# Combining phenotypic similarity and network propagation to improve performance and clinical consistency of rare disease diagnosis

Maroua Chahdil, Carolina Fabrizzi, Marc Hanauer, Caterina Lucano, Ana Rath, David Lagorce, Laurent Tichit

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Maroua Chahdil, Carolina Fabrizzi, Marc Hanauer, Caterina Lucano, Ana Rath, et al. Combining phenotypic similarity and network propagation to improve performance and clinical consistency of rare disease diagnosis. 2026. hal-05517071

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1 Combining phenotypic similarity and network

2 propagation to improve performance and clinical

3 consistency of rare disease diagnosis

4

5 Maroua Chahdil¹,², Carolina Fabrizzi¹, Marc Hanauer¹, Caterina Lucano¹, Ana Rath¹, David Lagorce¹*

6 Laurent Tichit²*

7 * corresponding authors

8 ¹INSERM, US14 – Orphanet, Plateforme Maladies Rares, 96 rue Didot, 75014, Paris, France

9 ²Aix Marseille Univ, CNRS, I2M, Marseille, France

10 Abstract

11 Achieving timely diagnosis for rare diseases remains challenging due to, among others,
12 phenotypic heterogeneity and incomplete clinical data. While the Solve-RD project developed
13 a phenotype-based gene prioritisation method, this approach did not account for the clinical
14 consistency among related diseases in Orphanet's hierarchical classifications.

15 We present a phenotype-based computational pipeline that ranks candidate ORPHAcodes
16 based on patient phenotypes. The pipeline computes patient-disease similarity using
17 asymmetric semantic aggregation of Human Phenotype Ontology terms, filtering subsumed
18 terms and incorporating Orphanet frequency annotations. Evaluated on 139 expert curated
19 Solve-RD cases representing 78 distinct ORPHAcodes, our methodology outperformed the
20 established Solve-RD baseline method, achieving a harmonic mean rank of 4.64 for confirmed
21 diagnoses (versus 7.97) and retrieving the correct suspected rare disease within the top 10
22 positions for 39% of patients (versus 29%). We then explore a disease similarity network using
23 Random Walk with Restart to generate ranked candidate lists. Two complementary
24 experiments demonstrate that RWR-ranked candidates exhibited improved clinical
25 consistency, reflected by their proximity within the Orphanet nomenclature of rare diseases.
26 This approach provides more interpretable and actionable differential diagnosis hypotheses
27 to guide clinical decision-making

## 28 Author summary

29 Many patients with rare diseases face prolonged diagnostic delays due to the extreme
30 heterogeneity of rare disorders associated with the variability of their clinical manifestations,
31 which complicates interpretation and requires structured phenotypic representations and
32 expert knowledge. We developed a computational pipeline that compares patients'
33 phenotypes with those documented for rare diseases in the Orphanet database. Rather than
34 relying solely on direct matching of clinical signs and symptoms, our approach leverages
35 relationships between diseases by propagating information through a network connecting
36 patients and diseases. Testing on 139 cases from the European Solve-RD project, our method
37 improved identification of correct diagnoses and generated more clinically coherent candidate
38 lists by accounting the Orphanet nomenclature. This work provides a methodology dedicated
39 to assisting clinicians in developing diagnostic hypotheses for rare diseases.

40 Introduction

41 A disease is defined in Europe as a Rare Disease (RD) when the number of affected patients
42 equal or fewer than 1 in 2,000 subjects [1]. According to Orphanet (www.orpha.net), more than
43 6,000 RDs have been identified worldwide, 72.2% of which have a genetic origin. However,
44 despite this predominance of genetic etiologies, around 35% of RDs still lack an identified
45 causative gene [2]. Establishing an accurate clinical diagnosis of RD remains particularly
46 challenging because these diseases often affect multiple organ systems or physiological
functions [3]. Consequently, patients often experience prolonged diagnostic delays and may receive initial misdiagnoses, with some remaining undiagnosed. Several large-scale initiatives aim to improve diagnostic outcomes for RD, including the UK 100,000 Genomes Project [4] and the European Solve-RD project (https://solve-rd.eu/) [5].

Within the Solve-RD project, a phenotype-based semantic similarity pipeline, employing the Human Phenotype Ontology (HPO) [6], was developed to guide variant prioritization and generate diagnostic hypotheses [7], alongside efforts to uncover molecular causes in patients remaining undiagnosed after whole exome sequencing [8,9]. The computational package RunSolveRD (RSD) [10] was developed to compute similarity between clinical entities based on phenotypic annotations. Nevertheless, RSD exhibits sensitivity to sparsely annotated diseases, resulting in variability in candidate gene lists, and its closed-source framework limits extensibility, maintenance and adaptation. Over the last decade, various graph-based methods and tools have been introduced to exploit ontology-based semantic similarity. These methods fall into three categories: (i) graph-based methods that compute ontology-based semantic similarity, such as the Wang method [11]; (ii) likelihood-ratio approaches, like RDmaster [12] (8) and PheLR [13], which combine HPO annotations with epidemiological data to compute phenotypic evidence for candidate diseases; and (iii) network-based methodologies such as RDmap [14] that model relationships between diseases and patients. Network propagation methods like Random Walk with Restart (RWR) can handle sparse or noisy phenotype annotations by diffusing information across neighbouring disease nodes [15]. More recent tools such as Phen2Disease [16] and PhenoDP [17] further integrate bidirectional matching or learned embeddings to prioritise candidate diseases or genes.

Despite these methodological advances, several aspects remain underexplored in phenotype-driven RD diagnostics, notably the integration of Orphanet's hierarchical rare disease classifications structure. In this study, we present a decision-support approach that combines group-wise semantic similarity measures with network propagation using RWR. Our method computes phenotypic similarity between patients' clinical signs and those annotated in each ORPHAcode (Orphanet's unique and time-stable RD identifiers), while incorporating
estimated phenotype frequency and disease classification level in order to improve both
ranking performance and clinical coherence of diagnostic hypotheses.

## 77 Materials and Methods

78 Orphanet nomenclature and clinical consistency Data used

79 The Human Phenotype Ontology (HPO)

80 HPO [6] provides a standardised vocabulary of phenotypic abnormalities encountered in
81 human disease. For this study, we used the HPO 2025-03-03 release which embedded 14570
82 unique HPO terms.

