	1.35	0.014	7.53	0.0014	4.63	0.0015	0.61	0.57
Vasculitis	47	27	0.57	0.0019	1.15	0.70	4.17	0.0014	2.85	0.0015	0.68	0.30

Table 5. Comparisons of network properties of the 28 disease modules of Table 1. Empirical one-tailed p-values were computed for each disease using 1,000 random diseases of the same size to build null distributions. `Size` is the number of nodes in the largest connected component; Size_% is the proportion of genes of the module that are included in the largest connected component; `Short_Dist` is the mean shortest distance within the module, as calculated by Dijkstra's algorithm; `Degree` is the mean degree of the vertices; `Strength` is the average weighted degree (sum of PPI scores per gene); `Rel_Strength` is the ratio between mean strength and mean degree. P-values are corrected for multiple comparisons by the Benjamini-Hochberg method, column by column. P-values that remain significant after correction are in bold. See also Table 4.

Network representation

For each disease, a network is plotted using igraph. These plots can be explored here: (Networks). As an example, the network for Parkinson's disease is reported in Figure 1, where you see how the genes harbouring rare mutations are connected to those prioritised by GWAS studies.

Figure 1. Gene network of Parkinson's disease. In red, genes prioritised by GWAS studies, thus harbouring common variants associated with the disease. In green, genes known to present rare mutations that cause or are associated with monogenic forms of the same condition. In white, genes that are prioritised by both GWAS studies and personal genomics studies.

Over-representation analysis

The results of over-representation analysis (ORA) against KEGG, GO, and Reactome for each one of the 28 diseases can be explored here: ORA. The results of ORA against the Human Proteome Atlas (HPA) are included here: Tissue. In this same folder, the plots of Tissue ORA are available for each disease. An example of these plots is Figure 2.

Figure 2. Results of tissue over-representation analysis against Human Protein Atlas, for Obesity The cut-off of significance, after correction for multiple comparisons, is indicated by the red line.

Pairwise disease similarity

Jaccard Index

Using the Jaccard index as a pairwise similarity score, the hierarchical clustering that reaches the highest agreement with ICD-10 classification is the one based on complete linkage (Table 6). According to this method, ME/CFS is classified in the same cluster as Diabetes Mellitus, Hypertension, and Obesity (Table 7). The dendrogram generated by this clustering is shown in Figure 3. The dendrograms generated by the other linkages are collected in Jaccard, while the clusters for all the linkages can be explored in Hierarchical_clustering_Clusters.csv. After correction for multiple comparisons (Bonferroni), ME/CFS does not show significant similarity with any of the other diseases (see Chronic Fatigue Syndrome_Jaccard.jpeg). This is not the case for other diseases, see Figure 4.

Linkage	ARI	p-value
complete	0.37	5e-05
ward.D	0.34	5e-05
ward.D2	0.34	5e-05
average	0.27	1e-04
mcquitty	0.27	1e-04
single	0.23	0.001
median	0.05	0.1
centroid	0.04	0.16

Table 6. Adjusted Rand Indices (with associated p-values) for hierarchical classifications based on Jaccard Index, according to several linkages, when compared with the ICD-10 classification of Table 1.

Disease	ICD-10 Category	Complete
Alzheimer disease	Diseases of the nervous system	1
Anxiety disorder	Mental and behavioural disorders	2
Arteriosclerosis disorder	Diseases of the circulatory system	3
Asthma	Diseases of the respiratory system	4
Attention deficit hyperactivity disorder	Mental and behavioural disorders	2
Bipolar Disorder	Mental and behavioural disorders	2
Blood coagulation disease	Diseases of the blood and blood-forming organs	5
Chronic Fatigue Syndrome	Diseases of the nervous system	6
Chronic obstructive pulmonary disease	Diseases of the respiratory system	4
Crohn disease	Diseases of the digestive system	7
Depressive Disorder	Mental and behavioural disorders	2
Diabetes Mellitus	Endocrine, nutritional and metabolic diseases	6
Epilepsy	Diseases of the nervous system	8
Heart failure	Diseases of the circulatory system	3
Hypercholesterolemia	Endocrine, nutritional and metabolic diseases	3
Hypertension	Diseases of the circulatory system	6
Lupus erythematosus	Diseases of the musculoskeletal system and connective tissue	7
Metabolic syndrome	Endocrine, nutritional and metabolic diseases	3
Multiple Sclerosis	Diseases of the nervous system	7
Obesity	Endocrine, nutritional and metabolic diseases	6
Parkinson	Diseases of the nervous system	9
Psoriasis	Diseases of the skin and subcutaneous tissue	7
Post-traumatic stress disorder	Mental and behavioural disorders	2
Rheumatoid arthritis	Diseases of the musculoskeletal system and connective tissue	7
Schizophrenia	Mental and behavioural disorders	2
Sleep Disorder	Diseases of the nervous system	2
Ulcerative colitis	Diseases of the digestive system	7
Vasculitis	Diseases of the musculoskeletal system and connective tissue	5

