Overview of PERADIGM

PERADIGM is a phenotype embedding similarity-based statistical framework designed to identify candidate genes associated with disease-specific phenotypes for rare diseases using ICD-10 codes and sequencing data. It aims to improve statistical power in gene discovery, particularly in biobank datasets where some cases may be missed or misclassified during diagnosis. In this context, we define “risk genes” as candidate genes whose rare variants are associated with phenotypic manifestations related to the target disease. Importantly, investigating genes associated with disease-specific phenotypes, rather than focusing solely on the disease diagnosis itself, may provide additional insights into the underlying mechanisms of disease progression, variability in clinical presentation, and potential genotype-phenotype relationships. The PERADIGM framework employs a two-stage procedure, as shown in Fig 1.

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Fig 1. Overview of the PERADIGM framework.

The core concept of PERADIGM is that carriers of pathogenic variants exhibit ICD-10 phenotype profiles more similar to patients with the target disease. A: Individual-level ICD-10 codes are embedded using a Word2Vec model, and patient embeddings are generated using weighted averages of code embeddings. B: Pairwise cosine similarity is computed between rare LoF carriers and disease patients. C: A gene-specific risk score is derived and significance is assessed through random sampling.

https://doi.org/10.1371/journal.pgen.1011976.g001

In the first stage, we utilize individual-level ICD-10 codes from EHR data to create embedding representations for each phenotype using a continuous bag-of-words (CBOW) Word2Vec model. Patient embeddings are then generated by taking a weighted average of the phenotype embeddings, where the weights are determined based on two considerations. First, we consider the statistical evidence of association between each phenotype and the target disease. Second, we account for the prevalence of each phenotype in the biobank. Further details are provided in the Methods section. This weighting strategy captures both the phenotype’s relevance to the target disease and its information content, resulting in an embedded phenotype profile for each individual.

In the second stage, we conduct a genome-wide scan to calculate a risk score for each candidate gene with respect to the target rare disease, based on the embedded individual profiles. We hypothesize that genes associated with the target disease-associated phenotypes will show greater phenotypic similarity between individuals carrying rare loss-of-function (LoF) variants and those diagnosed with the disease. In PERADIGM, the similarity between two individuals is measured using the cosine similarity of their embedded phenotype profile vectors. We then derive a gene-specific risk score by comparing the phenotype embedding similarity between individuals carrying rare LoF variants and individuals diagnosed with the target disease. A higher similarity, and thus a higher risk score, between LoF variant carriers and disease cases suggests a higher likelihood that the candidate gene is associated with the disease. We assess the statistical significance of the observed score by comparing it to an empirical null distribution generated from repeated random sampling of individuals without regard to carrier status.

We note that PERADIGM uses widely available ICD-10 codes to identify candidate genes associated with rare disease-asscociated phenotypes, while some existing methods [25–27] integrate phenotype similarity using Human Phenotype Ontology (HPO) terms. By leveraging ICD-10 codes, PERADIGM can be more easily applied across diverse datasets and large-scale biobanks. In the following sections, we demonstrate the utility of PERADIGM through its application to several rare diseases using the first 200K WES release from the UK Biobank.

ADPKD

We first applied PERADIGM to identify candidate genes associated with ADPKD-related phenotypes [28]. ADPKD is one of the most common inherited kidney disorders, affecting approximately 1 in 400 to 1 in 1,000 individuals. It is characterized by the development of numerous fluid-filled cysts in the kidneys, leading to progressive renal dysfunction and, eventually, kidney failure. Approximately 78% of ADPKD cases are caused by pathogenic variants in the PKD1 gene, while another 15% result from variants in the PKD2 gene [29]. These genes encode polycystin-1 and polycystin-2, respectively, which are essential for maintaining the structural integrity of renal tubular cells and regulating calcium signaling. Disruptions to these proteins impair normal cellular function, leading to cyst formation and kidney enlargement.

While PKD1 and PKD2 account for the majority of ADPKD cases, variants in other genes have also been implicated in a small subset of patients. Although these genes are less frequent causes, they contribute to the clinical variability of ADPKD and broaden the spectrum of associated phenotypes [30]. However, due to the low prevalence of ADPKD in the UK Biobank dataset, only 142 patients were coded as either Q61.2 or Q61.3, traditional rare variant association tests can only identify PKD1 and PKD2 significantly after p-value adjustment. This limitation underscores the challenge of rare disease gene discovery and the potential value of leveraging phenotype-based similarity methods like PERADIGM to identify additional candidate genes associated with ADPKD-related phenotypes.

Before applying the PERADIGM approach, we first examined the intra-group similarity among individuals diagnosed with ADPKD and carriers of rare loss-of-function (LoF) variants in the PKD1 and PKD2 genes. Intra-group similarity is defined as the average pairwise phenotype similarity within a selected group, calculated based on each individual’s complete phenotype profile. We aimed to determine whether individuals within these two groups exhibited greater phenotypic similarity compared to randomly selected individuals. For the ADPKD group, the control group consisted of individuals without an ADPKD diagnosis in the inpatient EHR. For the variant carrier analysis, the control group included individuals without LoF or deleterious missense variants in the target gene.