83 Orphanet data

84 We employed a reference collection based on the 'Phenotypes Associated with Rare
85 Disorders' May 2025 release from [Orphadata.com](https://Orphadata.com), which includes 4,319 disorder-level
86 ORPHAcodes, manually curated and annotated with HPO terms. At Orphanet, the Phenotypes
87 Database Manager is responsible to systematically review the literature to identify disease-
88 associated phenotypic abnormalities, map them to the most appropriate HPO terms, and
89 classify each sign by frequency of occurrence in the disease population. Indeed, for each HPO
90 term associated with a rare disease Orphanet assigns six frequency categories estimated from
91 qualitative prevalence in affected populations: obligate (100%), very frequent (99-80%),
92 frequent (79-30%), occasional (29-5%), very rare (4-1%) and excluded (0%). When no suitable
93 HPO term exists, the closest term is used and a request for a new term is submitted to the
94 HPO team. Herein this dataset for our study, to ensure a consistent unit of representation
95 across disease annotations and patient diagnosis aligned to the Orphanet nomenclature
96 principles, all implicated ORPHAcodes were harmonised to their reference ORPHAcode
97 Disorder level.

98
99 **Solve-RD case cohort subset**

100 To evaluate and validate the proposed pipeline, we used the anonymised “solved patients”
101 data from the Solve-RD project, stored in the Phenopackets format, a computer-readable
102 standard compliant with GA4GH specifications (https://www.ga4gh.org/). Between 2018 to
103 2023, clinicians affiliated with the Solve-RD consortium annotated medical records of patients
104 suffering from undiagnosed RDs, using a minimum of five HPO clinical signs. Diagnostics
105 information and HPO annotations were extracted directly from the corresponding phenopacket
106 files.

107 Within the Solve-RD dataset, a subset of 817 patients had a confirmed diagnosis mapped to
108 a known ORPHAcode with some could be associated with multiple patients. An Orphanet
109 medical expert manually reviewed these cases, and selected 139 patients whose phenotypic
110 profiles were consistent with the expected phenotype of the annotated ORPHAcode. Among
111 the 96 ORPHAcodes represented across the 139 patients, 18 corresponded to Subtype of
112 disorder level. Regardless of the Orphanet classification considered, a Disorder level always
113 has the same subtype(s) of disorder. Therefore, here again, for these 18 ORPHAcodes, we
114 have considered their parent Disorder level, resulting in 78 unique Disorder level
115 ORPHAcodes.

116 This curated set was used as the ground-truth dataset, based on two criteria: (i) diagnostic
117 accuracy and expert validation: the expert validation was used as the confirmed ORPHAcode;
118 (ii) cohort comprehensiveness and heterogeneity: the Solve-RD clinicians contributing these
119 patients are affiliated with four European Reference Networks, covering major RDs clusters
120 and ensuring that the cohort reflects the phenotypic and diagnostic diversity of the target
121 population.

122 Removing patients’ HPO redundant terms

123 It has been well argued that information overlap and/or imprecise clinical descriptions could
124 lead to over-estimation of relatedness or introduce noise in ranking accuracy [21,22]. To try to
avoid this issue we decided to remove parent terms if its child is also found in the annotations.

To apply such a principle, we used the minimal_set method from the ontologyIndex R package, part of the OntologyX suite [23], which provides functions for ontology-aware operations. This method removes ancestor terms while retaining their descendants by traversing the HPO directed acyclic graph. For instance, when both "Microcephaly" (HP:0000252) and its parent "Abnormality of head" (HP:0000234) appear together, only the more specific child term is kept. Applying this approach across 139 patient profiles eliminated 993 redundant annotations from 2,761 total unique HPO terms.

## 133 Measuring semantic similarity between ontology terms

Ontologies provide a formal representation of domain knowledge by organising concepts into structured hierarchies, often modelled as directed acyclic graphs in which nodes may have multiple parent and child relationships. Semantic similarity measures quantify the relatedness between ontology terms based on their positions in the graph, commonly using information content (IC), which reflects term specificity derived from annotation frequency. The IC of a term *x* is defined as $IC(x) = -log(p(x))$, where *p(x)* is the probability of observing *x* in the annotation corpus. This probability is computed as the number of occurrences of *x* and its descendants in the annotations divided by the total occurrences of all terms. The root term appears in all annotations, giving it an IC of 0. More specific terms have higher IC values. When comparing two terms, IC-based approaches rely on their Most Informative Common Ancestor (MICA), defined as the shared ancestor with the highest IC.

For our study, we benchmarked six established IC-based similarity measure approaches for comparing ontology terms: Resnik [24] which uses only the IC of the MICA; Lin [25] and Jiang-Conrath (JC) from HPOSim [26], derived from Jiang-Conrath distance [27] which both incorporate the IC of individual terms and their MICA; Graph information content (GraphIC) [26] and information coefficient (SimIC) [28] which further adjust similarity measures to
150 account for graph structure and shared IC and finally Relevance [29] which extends Lin's
151 measure by weighting similarity according to the probability of the MICA.

$$
152 \qquad \mathrm{Resnik}(a, b) = \mathrm{IC}(\mathrm{MICA}(a, b)) \qquad (1)
$$

153

$$
154 \qquad \mathrm{Lin}(a, b) = \frac{2 \times \mathrm{Resnik}(a,b)}{\mathrm{IC}(a) + \mathrm{IC}(b)} \qquad (2)
$$

155

$$
156 \qquad JC(a,b) = IC(a) + IC(b) - 2 \times IC(MICA(a,b)) \quad (3)
$$

157

$$
158 \qquad \mathrm{GraphIC}(a, b) = \frac{\sum_{c \in A(a) \cap A(b)} \mathrm{IC}(c)}{\sum_{c \in A(a) \cup A(b)} \mathrm{IC}(c)} \qquad (4)
$$

159

$$
160 \qquad \mathrm{SimIC}(a,b) = \mathrm{Lin}(a,b) \times \left(1 - \frac{1}{1 + \mathrm{Resnik}(a,b)}\right) \qquad (5)
$$

161

$$
162 \qquad \mathrm{Relevance}(a,b) = \mathrm{Lin}(a,b) \times (1 - p(\mathrm{MICA}(a,b))) \quad (6)
$$

163 **Aggregating pairwise similarity measures**

164 When comparing sets of terms, pairwise similarities are aggregated into a single groupwise
165 semantic similarity metric using an aggregation function. Let X = {x₁, x₂, ..., xₘ} denote the set
166 of m HPO terms associated with a patient's phenotype, and Y = {y₁, y₂, ..., Yₙ} denote the set
167 of n HPO terms associated with a candidate rare disease. Let S ∈ ℝ^{mxn} represent the
168 pairwise similarity matrix, where element Sᵢⱼ ∈ [0,1] denotes the semantic similarity between
169 patient term $x_i \in X$ and disease term $y_j \in Y$, computed using a pairwise similarity measure
170 (e.g., Resnik, Lin, or Jiang-Conrath).