Table 7. ICD-10 classification compared with hierarchical clustering based on the Jaccard index, with complete linkage (the clustering with the best performance, according to Table 6).

Figure 3. Dendrogram corresponding to hierarchical clustering based on the Jaccard index and complete linkage.

Figure 4. Pairwise comparisons between Lupus and all the other diseases in Table 1. On the y-axis -LOG(p), while on the y-axis, the Jaccard Index. The dashed line indicates the cut-off for significance, after Bonferroni correction (2*0.05/(28*28-28)

ORA correlation

Using correlation between ORA Z-scores as a pairwise similarity score, the hierarchical clustering that reaches the highest agreement with ICD-10 classification is the one based on centroid linkage (Table 8). According to this method, ME/CFS is classified in a cluster of its own (Table 9). The dendrogram generated by this clustering is shown in Figure 5. The dendrograms generated by the other linkages are collected in Correlation, while the clusters for all the linkages can be explored in Hierarchical_clustering_Clusters.csv. After correction for multiple comparisons (Bonferroni), ME/CFS does not show significant similarity with any of the other diseases (see Chronic Fatigue Syndrome_Correlation.jpeg). For ME/CFS this repositori also includes the pair-wise null distributions of the correlation coefficient (see Distributions). This is not the case for other diseases, see Figure 6.

Method	ARI	p-value
centroid	0.22	0.0011
single	0.18	0.0029
complete	0.08	0.053
average	0.08	0.054
mcquitty	0.08	0.051
ward.D	0.08	0.053
ward.D2	0.08	0.051
median	0.06	0.096

Table 8. Adjusted Rand Indices (with associated p-values) for hierarchical classifications based on correlation between ORA Z-scores, according to several linkages, when compared with the ICD-10 classification of Table 1.

Disease	ICD-10 Category	Centroid
Alzheimer disease	Diseases of the nervous system	1
Anxiety disorder	Mental and behavioural disorders	2
Arteriosclerosis disorder	Diseases of the circulatory system	1
Asthma	Diseases of the respiratory system	3
Attention deficit hyperactivity disorder	Mental and behavioural disorders	2
Bipolar Disorder	Mental and behavioural disorders	2
Blood coagulation disease	Diseases of the blood and blood-forming organs	4
Chronic Fatigue Syndrome	Diseases of the nervous system	5
Chronic obstructive pulmonary disease	Diseases of the respiratory system	6
Crohn disease	Diseases of the digestive system	3
Depressive Disorder	Mental and behavioural disorders	2
Diabetes Mellitus	Endocrine, nutritional and metabolic diseases	7
Epilepsy	Diseases of the nervous system	8
Heart failure	Diseases of the circulatory system	1
Hypercholesterolemia	Endocrine, nutritional and metabolic diseases	1
Hypertension	Diseases of the circulatory system	7
Lupus erythematosus	Diseases of the musculoskeletal system and connective tissue	3
Metabolic syndrome	Endocrine, nutritional and metabolic diseases	1
Multiple Sclerosis	Diseases of the nervous system	3
Obesity	Endocrine, nutritional and metabolic diseases	7
Parkinson	Diseases of the nervous system	2
Psoriasis	Diseases of the skin and subcutaneous tissue	3
Post-traumatic stress disorder	Mental and behavioural disorders	2
Rheumatoid arthritis	Diseases of the musculoskeletal system and connective tissue	3
Schizophrenia	Mental and behavioural disorders	9
Sleep Disorder	Diseases of the nervous system	2
Ulcerative colitis	Diseases of the digestive system	3
Vasculitis	Diseases of the musculoskeletal system and connective tissue	4

Table 9. ICD-10 classification compared with hierarchical clustering based on correlation between ORA Z-scores, with centroid (the clustering with the best performance, according to Table 8).