We first considered ADPKD patients. As shown in Fig 2A, there is an apparent separation of pairwise similarity scores between the ADPKD disease group and the ADPKD non-disease group. The ADPKD patients generally had higher pairwise similarity scores than non-patients, supported by the mean difference. This indicates that, on the phenotype level, ADPKD patients were more similar to each other compared to non-ADPKD individuals. These results suggest that the ADPKD patients shared some common and unique phenotypes which are significantly different from the non-patient group. We next considered the rare LoF variant carriers of PKD1 and PKD2. As shown in Fig 2B and 2C, PKD1 and PKD2 rare LoF variant carriers groups also exhibited more similar phenotypes. PKD1 rare LoF variant carriers had a wider range of pairwise similarity scores, while the non-carrier group was more concentrated around 0.1. PKD2 rare LoF variant carriers’ pairwise similarity score distribution showed a similar trend to ADPKD patients, compared to the controls, although the difference was more mitigated than in the ADPKD patients group. The PKD1 and PKD2 results show that while the pairwise similarity trends differed between the two genes’ rare LoF carriers, both had apparent differences compared to the control group. Moreover, the overall difference was less pronounced than the ADPKD patients group, suggesting that PKD1 and PKD2 only account for part of the phenotype patterns for ADPKD, and some other phenotype patterns cannot be explained by these two genes alone.

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Fig 2. Intra-group similarity and significant phenotypes in the ADPKD analysis.

A: Pairwise similarity within the ADPKD patient group and the control group. B: Pairwise similarity within the PKD1 rare LoF carrier group and the control group. C: Pairwise similarity within the PKD2 rare LoF carrier group and the control group. D: Top 10 significantly associated ICD-10 codes among ADPKD patients. E: Top 10 significantly associated ICD-10 codes among PKD1 carriers. F: Top 10 significantly associated ICD-10 codes among PKD2 carriers.

https://doi.org/10.1371/journal.pgen.1011976.g002

After analyzing the pairwise phenotype similarity among ADPKD patients, PKD1 and PKD2 genes, we next investigated which phenotypes contributed to the difference in phenotype patterns. In this analysis, we used logistic regression, adjusted for age and sex, to scan all the phenotypes available in the UK Biobank 200K dataset to identify phenotypes that are significantly associated with ADPKD. We considered 10,487 unique ICD-10 codes available in the UKBiobank 200K dataset.

For ADPKD, we identified 255 significantly associated phenotypes after p-value adjustment, excluding those present in only one patient. As illustrated in Fig 2D, the top 10 phenotypes demonstrate strong associations with kidney diseases, cystic conditions, and common ADPKD complications [29]. These results show that, as expected, ADPKD patients not only share the primary diagnosis but also exhibit a constellation of related phenotypes. Among the significant associations, conditions such as hyperkalemia and urinary tract infections, both commonly observed in chronic kidney disease and ADPKD, were also identified (see Supplementary Materials). The ability of our approach to capture these well-known phenotypic associations suggests that such phenotype data could be leveraged to enhance individual-level phenotype embeddings.

We further investigated the phenotypes associated with PKD1 and PKD2 rare LoF carrier status. As shown in Fig 2E and 2F, Q61.2 and Q61.3 were the two most significant phenotypes, as expected. Additionally, most of the top 10 significant phenotypes for PKD1 and PKD2 overlapped with those observed for ADPKD patients [8], further validating known genotype-phenotype relationships. Furthermore, we identified 68 significant phenotypes for PKD1 and 15 for PKD2 after p-value adjustment, which is substantially fewer than the 255 significant phenotypes identified for ADPKD patients. This discrepancy likely reflects the broader phenotypic spectrum captured in diagnosed ADPKD cases rather than solely the contributions of PKD1 and PKD2. Additionally, differences in coding practices among healthcare providers may contribute to variations in phenotype capture. Some providers may consistently document chronic kidney disease (CKD) as a general diagnosis during each visit while omitting more specific codes such as Q61.2 for ADPKD and other related findings. This limitation of ICD coding suggests that phenotype-based methods may help mitigate the effects of inconsistent coding practices. These results emphasize the potential of phenotype similarity-based approaches to improve the representation of individual disease profiles and enhance rare disease gene discovery.

After examining these phenotype patterns, we applied PERADIGM to all available genes in the UK Biobank 200K dataset to identify significant risk genes for ADPKD. After excluding genes without rare LoF variant carriers and those potentially affected by somatic mutations, and further restricting to genes with at least five rare LoF carriers, a total of 15,889 genes were included in the final analysis.

As shown in Fig 3A and Table 1, genome-wide scanning with PERADIGM identified three significant genes associated with ADPKD-related phenotypes after p-value adjustment. In comparison, SKAT-O identified only PKD1 and PKD2 after p-value adjustment (Fig 3B), whereas PERADIGM identified an additional candidate gene, IFT140 is a well-established gene in ciliopathies that has recently been implicated as a monogenic cause of renal cyst formation [31]. Mutations in IFT140 can disrupt cilia structure and function. However, SKAT-O failed to detect IFT140 as significant (raw p-value: 0.00146, adjusted p-value: 0.58, rank: 46), likely due to the small number of IFT140 rare LoF variant carriers among individuals with ADPKD diagnosed (only six individuals). This limited overlap reduces statistical power in binary status-based association tests like SKAT-O. In contrast, PERADIGM integrates phenotype information across all ADPKD-related phenotypes for each individual with rare LoF variants, providing a more comprehensive assessment beyond binary disease status. To further compare PERADIGM with SKAT-O, we examined overlapping genes among the top 100, 200, and 500 genes ranked by raw p-values. The results showed 6, 7, and 27 overlapping genes, respectively. The relatively small number of shared genes suggests that PERADIGM prioritizes different aspects of gene significance compared to SKAT-O, potentially capturing distinct biological signals related to ADPKD-specific phenotypes. These results demonstrate that incorporating phenotype similarity into gene discovery can enhance the identification of candidate genes associated with ADPKD-related phenotypes. By leveraging phenotype embeddings, PERADIGM not only validates known genetic contributors but also uncovers additional genes that may influence specific clinical manifestations, providing deeper insights into the phenotypic complexity of ADPKD.