171 We employed four established aggregating functions recognised as the most effective state-of-the-art methods: Best Match Average (BMA) [11], FunSimAvg [29,30], FunSimMax [29,30]
172 and FunSimMaxAsym [31]. BMA computes the arithmetic mean of best matches for each term
173 across both sets. FunSimAvg calculates the arithmetic mean of the average best matches
174 from each direction. FunSimMax selects the maximum of the two directional averages.
175

176 $BMA(S) = \frac{\sum_{i=1}^{m} \max_j(S_{ij}) + \sum_{j=1}^{n} ma_i(S_{ij})}{n+m} \quad (7)$

177 $FunSimAvg(S) = \frac{\frac{1}{m}\sum_{i=1}^{m} \max_j(S_{ij}) + \frac{1}{n}\sum_{j=1}^{n} ma_i(S_{ij})}{2} \quad (8)$

178 $FunSimMax(S) = max(\frac{1}{m}\sum_{i=1}^{m} \max_i(S_{ij}), \frac{1}{n}\sum_{j=1}^{n} \max_i(S_{ij})) \quad (9)$

179 $FunSimMaxAsym(S) = \frac{1}{m} \sum_{i=1}^{m} \max_j(S_{ij}) \quad (10)$

180 $FunSimMaxAsym$ extends $FunSimMax$ by aggregating semantic similarities in a single direction from patient to disease. Formally, for each patient term $x_i \in X$, we identify its best match among all disease terms in $Y$ by computing $\max_j S_{ij}$, then average these maximum similarities across all m patient terms. This contrasts with symmetric measures (equations 7–9) that aggregate matches in both directions, from patient to disease and from disease to patient. The asymmetric formulation prioritises complete coverage of the patient's observed phenotype: every patient term $x_i$ must find its best match within the disease's characteristic phenotypes $Y$, but not all disease terms $y_j$ need correspond to observed patient phenotypes.
181
182
183
184
185
186
187
188 This directional choice avoids penalising diseases for possessing additional characteristic phenotypes not manifested in the patient, thereby accommodating incomplete phenotypic expression, variable disease presentation, and observational noise in clinical documentation.
189
190
191 **Evaluation of optimal similarity measures and aggregation**
192 **methods**

193 To identify optimal combinations of similarity measures and aggregation functions, we
194 benchmarked all 24 combinations of the six semantic similarity measures with the four
195 aggregation functions presented above for each of our 139 patients. For each patient, we
196 determined the rank of their diagnosed disease among all candidate diseases and computed
197 the mean rank across the cohort.

198 To average ranks, the harmonic mean emphasises smaller ranks, making it suitable for
199 averaging ranks where lower ranks matter more than higher ones:

$$
200 \qquad H(S) = \frac{n}{\sum_{i=1}^{n} \frac{1}{S_i}} \quad (11)
$$

201 Where *n* is the number of elements in the set S.

202 To visualise global ranking performance, we calculated and plotted cumulative distribution
203 functions (CDFs). The CDF quantifies the probability P(X ≤ r) that the diagnosed disease ranks
204 at position r or better, providing a global view of ranking effectiveness across the cohort.

205 **HPO term frequency weighting and excluded terms**

206 We hypothesised that highly prevalent phenotypes within a disease should weigh more heavily
207 in similarity computations than rare phenotypes. To evaluate this, as applied in the Dream
208 Rare-X project [32], we mapped the frequency categories, excepting the "excluded" one, to
209 numerical weights using monotonic vectors of length five, where each position corresponds to
210 one category in descending frequency order. Hence, we generated 31 weighting schemes:
211 (5,4,3,2,1), (4,4,3,2,1), (4,3,3,2,1), ..., (2,1,0,0,0), (1,1,0,0,0), (1,0,0,0,0), testing all patterns
212 where weights decrease or remain constant from "obligate" to "very rare" categories.

213 We modified the aggregation function as follows:
214 $FunSimMaxAsymWeighted(S) = \frac{1}{m} \sum_{i=1}^{m} \max_j(\omega_i \omega_j S_{ij})$ (10)

215 where $\omega_i$ and $\omega_j$ represent the frequency-derived weight for the terms $x_i$ and $x_j$.

216 Clinical signs annotated as "excluded", indicating phenotypes incompatible with a diagnosis,
217 triggered automatic removal of the corresponding disease from ORPHAcode candidates list.

218 **Random-walk propagation on disease similarity network**

219 We constructed a network in which nodes represent RD and edges their phenotypic similarity.
220 For each pair of RD, we computed a single groupwise similarity measure based on HPO
221 annotations using the symmetric aggregation function FunSimMax.

222 To prioritise candidate RD for a given patient, we extended this network by adding a patient
223 node connected to each RD. The weight of each patient-RD edge was computed using the
224 asymmetric function FunSimMaxAsym.

225 We then applied a Random Walk with Restart propagation on this network [33,34]. At each
226 step the walker either follows an outgoing edge according to the transition probabilities derived
227 from edge weights or restarts to the patient node with a given probability. The walk converges
228 to a stationary distribution, which we interpret as a similarity score, with higher values
229 indicating greater phenotypic relatedness to the patient.

230 The damping factor $\alpha$ controls the balance between exploration and restart. Higher values of
231 $\alpha$ enable longer walks and global propagation, while lower values increase restart frequency
232 and emphasize local neighbourhoods.

233 By constraining the walk through an appropriately low damping factor $\alpha$, we maintain locality
234 around the patient node. This constraint limits the disproportionate influence of highly
235 connected hubs, which can otherwise introduce bias into the ranking process. This local
236 exploration prioritises clinically relevant RD candidates by integrating: (i) direct similarity
237 between patient and RD and (ii) indirect phenotypic relationships mediated through the RD-
238 RD similarity network structure.