Figure 5. Dendrogram corresponding to hierarchical clustering based on the ORA Z-score correlations and centroid linkage.

Figure 6. Pairwise comparisons between Lupus and all the other diseases in Table 1. On the y-axis -LOG(p), while on the y-axis, the correlation coefficient between the Z-scores of Over-representation analysis. The dashed line indicates the cut-off for significance, after Bonferroni correction (2*0.05/(28*28-28)

Network Separation

Using network separation as a pairwise similarity score, the hierarchical clustering that reaches the highest agreement with ICD-10 classification is the one based on ward.D linkage (Table 10). According to this method, ME/CFS is classified in the same cluster as Alzheimer's disease, Obesity, Diabetes Mellitus, and Sleep disorder (Table 11). The dendrogram generated by this clustering is shown in Figure 7. The dendrograms generated by the other linkages are collected in Separation, while the clusters for all the linkages can be explored in Hierarchical_clustering_Clusters.csv. After correction for multiple comparisons (Bonferroni), ME/CFS does not show significant similarity with any of the other diseases (see Chronic Fatigue Syndrome_Separation.jpeg). For ME/CFS this repository also includes the pair-wise null distributions of the correlation coefficient (see Distributions).

Method	ARI	p-value
ward.D	0.52	5e-05
ward.D2	0.39	5e-05
average	0.27	1.5e-04
mcquitty	0.26	2e-04
single	0.22	5e-05
complete	0.16	0.0058
median	0.03	0.23
centroid	0.01	0.33

Table 10. Adjusted Rand Indices (with associated p-values) for hierarchical classifications based on network separation, according to several linkages, when compared with the ICD-10 classification of Table 1.

Disease	ICD-10 Category	Wwrd.D
Alzheimer disease	Diseases of the nervous system	1
Anxiety disorder	Mental and behavioural disorders	2
Arteriosclerosis disorder	Diseases of the circulatory system	3
Asthma	Diseases of the respiratory system	4
Attention deficit hyperactivity disorder	Mental and behavioural disorders	2
Bipolar Disorder	Mental and behavioural disorders	2
Blood coagulation disease	Diseases of the blood and blood-forming organs	5
Chronic Fatigue Syndrome	Diseases of the nervous system	1
Chronic obstructive pulmonary disease	Diseases of the respiratory system	4
Crohn disease	Diseases of the digestive system	6
Depressive Disorder	Mental and behavioural disorders	2
Diabetes Mellitus	Endocrine, nutritional and metabolic diseases	1
Epilepsy	Diseases of the nervous system	7
Heart failure	Diseases of the circulatory system	3
Hypercholesterolemia	Endocrine, nutritional and metabolic diseases	8
Hypertension	Diseases of the circulatory system	3
Lupus erythematosus	Diseases of the musculoskeletal system and connective tissue	6
Metabolic syndrome	Endocrine, nutritional and metabolic diseases	8
Multiple Sclerosis	Diseases of the nervous system	6
Obesity	Endocrine, nutritional and metabolic diseases	1
Parkinson	Diseases of the nervous system	9
Psoriasis	Diseases of the skin and subcutaneous tissue	6
Post-traumatic stress disorder	Mental and behavioural disorders	2
Rheumatoid arthritis	Diseases of the musculoskeletal system and connective tissue	6
Schizophrenia	Mental and behavioural disorders	2
Sleep Disorder	Diseases of the nervous system	1
Ulcerative colitis	Diseases of the digestive system	6
Vasculitis	Diseases of the musculoskeletal system and connective tissue	5

Table 11. ICD-10 classification compared with hierarchical clustering based on network separation, with ward.D linkage (the clustering with the best performance, according to Table 10).