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Fig 3. QQ plots of ADPKD analysis.

A: QQ plot of ADPKD risk genes identified by PERADIGM. B: QQ plot of ADPKD risk genes identified by SKAT-O. C: QQ plot from PERADIGM using pre-selected ADPKD-related phenotypes. D: QQ plot from PERADIGM after excluding CKD patients. Blue points indicate previously validated genes; red points indicate newly identified genes.

https://doi.org/10.1371/journal.pgen.1011976.g003

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Table 1. Comprehensive summary of ADPKD gene-level analyses.

https://doi.org/10.1371/journal.pgen.1011976.t001

Beyond the significant genes identified by PERADIGM (Table 1), additional evidence supports its enhanced power. Several genes previously linked to ADPKD, including ALG8 [32], ALG9 [33], and COL4A1 [34], showed marginally significant associations when analyzed with PERADIGM. These genes had minimal overlap between rare LoF variant carriers and ADPKD diagnosis (ALG8: 1, ALG9: 0, COL4A1: 0), which likely contributed to their lack of significance in SKAT-O. Among them, PERADIGM identified marginal associations for all three genes (Table 1). This result highlights how limited overlap between rare variant carriers and ADPKD diagnoses can reduce SKAT-O’s power. However, this may reflect incomplete ICD coding, undiagnosed cases, or reduced penetrance rather than a true absence of association. In contrast, PERADIGM remains effective by leveraging broader phenotype patterns.

Moreover, we conducted an additional analysis to refine the ADPKD-related phenotype representation for diagnosed patients. Instead of using the entire phenotype profile, we preselected ADPKD-related phenotypes based on prior expertise when generating patient group embeddings. This stricter phenotype selection enhances specificity, further validates PERADIGM’s results, and provides more explainable associations between significant genes and ADPKD-specific phenotypes. For ADPKD, we selected ADPKD, aneurysms, and liver cysts as key ADPKD-related phenotypes.

As shown in Fig 3C and Table 1, the significant genes identified remained nearly the same as those found using PERADIGM without phenotype preselection, with one additional identified gene ADTRP. This consistency indicates that both approaches yield robust gene discovery results and highlights PERADIGM’s ability to automatically assign higher weights to phenotypes most relevant to ADPKD. However, the results using the preselected phenotype group showed a stronger association of PKD1 and PKD2 with ADPKD-related phenotypes (both adjusted p-values = 0.00). This shift suggests that preselecting ADPKD-related phenotypes can slightly enhance statistical power, but the overall results remain consistent with those obtained without phenotype preselection, demonstrating the robustness of PERADIGM.

In addition, ADPKD is a specific subtype of chronic kidney disease (CKD), and the two conditions share many overlapping phenotypes. While CKD is often present in ADPKD patients, many of the complications and phenotypes observed in CKD can arise from a variety of non-genetic causes. To distinguish genes associated specifically with ADPKD-related phenotypes from those potentially confounded by common CKD, we conducted an additional analysis. Specifically, we excluded individuals diagnosed with CKD (ICD-10 code: N18) who did not also have a diagnosis of ADPKD. This filtering step aimed to remove individuals with non-ADPKD forms of CKD that could obscure the genetic signals specific to ADPKD. We then applied PERADIGM using this refined comparison group to identify genes associated with ADPKD-specific phenotypes. As shown in Fig 3D, all previously identified genes remained significant, consistent with our original findings. This result demonstrates the robustness of PERADIGM and its ability to detect ADPKD-related genetic associations even after removing potentially confounding CKD cases.

Marfan syndrome

We next applied PERADIGM to Marfan syndrome [35], an autosomal dominant connective tissue disorder primarily caused by mutations in FBN1. This gene encodes fibrillin-1, a crucial protein for elastic fiber formation. Defective fibrillin-1 disrupts connective tissue integrity, leading to characteristic features such as tall stature, long limbs, flexible joints, lens dislocation, and serious cardiovascular complications, including aortic aneurysms and dissections. A patient cohort is clinically defined by the revised Ghent nosology [36], which requires the presence of cardinal manifestations, principally aortic root dilatation (aneurysm) or ectopia lentis (lens dislocation). In the absence of one of these, the diagnosis for a cohort subject requires a pathogenic FBN1 mutation or a systemic score ( 7) based on characteristic features. These features include the skeletal manifestations of tall stature, long limbs (dolichostenomelia), and flexible joints, as well as pectus deformities (carinatum or excavatum), scoliosis, and mitral valve prolapse [37]. While FBN1 mutations are the main cause, other genes have been implicated in Marfan syndrome and Marfan-like conditions, including TGFBR1 and TGFBR2 [38]. Mutations in these genes can also impair connective tissue function, contributing to the syndrome’s clinical manifestations. This suggests that beyond FBN1, multiple genes may influence connective tissue integrity and related pathways. In the UK Biobank 200K dataset, rare variant association tests such as SKAT-O, SKAT, and Burden tests identified only FBN1 as a significant gene after p-value adjustment. We applied PERADIGM to Marfan syndrome to explore additional candidate genes associated with Marfan-related phenotypes.