239 Technical implementation

240 Our framework is implemented in the Python Programming Language version 3.12 and takes
241 advantage of Python's extensive collection of data science libraries. In particular, pandas 2.2
242 is used for data manipulation and NetworkX v3.4 for network-related tasks. Ontology queries
243 and HPO term inspection were performed with the hpo3 library (v1.4), which includes the
244 March 2025 HPO release, and ontologyX 2024-02-20 R package for the subsuming HPO
245 section. The workflow is executed in a Linux environment (Ubuntu 22.04) and organised into
246 a reproducible workflow using Snakemake 9.3. To ensure full reproducibility, the repository
247 provides a Conda 25.3 environment. The Snakemake workflow automates the entire pipeline,
248 including semantic similarity computation, network construction, random-walk execution, and
249 ranking evaluation results. All source code and documentation required to reproduce the
250 analyses presented in this study are available at
251 https://github.com/Orphanet/OrphaScape_SimWalk

252 Data availability

253 The Solve-RD subset analysed during the current study is based on datasets available as
254 phenopackets at the EGA (EGAD00001009767, EGAD00001009768, EGAD00001009769
255 and EGAD00001009770 under Solve-RD study EGAS00001003851).
256 **Results**

257 **A phenotype-based pipeline for rare disease diagnosis**
258 **guidance**

259

<figure><img src="image_3.png" /><figcaption>260 **Fig. 1. Overview of the phenotype-based pipeline.**</figcaption></figure>

261

262 Following up the Solve-RD project [7], we developed a phenotype-based pipeline to guide rare
disease diagnosis (Fig. 1). The pipeline takes three inputs: the HPO ontology, the Orphadata
263
264 'Phenotypes Associated with Rare Disorders' dataset and a patient's HPO-encoded
265 phenopacket (Fig. 1a). It computes phenotypic similarity between the patient and
266 ORPHAcodes (Fig. 1d), then constructs a weighted network where nodes represent diseases
267 and the patient, with edge weights reflecting phenotypic similarity (Fig. 1e). Random walk with
268 restart (RWR) propagates information from the patient node through this network, yielding a
269 ranked list of candidate ORPHAcodes (Fig. 1g). Users can export the output network to graph
270 database systems for visualisation and analysis. This enables exploration of the patient's local
271 neighbourhood, including disease-associated genes, to guide subsequent variant
272 investigation (Fig. 1h).

273 Before computing semantic similarity, we applied two pre-processing steps (Fig. 1b-c): firstly,
274 we incorporated estimated frequency categories for each HPO term associated with a disease
275 from Orphanet data, and secondly we removed subsumed HPO terms from patient profiles
276 when more specific descendant terms were present.

277 To determine the optimal semantic similarity approach (Fig. 1d), we benchmarked all 24
278 combinations of six IC-based similarity measures with four groupwise aggregation methods,
279 all described in the Methods section. Each combination produces a single similarity score
280 between the patient and each ORPHAcode.

281 Resnik + FunSimMaxAsym outperforms other groupwise
282 semantic similarity measures

283 We evaluated 24 configurations combining six pairwise similarity measures (Resnik, Lin,
284 Jiang-Conrath, Relevance, Information Coefficient, GraphIC) with four aggregation functions
285 (BMA, FunSimAvg, FunSimMax, FunSimMaxAsym) across the 139-patient cohort. Figure 2
286 presents cumulative distribution functions for the seven highest-performing configurations
287 alongside the RSD baseline. Resnik + FunSimMaxAsym (red) consistently ranked confirmed
288 diagnoses lowest, placing 38% of correct ORPHAcodes within the top 10 positions compared
289 with 29% for RSD (blue). This configuration achieved a harmonic mean rank of 5.45 versus
290 7.97 for RSD (Table 1). Complete results for all 24 configurations appear in Supplementary
291 Table S1.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Performance comparison of semantic similarity measures and aggregation methods for ranking rare disease diagnoses. Cumulative distribution functions for the seven highest-performing configurations (out of 24) and the RSD baseline (blue) across 139 patients. The x-axis represents the rank position of the correct ORPHAcode; the y-axis shows the cumulative proportion of patients whose correct diagnosis appears at or above that rank. CDFs positioned towards the upper-left indicate superior performance.</figcaption></figure>
<table><caption>Table 1. Harmonic mean ranks of correct diagnoses across semantic similarity configurations (7 best + RSD).</caption><thead><tr><th>Pairwise semantic similarity measure</th><th>Aggregation method</th><th>Harmonic mean rank</th></tr></thead><tbody><tr><td>Resnik</td><td>FunSimMaxAsym</td><td>5.45</td></tr><tr><td>SimIc</td><td>FunSimMaxAsym</td><td>5.85</td></tr><tr><td>Relevance</td><td>FunSimMaxAsym</td><td>5.96</td></tr><tr><td>Lin</td><td>FunSimMaxAsym</td><td>6.26</td></tr><tr><td>SimIc</td><td>FunSimMax</td><td>6.37</td></tr><tr><td>Relevance</td><td>FunSimMax</td><td>6.52</td></tr><tr><td>Resnik</td><td>FunSimAvg</td><td>7.81</td></tr><tr><td>RSD</td><td></td><td>7.97</td></tr></tbody></table>

Performance of 7 best combinations of pairwise semantic similarity measures and aggregation methods, plus the RSD baseline, evaluated across 139 patients with 78 distinct confirmed ORPHAcodes. Lower harmonic mean ranks indicate superior diagnostic ranking performance. Complete results for all 24 configurations appear in Supplementary Table S2.

Effect of subsumed HPO terms removal on ranking

Figure 3 compares ranking performance with (green) and without (red) subsumed terms using

Resnik + FunSimMaxAsym. Filtering subsumed terms retrieves the confirmed ORPHAcodes.
315 within the top ten positions for 38% of patients, compared with 35% before filtering and 25%
316 for the RSD baseline (blue).

317

<figure><img src="image_5.png" /></figure>

318

319 **Figure 3. Diagnostic ranking performance with and without subsumed term filtering.** Comparison
320 of Resnik + FunSimMaxAsym using unfiltered (green) versus filtered (red) patient profiles, and RSD
321 baseline (blue). The cumulative distribution function shows the proportion of patients whose confirmed
322 diagnosis ranked at position *r* or better.

323 Removing subsumed HPO terms improves ranking performance. As shown in Table 2, the
324 harmonic mean rank of the confirmed ORPHAcode decreases from 5.45 to 4.73 after filtering
325 (lower is better).

326 This filtering strategy is applied exclusively to patient profiles. In contrast, HPO annotated
327 ORPHAcodes are not filtered because they represent population-level descriptions with
328 frequency estimates assigned to terms at multiple granularity levels. Removing subsumed
329 terms would eliminate this frequency information and reduce the specificity of disease
330 annotations.