Figure 7. Dendrogram corresponding to hierarchical clustering based on network separation and ward.D linkage.

Similarity Network Fusion

I integrated the distances generated by the three similarity scores using the Similarity Network Fusion (SNF) algorithm. This generates a fourth metric, called SNF. When we apply hierarchical clustering based on this metric, the linkage that reaches the highest agreement with ICD-10 classification is ward.D (Table 12). ME/CFS is classified in the same cluster as Obesity, Alzheimer's disease, Sleep Disorders, and Diabetes Mellitus. (Table 13). The dendrogram generated by this clustering is shown in Figure 8. The dendrograms generated by the other linkages are collected in SNF, while the clusters for all the linkages can be explored in Hierarchical_clustering_Clusters.csv.

Method	ARI	p-value
ward.D	0.52	5e-05
ward.D2	0.39	5e-05
average	0.27	1.5e-04
mcquitty	0.26	1.5e-04
single	0.22	1e-04
complete	0.16	0.0057
median	0.03	0.22
centroid	0.01	0.33

Table 12. Adjusted Rand Indices (with associated p-values) for hierarchical classifications based on network separation, according to several linkages, when compared with the ICD-10 classification of Table 1.

Disease	ICD-10 Category	ward.D
Alzheimer disease	Diseases of the nervous system	1
Anxiety disorder	Mental and behavioural disorders	2
Arteriosclerosis disorder	Diseases of the circulatory system	3
Asthma	Diseases of the respiratory system	4
Attention deficit hyperactivity disorder	Mental and behavioural disorders	2
Bipolar Disorder	Mental and behavioural disorders	2
Blood coagulation disease	Diseases of the blood and blood-forming organs	5
Chronic Fatigue Syndrome	Diseases of the nervous system	1
Chronic obstructive pulmonary disease	Diseases of the respiratory system	4
Crohn disease	Diseases of the digestive system	6
Depressive Disorder	Mental and behavioural disorders	2
Diabetes Mellitus	Endocrine, nutritional and metabolic diseases	1
Epilepsy	Diseases of the nervous system	7
Heart failure	Diseases of the circulatory system	3
Hypercholesterolemia	Endocrine, nutritional and metabolic diseases	8
Hypertension	Diseases of the circulatory system	3
Lupus erythematosus	Diseases of the musculoskeletal system and connective tissue	6
Metabolic syndrome	Endocrine, nutritional and metabolic diseases	8
Multiple Sclerosis	Diseases of the nervous system	6
Obesity	Endocrine, nutritional and metabolic diseases	1
Parkinson	Diseases of the nervous system	9
Psoriasis	Diseases of the skin and subcutaneous tissue	6
Post-traumatic stress disorder	Mental and behavioural disorders	2
Rheumatoid arthritis	Diseases of the musculoskeletal system and connective tissue	6
Schizophrenia	Mental and behavioural disorders	2
Sleep Disorder	Diseases of the nervous system	1
Ulcerative colitis	Diseases of the digestive system	6
Vasculitis	Diseases of the musculoskeletal system and connective tissue	5

Table 13. ICD-10 classification compared with hierarchical clustering based on Similarity Network Fusion of the three metrics, with ward.D linkage (the clustering with the best performance, according to Table 12).

Figure 8. Dendrogram corresponding to hierarchical clustering based on SNF and ward.D linkage.

Comparison between similarity scores

Figure 9. Pairwise second-order polynomial regressions between the four similarity metrics employed in this study, with 95% prediction interval, p-value (F-test), and R2 adjusted.

Degree of nodes within disease modules vs degree in the complete network

The degree of disease genes within disease modules linearly regresses with the corresponding degree in the complete STRING database, suggesting that the lack of connectivity that we often see in gene networks from disease modules (see Figure 1) may reflect gaps in the STRING database rather than false positive gene-disease associations.

Figure 10. Degree of disease genes within disease modules (y-axis) and corresponding degree within the STRING database (x-axis).