We first examined the intra-group similarity among Marfan syndrome patients and rare LoF variant carriers of FBN1. In the UK Biobank dataset, 39 individuals were diagnosed with Marfan syndrome (ICD-10 code: Q87.4). As shown in Fig 4A, the intra-group similarity scores of Marfan syndrome patients differed substantially from those of non-patients. The boxplot revealed an average pairwise similarity score difference of 0.55, which is notably higher than that for ADPKD. This strong intra-group similarity indicates that Marfan syndrome patients exhibit distinct and characteristic phenotype patterns. We then analyzed the intra-group similarity scores of 9 individuals carrying rare LoF variants in FBN1, five of whom were diagnosed with Marfan syndrome. Although the number of carriers was small, Fig 4B shows a clear difference between carriers and controls. The similarity scores were sparse due to the limited number of carriers, but the overall trend suggests slightly higher intra-group similarity among FBN1 carriers. Notably, the phenotype pattern of FBN1 rare LoF carriers was weaker than that of diagnosed Marfan syndrome patients, as reflected by lower intra-group similarity scores. This suggests that FBN1 exhibits incomplete penetrance for Marfan syndrome and that additional phenotype patterns may exist beyond those explained by FBN1 alone. These findings indicate the potential involvement of other genetic contributors in Marfan syndrome.

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Fig 4. Intra-group similarity and significant phenotypes in the Marfan syndrome analysis.

A: Pairwise similarity within the Marfan syndrome patient group and the control group. B: Pairwise similarity within the FBN1 variant carrier group and the control group. C: Top 10 significantly associated ICD-10 codes among Marfan syndrome patients. D: Top significantly associated ICD-10 codes among FBN1 variant carriers.

https://doi.org/10.1371/journal.pgen.1011976.g004

Next, we examined the significantly associated phenotypes of Marfan syndrome and FBN1 rare LoF variant carriers to better understand the phenotypic contributors to Marfan syndrome. After p-value adjustment, 51 significantly associated phenotypes remained, excluding those present in only one patient. Fig 4C illustrates the top 10 significant phenotypes associated with Marfan syndrome, which are predominantly related to the aorta, congenital heart disease, and blood abnormalities—all common complications of the disorder [39]. Additionally, some significant phenotypes without a direct known relationship to Marfan syndrome were identified, such as retinal detachment with retinal break and ingrowing nails (see Supplementary Materials). This pattern of significant phenotypes, comprising both common complications and less typical associations, is consistent with our findings in ADPKD. We then investigated whether FBN1 rare LoF carriers exhibited similar significant phenotypes to Marfan syndrome patients. Due to the limited number of carriers, only six phenotypes were significantly associated with FBN1 rare LoF variant status. Despite the small sample size, all six phenotypes were known complications of Marfan syndrome (Fig 4D) and were also observed in diagnosed patients. However, many additional significant phenotypes observed in Marfan syndrome patients were absent in FBN1 rare LoF carriers. This indicates that FBN1 exhibits incomplete penetrance for Marfan syndrome, suggesting that other factors may influence the broader spectrum of significant phenotypes associated with the disease.

After exploring the phenotype patterns of Marfan syndrome and FBN1 rare LoF carriers, we applied PERADIGM to scan all genes in the UK Biobank 200K dataset to identify significant genes associated with Marfan syndrome-specific phenotypes [40]. As shown in Fig 5A and Table 2, the whole-genome scan identified 2 significant genes after p-value adjustment, whereas SKAT-O identified only FBN1 (Fig 5B). While FBN1 is a well-established gene for Marfan syndrome, COL5A1, primarily associated with Ehlers-Danlos syndrome (EDS), has been reported in cases where EDS and Marfan syndrome are difficult to distinguish due to overlapping connective tissue abnormalities [41]. COL5A1 mutations result in abnormal type V collagen production, leading to symptoms that resemble certain aspects of Marfan syndrome. In our dataset, none of the 26 COL5A1 rare LoF carriers overlapped with diagnosed Marfan syndrome patients, highlighting the limitations of traditional rare variant association methods in detecting such associations. The ICD-10 coding system sometimes struggles to distinguish rare diseases like Marfan syndrome and EDS, leading to potential misdiagnoses.

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Fig 5. QQ plots of Marfan syndrome analysis.

A: QQ plot of Marfan syndrome risk genes identified by PERADIGM. B: QQ plot of Marfan syndrome risk genes identified by SKAT-O. C: QQ plot from PERADIGM using pre-selected Marfan-related phenotypes. Blue points indicate validated genes; red points indicate newly identified genes.

https://doi.org/10.1371/journal.pgen.1011976.g005

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Table 2. Comprehensive summary of Marfan syndrome gene-level analyses.