331

<table><thead><tr><td>Method</td><td>Harmonic mean rank</td></tr></thead><tbody><tr><td>Removal</td><td>4.73</td></tr><tr><td>No removal</td><td>5.45</td></tr><tr><td>RSD</td><td>7.97</td></tr></tbody></table>

332 Table 2. Harmonic mean rank of confirmed ORPHAcodes before and after filtering subsumed
333 HPO terms.

334 Lower values indicate better performance.

335

336 Effect of frequency-based weighting on ranking
337 performance

338 We developed and evaluated a weighted variant of *FunSimMaxAsym* where HPO terms are
339 weighted according to their annotated frequency in the five categories involved: obligate, very
340 frequent, frequent, occasional, very rare (see Materials and Methods).

341 Figure 4 and Table 3 suggest that down-weighting very rare clinical signs improves ranking
342 performance. Given our limited sample size, these represent preliminary trends. The weighting
343 scheme (2,2,2,2,1), which reduces the contribution of very rare signs (to half the weight of
344 other categories), performed best, followed by (1,1,1,1,0), which excludes very rare terms
345 entirely.
346

<figure><img src="image_6.png" /></figure>

347

<caption>Figure 4. Impact of frequency-based weighting on diagnostic ranking performance.</caption>

348
349 Cumulative distribution functions comparing four approaches: three frequency-weighting schemes for
350 *FunSimMaxAsym*: (2,2,2,2,1) (red), (1,1,1,1,0) (purple), unweighted control (1,1,1,1,1) (green), and the
351 RSD baseline method (blue). The weighting vectors correspond to the five Orphanet frequency
352 categories in descending order: obligate, very frequent, frequent, occasional, very rare.

353

354

355

356

357

358
<table><caption>Table 3. Harmonic mean rank of correct diagnoses under frequency-weighting schemes.</caption><thead><tr><td>Weighting</td><td>Harmonic mean rank</td></tr></thead><tbody><tr><td>2,2,2,2,1</td><td>4.64</td></tr><tr><td>1,1,1,1,0</td><td>4.69</td></tr><tr><td>1,1,1,1,1</td><td>4.73</td></tr><tr><td>RSD</td><td>7.97</td></tr></tbody></table>

Performance comparison of four approaches: three frequency-weighting variants of FunSimMaxAsym: (2,2,2,2,1), (1,1,1,1,0), and unweighted control (1,1,1,1,1), and the RSD baseline method. Weighting vectors correspond to the five Orphanet frequency categories in descending order: obligate, very frequent, frequent, occasional, very rare. Lower harmonic mean ranks indicate superior diagnostic ranking performance. Complete results for all 31 tested weighting schemes are provided in the Supplementary Table S3.

Effect of network propagation on clinical consistency of top-ranked candidates

Rather than focusing only on changes in the average rank of the confirmed diagnosis before and after applying RWR (Figure S1), we evaluated whether network propagation yields clinically more coherent candidate rankings according to the Orphanet nomenclature. Specifically, we assessed RWR's ability to improve clinical consistency amongst the candidates. We conducted two complementary analyses to address this question.

Both analyses evaluated clinical consistency by counting the number of GDs shared between each candidate ORPHAcode and the confirmed ORPHAcode, but differed in their scope of hierarchy traversal.
In the first analysis, we considered, for each disease, only its immediate parent GD (i.e. the most specific GD) across all Orphanet classifications in which it appears. We computed the harmonic mean rank of candidate ORPHAcodes sharing at least one of these immediate parent GDs with the confirmed diagnosis. This horizontal approach in Orphanet classifications captures the diversity of clinical contexts in which a disease may be classified, without the constraint of a single preferential hierarchy, whilst limiting depth to the most specific classification level.

The damping factor $\alpha$ substantially influenced performance, with optimal results at $\alpha \in [0.25, 0.5]$. At $\alpha = 0.3$, diseases sharing the relevant GDs achieved a harmonic mean rank of 14.13, compared with 16.7 before propagation ($\alpha = 0$) and 25.57 for RSD (Table 4).

<table><thead><tr><td>Damping factor value</td><td>Harmonic mean rank of ORPHAcodes with shared GDs</td></tr></thead><tbody><tr><td>RSD</td><td>25.57</td></tr><tr><td>0 (no random walk)</td><td>16.70</td></tr><tr><td>0.05</td><td>17.50</td></tr><tr><td>0.1</td><td>17.50</td></tr><tr><td>0.15</td><td>17.63</td></tr><tr><td>0.2</td><td>17.74</td></tr><tr><td>0.25</td><td>14.14</td></tr><tr><td>0.3</td><td>14.13</td></tr><tr><td>0.35</td><td>14.23</td></tr><tr><td>0.4</td><td>14.32</td></tr><tr><td>0.45</td><td>14.51</td></tr></tbody></table>
<table><caption>Table 4: Harmonic mean rank of ORPHAcodes sharing at least one lowest-level GD with the confirmed ORPHAcode across varying damping factor α values.</caption><tr><td>0.5</td><td>14.53</td></tr><tr><td>0.6</td><td>17.27</td></tr><tr><td>0.7</td><td>20.19</td></tr><tr><td>0.8</td><td>30.84</td></tr><tr><td>0.9</td><td>120.09</td></tr><tr><td>1.0</td><td>722.76</td></tr></table>

In the second analysis, we restricted our approach to the preferential parent hierarchy of each disease, considering all GDs within this single classification branch. This vertical approach captures clinical consistency along the most relevant classification path for each disease, avoiding noise from distantly related alternative classifications whilst maintaining rich clinical information across multiple hierarchical levels within that branch.

RWR increased the proportion of patients with at least one shared GD between top 10 candidates and confirmed diagnosis from 14% (α = 0) to 30% (α = 0.3). Patients with multiple shared GDs increased from 0.7% to 13%. Table 5 presents detailed GDs overlap counts for 10 representative patients with highest baseline overlap, demonstrating that 9 out of 10 showed increased GDs sharing after RWR. Across the full cohort, 16% of patients showed improved GD overlap following propagation.