https://doi.org/10.1371/journal.pgen.1011976.t002

We also conducted an additional analysis to refine the representation of the Marfan syndrome phenotype in diagnosed patients. Instead of using the entire phenotype profile, we embedded the diagnosed patients using only their longitudinal ICD-10 codes for Marfan syndrome, ensuring that the embeddings were derived solely from repeated Marfan syndrome diagnoses over time. This stricter embedding process focuses more specifically on Marfan syndrome itself, providing more explainable results. As shown in Fig 5C and Table 2, six genes were significantly associated with Marfan syndrome-specific phenotypes. These include the two previously identified genes, indicating that refining phenotype representation can help uncover additional relevant genes. Also, PERADIGM identified TGFBR2 gene associated with Loeys-Dietz syndrome [42], which has overlapping cardiovascular and skeletal manifestations with Marfan syndrome. Mutations in TGFBR2 disrupt the TGF-β signaling pathway, which is essential for connective tissue maintenance and repair, leading to clinical features that can resemble Marfan syndrome. In the UK Biobank dataset, there was no overlap between Marfan syndrome patients and TGFBR2 rare LoF carriers, preventing traditional binary-based methods from detecting this association. By leveraging full phenotype embeddings, our approach can help mitigate these issues by capturing broader phenotype patterns. These results further demonstrate that PERADIGM can effectively identify genetic contributors to Marfan syndrome-specific phenotypes by integrating comprehensive phenotype information. By utilizing phenotype embeddings, PERADIGM enables the discovery of genes that contribute to disease manifestations through shared pathways or overlapping syndromes, even when there is no direct overlap between gene carriers and diagnosed patients.

NF1

Neurofibromatosis type 1 (NF1) [43] is a complex genetic disorder characterized by the formation of multiple benign tumors, primarily neurofibromas, along nerves in the skin, brain, and other tissues. The disorder is primarily caused by mutations in the NF1 gene, which encodes neurofibromin, a tumor suppressor protein that regulates cell growth and division. While NF1 mutations are the main genetic driver, recent studies suggest that additional genes may influence disease severity and phenotypic variability among NF1 patients. Identifying such modifier genes could improve our understanding of NF1 pathogenesis and facilitate more personalized diagnostic and therapeutic strategies. In the UK Biobank 200K European ancestry dataset, there are 62 NF1 cases, limiting the statistical power of traditional rare variant association tests to detect genetic factors beyond NF1 itself. To address this limitation, we applied PERADIGM to identify genetic contributors that may influence NF1-specific phenotypes or modify the clinical presentation, expanding beyond the established role of NF1.

We first examined the intra-group similarity among NF1 patients and rare LoF carriers of the NF1 gene. The UK Biobank 200K European ancestry dataset contained 62 individuals diagnosed with NF1 (ICD-10 code: Q85.0). As shown in Fig 6A, NF1 patients exhibited significantly higher intra-group similarity compared to the control group, indicating distinct phenotypic characteristics. We then analyzed intra-group similarity for 105 individuals carrying rare LoF variants in NF1, among whom only 19 had a documented NF1 diagnosis. This suggests that while NF1 mutations are the primary cause of NF1, many NF1 rare LoF variant carriers exhibit reduced or incomplete penetrance and conversely, some diagnosed patients do not carry detectable NF1 rare LoF variants. As depicted in Fig 6B, the difference in intra-group similarity between NF1 rare LoF carriers and controls was less pronounced than that observed for diagnosed NF1 patients. These findings are consistent with results from ADPKD and Marfan syndrome, suggesting that additional genetic or environmental factors likely influence NF1 disease manifestation beyond NF1 mutations alone.

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Fig 6. Intra-group similarity and significant phenotypes in the NF1 analysis.

A: Pairwise similarity within the NF1 patient group and the control group. B: Pairwise similarity within the NF1 variant carrier group and the control group. C: Top 10 significantly associated ICD-10 codes among NF1 patients. D: Top significantly associated ICD-10 codes among NF1 variant carriers.

https://doi.org/10.1371/journal.pgen.1011976.g006

We examined phenotypes significantly associated with NF1 disease and NF1 rare LoF variant carrier status, identifying 38 phenotypes associated with NF1 disease (Fig 6C). The top 10 significant phenotypes closely aligned with known clinical manifestations, reinforcing the multisystem involvement characteristic of NF1 [44]. These phenotypes primarily affected the nervous system, skin, and skeleton, with some involvement of other organ systems. This comprehensive phenotypic profile enhances our understanding of NF1’s diverse clinical presentation. In contrast, despite a larger number of NF1 rare LoF variant carriers compared to diagnosed NF1 patients, only four phenotypes remained significant after p-value adjustment (Fig 6D). As expected, NF1 disease (Q85.0) itself was the most significant phenotype, followed by D36.1, which is directly related to NF1. Interestingly, the remaining two significant phenotypes (I83.1 and N20.2) are not commonly associated with NF1, suggesting potential novel genotype-phenotype correlations or incidental findings. NF1 patients exhibit a distinct and consistent phenotypic profile, whereas NF1 rare LoF variant carriers present a more variable and diluted phenotype pattern. Apart from the strong association with NF1 disease itself, other phenotype relationships in carriers were less pronounced. This finding highlights the complexity of genotype-phenotype relationships in NF1 and suggests that additional genetic modifiers or environmental factors may influence disease manifestation.

Following our exploration of phenotype patterns in NF1 disease patients and NF1 rare LoF variant carriers, we applied PERADIGM to scan all available genes in our dataset for associations with NF1-specific phenotypes. We then compared our results with those obtained using SKAT-O. As shown in Fig 7A, after p-value adjustment, PERADIGM identified only NF1 as a statistically significant gene associated with NF1-specific phenotypes, consistent with SKAT-O results (Fig 7B). Both methods converged on NF1 as the sole significant genetic factor in our dataset. Similarly, we conducted an additional analysis to refine the representation of the NF1 phenotype among diagnosed patients. Instead of using the entire phenotype profile, we embedded patients only with their NF1-related ICD-10 codes. As shown in Fig 7C, the NF1 gene remained the only one identified, though with a smaller p-value compared to the SKAT-O result. The difficulty in identifying additional significant genes may be due to the relatively diluted phenotypic patterns observed among NF1 rare LoF variant carriers, as noted in our previous analyses. This suggests that while NF1 is the primary genetic driver, the complexity of NF1 disease manifestation may involve additional genetic modifiers or environmental influences that remain undetected with current sample sizes and methods

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Fig 7. QQ plots of NF1 analysis.

A: QQ plot of NF1 risk genes identified by PERADIGM. B: QQ plot of NF1 risk genes identified by SKAT-O. C: QQ plot from PERADIGM using pre-selected NF1-related phenotypes.

https://doi.org/10.1371/journal.pgen.1011976.g007

From the QQ plot, we observed a departure from the central line at the tail using PERADIGM, suggesting potential additional signals. The top 10 genes are listed in Table 3. Among them, P2RX4 encodes a purinergic receptor involved in cell signaling, particularly within the nervous system [45]. Impaired P2X receptor signaling has been reported in microglia with NF1 mutations, highlighting the importance of purinergic receptors in NF1-related neurological abnormalities. Given its role, P2RX4 may contribute to disrupted signaling pathways affecting microglial motility and phagocytosis in NF1 [46]. Although these genes do not reach statistical significance after p-value adjustment, they may still provide valuable insights into genetic factors influencing NF1-specific phenotypes. Further investigation is needed to determine their potential contributions to NF1 pathophysiology.

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Table 3. Comprehensive summary of NF1 gene-level analyses.

https://doi.org/10.1371/journal.pgen.1011976.t003

Furthermore, we examined SPRED1 [47] and LZTR1 [48], two genes previously implicated as potential contributors to NF1-specific phenotypes. Although neither gene reached statistical significance in PERADIGM or SKAT-O after p-value correction, our analysis revealed that SPRED1 had 13 rare LoF variant carriers, none of whom were diagnosed with NF1 in our dataset. Similarly, LZTR1 had 304 rare LoF variant carriers. As shown in Table 3, both SPRED1 and LZTR1 exhibited marginal significance in PERADIGM, whereas SKAT-O identified only LZTR1 as marginally significant. This discrepancy arises because SKAT-O relies heavily on direct overlap between LoF variant carriers and diagnosed patients, whereas PERADIGM can detect associations by leveraging shared phenotypic patterns. For example, despite the lack of overlap between SPRED1 carriers and NF1 patients, PERADIGM still identified a marginal association by capturing phenotypic similarities. These findings further demonstrate the potential of PERADIGM to identify additional genes associated with NF1-specific phenotypes beyond traditional rare variant association methods.

UK Biobank 200K dataset and genotype data quality control

We utilized the UK Biobank 200K dataset [4,50] in our analysis. To mitigate potential confounding effects due to population stratification, we restricted our analysis to individuals of European ancestry. We applied several filtering criteria to ensure data quality and completeness. Specifically, we excluded individuals who lacked Hospital inpatient data or whole-exome sequencing data. To eliminate potential biases due to sample relatedness, we also removed related individuals from the UK Biobank dataset. Specifically, we used the kinship coefficients provided by UK Biobank to identify all pairs of related participants and excluded individuals with first- or second-degree relationships. Within each related family, one individual was randomly retained to ensure that the final analysis cohort consisted entirely of unrelated samples. After applying these filters, our final study cohort comprised 121,330 individuals of European ancestry. This refined dataset ensures a more homogeneous population with comprehensive phenotypic and genetic information, thereby enhancing the reliability and interpretability of our subsequent analyses.

To ensure the quality and reliability of the rare variant analysis, we implemented stringent quality control (QC) measures on the whole-exome sequencing (WES) data using PLINK [51]. Our QC protocol comprised several steps. We first removed variants with a minor allele frequency (MAF) exceeding 0.01, thereby retaining only rare variants for subsequent analysis. We then excluded variants that significantly deviated from the Hardy-Weinberg equilibrium (HWE), with a threshold of p < 1e-6. A significant departure from HWE can indicate genotyping errors or population stratification. Furthermore, we removed samples with missing sex information. Following these QC steps, we identified all rare predicted loss of function (pLoF) variants. These included stop-gain, stop-loss, frameshift insertion, frameshift deletion, and essential splice variants. This allowed us to focus on potentially impactful genetic alterations [52]. To reduce the impact of somatic mutations, we added a filtering step. Although UK Biobank WES data are derived from blood samples, prior studies [53] have shown that some rare variants may reflect somatic rather than germline mutations. Since somatic variants are more frequent in older individuals, we compared the age distributions of rare LoF variant carriers and non-carriers for each gene using the Wilcoxon rank-sum test, followed by Bonferroni correction. Genes whose carriers were significantly older were flagged as potential CHIP-related signals. Three genes, ASXL1, TET2, and DNMT3A, met this criterion and were removed from our genome-wide analyses. This filtering step enhances the robustness of our results by minimizing confounding from age-related somatic mutations and comorbidity-driven phenotypic similarity.