<table><thead><tr><td>Patient and confirmed ORPHAcode</td><td>Shared GDs within top-10 candidates (pre-RWR)</td><td>Shared GDs within top-10 candidates (post-RWR)</td></tr></thead><tbody><tr><td>P3294 (ORPHA:199)</td><td>8</td><td>19</td></tr></tbody></table>
<table><tr><td>P6438 (ORPHA:90652)</td><td>8</td><td>6</td></tr><tr><td>P6774 (ORPHA:1465)</td><td>7</td><td>12</td></tr><tr><td>P6777 (ORPHA:1465)</td><td>7</td><td>9</td></tr><tr><td>P3237 (ORPHA:442835)</td><td>6</td><td>7</td></tr><tr><td>P3837 (ORPHA:2332)</td><td>5</td><td>7</td></tr><tr><td>P5345 (ORPHA:2020)</td><td>4</td><td>5</td></tr><tr><td>P8285 (ORPHA:2152)</td><td>3</td><td>6</td></tr><tr><td>P9601 (ORPHA:36386)</td><td>2</td><td>4</td></tr><tr><td>P8535 (ORPHA:352577)</td><td>2</td><td>3</td></tr></table>

Table 5. Top ten patients with the highest number of distinct shared GDs between their top ten ranked ORPHAcode candidates and the confirmed ORPHAcode, restricted to the preferential parent classification. Patients are ranked based on the number of GD prior to applying the RWR.

Both analyses demonstrate that RWR enhances clinical consistency: the ORPHAcodes sharing lowest-level DG with confirmed diagnoses rank higher within top 10 predictions after network propagation and among these, the ORPHAcodes sharing the highest number of GD restricted to the preferential parent come from after applying the RWR, providing clinically interpretable candidate clusters that facilitate differential diagnosis.

## Effect of network propagation on diagnostic performance

We evaluated damping factor ($\alpha$) values to assess the trade-off between individual diagnosis ranking and clinical consistency of top predictions. Increasing $\alpha$ progressively decreased ranking performance for confirmed ORPHAcodes. As previously mentioned, at $\alpha=0$ (no
411 network propagation), the method achieved a harmonic mean rank of 4.64. Applying RWR
412 with α=0.3 yielded a harmonic mean rank of 5.55, while α values above 0.7 performed worse
413 than the RSD baseline (7.97).

414 Despite lower individual ranking performance, α=0.3 maximized clinical consistency by
415 prioritizing ORPHAcodes that share GDs with the confirmed diagnosis within the top 10
416 predictions, where shared GDs were restricted to the preferential parent hierarchy (see clinical
417 consistency analysis). This configuration balances two objectives: maintaining competitive
418 ranking (5.55 vs 4.64 without RWR) while enriching top predictions with clinically related
419 diseases that aid differential diagnosis. For applications prioritising strict ranking accuracy,
420 α=0 remains optimal; for clinical decision support requiring interpretable disease candidates,
421 α=0.3 provides superior utility. Complete results for all α values appear in Supplementary
422 Table S1.

423

424

Discussion

425 This study demonstrates that combining phenotype-based semantic similarity with network
426 propagation effectively ranks rare disease diagnostic hypotheses and promotes clinical
427 consistency among top candidates according to Orphanet nomenclature. Three
428 methodological refinements contributed to performance: first, aggregating pairwise Resnik
429 similarities using FunSimMaxAsym provided robust patient-disease comparison; second,
430 removing subsumed HPO terms reduced ontological redundancy, yielding more discriminative
431 phenotype representations; third, down-weighting very rare clinical features refined ranking by
432 emphasising characteristic disease features.
433 Network propagation enhances clinical consistency

434 through group of disorders alignment

435 Random walk with restart on the ORPHAcode similarity network leverages both direct
436 phenotypic matches and indirect relationships through shared network topology. This
437 approach addresses a fundamental limitation of direct similarity measures: annotation density
438 bias. Orphanet's phenotypic annotations are manually curated by clinical experts and maintain
439 high individual quality. However, annotation completeness varies across diseases due to three
440 factors: (i) the period when annotation was performed, (ii) available medical knowledge and
441 case reports at that time, and (iii) the HPO release version used. Despite regular updates,
442 diseases with sparse annotations may rank poorly even when clinically relevant, while
443 extensively annotated diseases tend to rank highly regardless of appropriateness (31).

444 RWR mitigates this bias by exploring the local neighbourhood around the patient node,
445 identifying indirectly related diseases through network connectivity rather than direct
446 annotation overlap. By leveraging Orphanet's classification hierarchy, RWR compensates for
447 incomplete annotations and captures phenotypically homogeneous disease clusters. Within
448 the top 10 predictions, RWR consistently prioritised diseases sharing many lowest-level GDs
449 with confirmed diagnoses or exhibiting the same GDs when constrained to preferential parent
450 classifications (Table 4). This clinical consistency proves particularly valuable: although
451 individual confirmed diagnoses occasionally ranked lower, their GD neighbours appeared
452 prominently, maintaining diagnostic utility. The dual benefits of RWR, exploiting indirect node
453 similarities and reinforcing topologically coherent candidates, address challenges from
454 phenotypic heterogeneity and incomplete patient presentations that challenge purely
455 similarity-based approaches.

456 These findings support clinical decision support systems that present disease clusters rather
457 than isolated predictions, improving interpretability when clinicians evaluate differential
458 diagnoses for rare diseases. Ongoing efforts at Orphanet focus on improving annotation depth
459 and consistency, with emerging Retrieval-Augmented Generation techniques showing
460 promise for enhancing annotation accuracy and workflow efficiency.

461 **Frequency weighting and exclusion criteria enhance**
462 **accuracy despite coverage limitations**

463 Incorporating Orphanet frequency annotations improved ranking performance (Table 3, Fig. 4). The optimal weighting scheme (2,2,2,2,1) down-weighted very rare phenotypes while preserving contributions from obligate through occasional features, thereby emphasising characteristic disease patterns over nonspecific findings.

467 Orphanet also flags certain phenotypes as "excluded," indicating clinical signs whose
468 presence precludes a diagnosis. Our pipeline integrates these exclusion criteria by
469 automatically removing incompatible diseases from candidate lists. However, annotation
470 coverage remains limited: fewer than 400 of approximately 4,300 annotated ORPHAcodes
471 (8.05%) contain exclusion flags, and excluded phenotypes represent only 0.62% of all HPO
472 annotations (see proportions in Supplementary Information S4). Although Orphanet continues
473 expanding these annotations, current sparsity constrains their diagnostic impact. However,
474 this small number of exclusion annotations does not stand for a weakness in the annotation
475 process but arises because relatively few RDs require the exclusion of a phenotype to
476 establish a valid diagnosis. This is due to the phenotypic variability of RDs, and it is very
477 difficult to assert that a clinical sign never occurs in a specific RD, except in a relatively small
478 number of cases.
479 **Structural challenges in ontology-based similarity**
480 **computation**

481 Ontology-based similarity measures face inherent challenges when applied to HPO. First,
482 HPO's multiple inheritance structure, where terms belong to several branches, introduces
483 path-length variability that influences similarity scores inconsistently across the ontology [35].
484 Second, sibling terms sharing a parent node receive high similarity scores despite potentially
485 opposing clinical meanings; for example, Hypertonia (HP:0001276) and Hypotonia
486 (HP:0001252) both descend from Abnormal muscle tone (HP:0003808) yet represent
487 contradictory phenotypes [36]. Such structural ambiguities can produce misleading similarity
488 scores that do not reflect clinical reality.

489 Our approach partially mitigates these limitations: removing subsumed terms reduces path-
490 length effects; FunSimMaxAsym's patient-centred directionality focuses on observed
491 phenotypes rather than complete disease profiles; network propagation supplements
492 phenotypic similarity with disease group topology. However, fundamental ontological
493 ambiguities remain unresolved. The requirement for patients to present at least five clinical
494 signs [22,37] addresses data sparsity rather than structural issues, though richer phenotypic
495 profiles do improve discriminative power.

496 These limitations underscore that purely phenotype-based approaches cannot fully capture
497 diagnostic complexity. Integrating additional information sources (genetic data, temporal
498 progression, or biochemical markers) represents a necessary direction for robust rare disease
499 decision support systems.

500 **Limitations**

501 Phenotype-based similarity measures depend critically on the completeness and specificity of
502 clinical annotations especially for patients. Our ground-truth cohort from Solve-RD exhibits
several feature biases that may affect generalisability. First, the historical annotation protocol restricted clinicians to a predefined HPO subset, limiting representation of phenotypic heterogeneity. Second, patient recruitment through specific European Reference Networks may have introduced domain-specific HPO usage patterns that inadequately capture the multisystemic nature of many rare diseases. Third, individual clinician expertise likely introduced variation in term selection and granularity. These biases may contribute to suboptimal classification of confirmed diagnoses in cases where patient phenotyping differs from Orphanet annotations, which are made on the basis that in scientific literature a population of patients presents a certain clinical sign(s) with a specified occurrence.

The cohort size (139 patients representing 78 distinct ORPHAcodes) further limits statistical power for detecting performance differences between methods, particularly for rare weighting schemes and damping factor configurations. External validation on independent cohorts with different annotation workflows is required to assess generalisability. Future annotation strategies should encourage cross-specialty, multi-domain phenotyping to better reflect the complexity of rare disease presentations and improve diagnostic tool performance.

Beyond addressing these current limitations, future work will integrate genetic data, including disease-associated genes and variant information, to guide candidate prioritisation within patients' network neighbourhoods, enabling combined phenotypic-genomic diagnostic workflows that address the inherent limitations of purely phenotype-based approaches identified in this study.

523
524 **Supporting Information**

525 S1 Table. Effect of damping factor on ranking performance.

526 S2 Table. Harmonic mean ranks of correct diagnoses across semantic similarity configurations

527 (7 best + RSD).

528 S3 Table. Harmonic mean rank of correct diagnoses under frequency-weighting schemes (full

529 data)

530 S4: Distribution of HPO frequency categories across all disease annotations

531 S4.a : Proportion of HPO term frequency categories across all 115767 ORPHAcode's HPO

532 term annotations

533 S4.b: Proportion of HPO term frequencies across all 4319 annotated ORPHAcodes from the

534 "Phenotypes Associated with Rare Disorders" May 2025 release

535 **Acknowledgements**

536 The Solve-RD project has received funding from the European Union's Horizon 2020 research

537 and innovation programme under grant agreement No 779257.

538 The authors gratefully acknowledge Anaïs Baudot, who reviewed this manuscript and provided

539 insightful feedback, and Jonas Marcello for his valuable technical guidance and advice

540 regarding the hpo3 library.
541 Competing Interests

542 The authors declare no competing interests.

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<table><caption>S1 Table. Effect of damping factor on ranking performance.</caption><thead><tr><td>Damping factor value</td><td>Harmonic mean rank of confirmed ORPHAcode</td></tr></thead><tbody><tr><td>RSD</td><td>7.97</td></tr><tr><td>0 (no random walk)</td><td>4.64</td></tr><tr><td>0.05</td><td>5.05</td></tr><tr><td>0.1</td><td>5.06</td></tr><tr><td>0.15</td><td>5.17</td></tr><tr><td>0.2</td><td>5.41</td></tr><tr><td>0.25</td><td>5.47</td></tr><tr><td>0.3</td><td>5.55</td></tr><tr><td>0.35</td><td>5.48</td></tr><tr><td>0.4</td><td>5.72</td></tr><tr><td>0.45</td><td>5.89</td></tr><tr><td>0.5</td><td>5.93</td></tr><tr><td>0.6</td><td>6.44</td></tr><tr><td>0.7</td><td>7.76</td></tr><tr><td>0.8</td><td>11.61</td></tr><tr><td>0.9</td><td>30.39</td></tr><tr><td>1.0</td><td>90.64</td></tr></tbody></table>

Harmonic mean ranks of confirmed ORPHAcodes across 139 patients for damping factor (α) values from 0 to 0.9. α=0 (no network propagation) achieves optimal ranking performance (4.64), whilst α=0.3 balances ranking accuracy (5.55) with maximal clinical coherence of top predictions by leveraging disease group topology. Higher α values yield progressively lower ranking performance.