Embedding model

Embedding learning and semantic matching have a rich history in natural language processing. Mikolov et al. introduced the continuous Bag-of-Words (CBOW) and Skip-gram models, collectively known as Word2Vec, to represent words in a vector space [22]. These neural network-based models achieve state-of-the-art performance in measuring syntactic and semantic word similarity. Many studies have leveraged Word2Vec to embed medical concepts for patients using Electronic Health Record (EHR) corpora, directly utilizing textual medical records as input.

In our embedding analysis, we applied the CBOW Word2Vec model to embed the ICD-10 phenotype data from the UK Biobank. The CBOW model is an architecture used in word embedding where the surrounding context words are used to predict a target word. In CBOW, a window of context words around a target word is input to the model, and the goal is to predict the central (target) word from these context words. The model optimizes weights to maximize the probability of predicting the correct target word based on the given context. This approach is particularly well-suited for embedding ICD-10 codes based on the surrounding diagnosis records of individual patients. It effectively captures the contextual relationships between phenotypes, enabling the representation of medical concepts in a dense, continuous vector space. By leveraging these contextual relationships, the model can potentially uncover latent patterns and associations within the medical data that might not be immediately apparent through traditional analysis methods.

Embedding for ICD-10 codes

We aim to map phenotypes onto a static high-dimensional space, enabling numerical representation of their characteristics and facilitating similarity measurements between different phenotypes. We employed the Word2Vec embedding model to obtain static embedding vectors for the phenotypes. In the UK Biobank database, hospital inpatient data are recorded in the form of ICD-10 codes, each representing a specific disease. For instance, Q61.2 denotes, Polycystic kidney, adult type. Consequently, each patient’s record yields a sequence of ICD-10 codes, comprehensively describing their longitudinal inpatient condition. Based on this information, we developed the following approach to embedding the ICD-10 codes. For each ICD-10 code, we extracted keywords from its description, excluding punctuation and English stopwords. This process generated a vector of words for each patient based on his/her ICD-10 descriptions, with each word serving as a token in the training dataset. Each patient’s ICD-10 description was treated as a sentence. The output comprised embedding vectors for each word appearing in the inpatient dataset. We then employed an average embedding to derive the embedding vector for each ICD-10 code. This approach not only captured sequential information between different description tokens for each ICD-10 code but also leveraged detailed word tokens when two ICD-10 codes contain similar words.

Embedding for individual using ICD-10 codes

After obtaining the embedding vector for each ICD-10 code in the UK Biobank data, we proceeded to embed individuals using a weighted average embedding approach. This method enhances simple averaging of ICD-10 code embedding vectors by focusing only on less common ICD-10 codes (frequency ) and assigning differential weights to these codes. We assigned weights by considering two pieces of information for an ICD code: (1) the significance level of each code with respect to the target disease, a process to be detailed in subsequent sections, and (2) the information content of each ICD-10 code, derived from its frequency.

For risk gene mapping, we focus on a specific disease of interest. Different phenotypes have varying degrees of associations with the target disease. Consequently, simply averaging all available ICD-10 embeddings to represent an individual’s overall phenotype embedding may be less effective to capture its relevance to the target disease. A more informative approach to characterizing an individual’s phenotypic profile in relation to a target disease involves assigning differential weights to distinct ICD-10 codes, with higher weights indicating a stronger relationship with the target disease. Target disease relevance is captured through the logistic regression model:

(1)

where c_ij denotes the i-th ICD-10 code status of individual j, d_j represents the target disease status of individual j, and z_j is the vector of covariates, specifically age and sex. We conducted a comprehensive scan of all ICD-10 codes in the UK Biobank inpatient dataset for the disease of interest, calculating a p-value for each ICD-10 code. Subsequently, we utilized these p-values to derive the weight for each ICD-10 code. By employing this weighting scheme, ICD-10 codes exhibiting a more significant association with the disease of interest are assigned larger weights, thereby playing a more prominent role in the individual embedding process. We also considered each ICD-10 code’s prevalence, denoted as r_k, in the embedding for each individual.

(2)

This formulation of information content assigns higher values to rarer phenotypes, reflecting our assumption that rarer phenotypes carry more information about rare diseases.

The weight w_k for the k-th ICD-10 code is then calculated as:

(3)

where the p-value represents the significance level of the k-th ICD-10 code in relation to the disease of interest. We use a sigmoid function to map the p-value onto a [0.5, 1] scale, with greater weights indicating phenotypes more relevant to the disease of interest.

The rationale behind this weighted average embedding is twofold. First, it aims to capture the differential importance of various phenotypes in relation to specific diseases, acknowledging that different phenotypes contribute distinctly to each disease. Second, it assigns more weight to rare ICD-10 codes to prevent common ICD-10 codes from overwhelming the information provided by less frequent, but potentially more informative, codes. This approach is based on the assumption that for rare diseases, the rare phenotypes each individual exhibits will carry more information about the disease. Consequently, this method ensures a more comprehensive and disease-specific representation of each individual’s phenotypic profile, potentially enhancing the detection of subtle disease associations. With such defined weights, the embedding vector for an individual i is calculated as:

(4)

where D_i is the embedding vector for individual i, n_i is the total number of less common ICD-10 codes (frequency ) recorded in individual i, e_k is the embedding vector of the k-th ICD-10 code, and w_k is the weight of the ICD-10 code e_k. This equation shows how we represent an individual using weighted ICD-10 code embeddings.