<table><caption>S2 Table. Harmonic mean ranks of correct diagnoses across semantic similarity configurations (7 best + RSD).</caption><thead><tr><td>Pairwise semantic similarity measure</td><td>Aggregation method</td><td>Average rank</td></tr></thead><tbody><tr><td>Resnik</td><td>FunSimMaxAsym</td><td>5.45</td></tr><tr><td>SimIc</td><td>FunSimMaxAsym</td><td>5.85</td></tr><tr><td>Relevance</td><td>FunSimMaxAsym</td><td>5.96</td></tr><tr><td>Lin</td><td>FunSimMaxAsym</td><td>6.26</td></tr><tr><td>SimIc</td><td>FunSimMax</td><td>6.37</td></tr><tr><td>Resnik</td><td>FunSimMax</td><td>6.43</td></tr><tr><td>Relevance</td><td>FunSimMax</td><td>6.52</td></tr><tr><td>Relevance</td><td>FunSimAvg</td><td>6.65</td></tr></tbody></table>
<table><tr><td>SimIc</td><td>FunSimAvg</td><td>6.87</td></tr><tr><td>Lin</td><td>FunSimMax</td><td>7.00</td></tr><tr><td>GraphIC</td><td>FunSimMaxAsym</td><td>7.17</td></tr><tr><td>Lin</td><td>FunSimAvg</td><td>7.35</td></tr><tr><td>JC</td><td>FunSimMaxAsym</td><td>7.54</td></tr><tr><td>Resnik</td><td>FunSimAvg</td><td>7.81</td></tr><tr><td colspan="2">RSD</td><td>7.97</td></tr><tr><td>GraphIC</td><td>FunSimMax</td><td>8.33</td></tr><tr><td>Lin</td><td>FunSimMax</td><td>8.37</td></tr><tr><td>GraphIC</td><td>FunSimAvg</td><td>8.78</td></tr><tr><td>JC</td><td>FunSimAvg</td><td>8.95</td></tr><tr><td>JC</td><td>BMA</td><td>15.63</td></tr><tr><td>SimIc</td><td>BMA</td><td>15.72</td></tr><tr><td>Lin</td><td>BMA</td><td>15.91</td></tr><tr><td>Relevance</td><td>BMA</td><td>16.10</td></tr><tr><td>Resnik</td><td>BMA</td><td>16.44</td></tr><tr><td>GraphIC</td><td>BMA</td><td>16.51</td></tr></table>

Performance of 24 combinations of pairwise semantic similarity measures (Resnik, Lin, Jiang-Conrath, Relevance, InformationCoefficient, GraphIC) and aggregation methods (BMA, FunSimAvg, FunSimMax, FunSimMaxAsym), plus the RSD baseline, evaluated across 139 patients with 78 distinct confirmed ORPHAcodes. Lower harmonic mean ranks indicate superior diagnostic ranking performance.

<table><caption>S3 Table. Harmonic mean rank of correct diagnoses under frequency-weighting schemes (full data)</caption><thead><tr><td>Weighting</td><td>Average rank</td></tr></thead><tbody><tr><td>2,2,2,2,1</td><td>4.64</td></tr><tr><td>1,1,1,1,0</td><td>4.69</td></tr><tr><td>1,1,1,1,1</td><td>4.73</td></tr><tr><td>3,2,2,2,1</td><td>4.78</td></tr><tr><td>3,3,3,2,1</td><td>5.47</td></tr><tr><td>4,3,3,2,1</td><td>5.52</td></tr><tr><td>2,1,1,1,0</td><td>5.61</td></tr><tr><td>2,2,2,1,0</td><td>5.62</td></tr><tr><td>2,2,2,1,1</td><td>5.64</td></tr><tr><td>2,1,1,1,1</td><td>5.66</td></tr><tr><td>1,1,1,0,0</td><td>5.78</td></tr><tr><td>3,2,2,1,0</td><td>5.80</td></tr><tr><td>3,2,2,1,1</td><td>5.81</td></tr></tbody></table>
<table><tr><td>3,3,2,2,1</td><td>6.23</td></tr><tr><td>4,3,2,2,1</td><td>6.28</td></tr><tr><td>4,4,3,2,1</td><td>6.75</td></tr><tr><td>5,4,3,2,1</td><td>6.84</td></tr><tr><td>2,1,1,0,0</td><td>6.99</td></tr><tr><td>3,3,2,1,1</td><td>7.07</td></tr><tr><td>4,3,2,1,1</td><td>7.10</td></tr><tr><td>3,3,2,1,0</td><td>7.23</td></tr><tr><td>4,3,2,1,0</td><td>7.24</td></tr><tr><td>2,2,1,1,1</td><td>7.37</td></tr><tr><td>3,2,1,1,1</td><td>7.60</td></tr><tr><td>2,2,1,1,0</td><td>7.96</td></tr><tr><td>RSD</td><td>7.97</td></tr><tr><td>3,2,1,1,0</td><td>8.25</td></tr><tr><td>2,2,1,0,0</td><td>8.33</td></tr><tr><td>3,2,1,0,0</td><td>8.77</td></tr><tr><td>1,1,0,0,0</td><td>11.59</td></tr><tr><td>2,1,0,0,0</td><td>18.32</td></tr><tr><td>1,0,0,0,0</td><td>33.90</td></tr></table>

Performance comparison of frequency-weighting variants of FunSimMaxAsym and the RSD baseline method. Weighting vectors correspond to the five Orphanet frequency categories in descending order: obligate, very frequent, frequent, occasional, very rare. Lower harmonic mean ranks indicate superior diagnostic ranking performance.

S4.a : Proportion of HPO term frequency categories across all 115767 ORPHAcode's HPO term annotations

<table><thead><tr><td>HPO term frequency</td><td>Number HPO annotations</td><td>Proportion (%)</td></tr></thead><tbody><tr><td>Obligate (100%)</td><td>624</td><td>0.54</td></tr><tr><td>Very frequent (99-80%)</td><td>25698</td><td>22.20</td></tr><tr><td>Frequent (79-30%)</td><td>39412</td><td>34.04</td></tr><tr><td>Occasional (29-5%)</td><td>42764</td><td>36.94</td></tr><tr><td>Very rare (&lt;4-1%)</td><td>6550</td><td>5.66</td></tr><tr><td>Excluded (0%)</td><td>719</td><td>0.62</td></tr></tbody></table>
<table><caption>S4.b: Proportion of HPO term frequencies across all 4319 annotated ORPHAcodes from the "Phenotypes Associated with Rare Disorders" May 2025 release</caption><thead><tr><td>HPO term frequency</td><td>Number of ORPHAcodes</td><td>Proportion (%)</td></tr></thead><tbody><tr><td>Obligate (100%)</td><td>356</td><td>8.24</td></tr><tr><td>Very frequent (99-80%)</td><td>3651</td><td>84.53</td></tr><tr><td>Frequent (79-30%)</td><td>3831</td><td>88.70</td></tr><tr><td>Occasional (29-5%)</td><td>3426</td><td>79.32</td></tr><tr><td>Very rare (&lt;4-1%)</td><td>1093</td><td>25.31</td></tr><tr><td>Excluded (0%)</td><td>348</td><td>8.06</td></tr></tbody></table>