Risk gene mapping

Based on the phenotype embedding of each individual, we can assign each gene a risk score for a disease of interest by investigating the similarity of the phenotype embeddings from rare LoF variant carriers with those having the target disease. A larger risk score indicates a higher likelihood that the candidate gene is associated with the disease of interest. Unlike other gene prioritization tools based on pathways or other biological criteria, we calculated the risk score solely based on phenotype similarities. This is accomplished in four steps. First, we extracted all the rare Loss of Function (LoF) variant carriers for each candidate gene, along with their genotype and phenotype information. Second, we extracted all individuals diagnosed with the target disease and their phenotype information. Third, we used the method described in the previous section to embed the LoF set carriers and disease patients, obtaining their embedding representations. Fourth, we calculated the disease risk score by comparing the phenotype similarity at the individual level between the different genes’ LoF set carriers and the diseased individuals.

Our underlying assumption is that greater similarity between disease patients and gene LoF set carriers at the phenotype embedding level indicates higher pathogenicity of the gene for the disease of interest. This is based on the hypothesis that rare LoF variants have a large effect size on the phenotype compared to common variants. Notably, we considered not only the disease status as a binary value but all relevant phenotype information related to the disease, providing a more comprehensive and reasonable approach. Finally, we ranked each gene’s risk score based on the calculated average similarity score.

(5)

where S_i is the average similarity score for individual i compared to the disease patients group, m is the number of patients in the disease of interest comparison group, D is the embedding vector for each individual, and the function represents cosine similarity, commonly used in calculating the similarity between two embedding vectors. Based on the similarity score for each LoF mutation carrier, we can calculate the overall score for each candidate gene as

(6)

where is the risk score of gene i to the disease of interest, and is number of LoF carriers for gene i.

For each observed risk score, we employed random sampling to determine its significance level. Under the null hypothesis (H₀), we derived an empirical distribution of the risk score for the target gene by repeatedly randomly selecting n_i samples from the UK Biobank 200K inpatient dataset and computed the risk score for each group. This process was repeated 10,000 times to construct the empirical risk score distribution for gene i under the null hypothesis for the target disease.

The estimated p-value for the observed risk score is derived by calculating the Z-score using the formula:

(7)

where is the observed risk score, is the average of the risk scores from randomly sampled sets of individuals, and σ is the standard deviation of the simulated risk scores. The p-value is then computed from the standard normal distribution. We applied a one-tailed test with a significance level of 0.05 and used the Bonferroni correction to control for multiple testing, assessing whether the gene’s risk score is significantly higher than expected by chance.

Intra-group similarity calculation

To elucidate the overall phenotype patterns within the disease group and among carriers of rare LoF variants of a candidate gene, we calculated the intra-group phenotype similarity in the embedding space. This analysis aimed to explore whether individuals within these groups share greater phenotypic similarity compared to randomly selected individuals from the UK Biobank.

First, we considered all individual pairs within the target group and calculated similarity scores for each pair within the target group. We then randomly selected an equal number of individuals from the UK WES 200K excluding the target group, and calculated pairwise similarity scores.

A difference in the similarity score box plot of the two groups would suggest that the given group exhibits a distinct intra-group phenotype pattern compared to the overall dataset. For example, this analysis could reveal whether carriers of rare LoF variants in the PKD1 gene demonstrate greater phenotypic similarity to each other than a randomly selected control group from the UK Biobank.

Disease cohort definition

For each target disease, we defined the case cohort based on the corresponding International Classification of Diseases, 10th Revision (ICD-10) codes recorded in the UK Biobank electronic health records. Individuals with at least one record of the disease-specific ICD-10 code were included as cases, while all other participants were considered part of the background control population. This definition ensures that cohort membership is determined directly from standardized diagnostic codes without requiring additional phenotype modeling or manual curation. Specifically, autosomal dominant polycystic kidney disease (ADPKD) cases were identified using ICD-10 codes Q61.2 and Q61.3; Marfan syndrome cases were identified using Q87.4; and neurofibromatosis type 1 (NF1) cases were identified using Q85.0. For each disease, individuals carrying any of these codes were assigned to the corresponding disease cohort. Control individuals were drawn from the remaining participants who did not possess the disease-specific ICD-10 codes. All disease and control cohorts were restricted to unrelated individuals of European ancestry, as defined by UK Biobank-provided kinship coefficients and ancestry principal components, to minimize population structure and relatedness confounding.

Type I error rate control simulation

Assessing the type I error rate of PERADIGM is essential for establishing the reliability of our framework. We conducted comprehensive simulations to evaluate calibration under the null hypothesis. For each disease (ADPKD, Marfan syndrome, and NF1), we used the observed distribution of target-disease similarity scores to generate simulated datasets. In each replicate, individuals were randomly assigned to synthetic “gene carrier groups” that matched the observed carrier-count distribution of real genes (denoted N_g). A pseudo gene-level risk score was then calculated as the average similarity score across individuals within each simulated group, and the same random-sampling association test used in the real analysis was applied to obtain null p-values. We assessed type I error control through four complementary analyses: (1) QQ plots were drawn to visually inspect inflation or deflation in the null p-value distribution. (2) Empirical type I error rates were computed as the proportion of null p-values below nominal thresholds (e.g., 0.05 and 0.01). (3) Kolmogorov–Smirnov (KS) tests were performed to evaluate deviations from the expected uniform distribution. (4) The genomic inflation factor (λ) was calculated to measure systematic inflation or deflation, with values near 1 indicating proper calibration. All simulation results are provided in the S1 Text, S1 Table, and S1 Fig.

Alternative weighting schemes analysis

To evaluate the impact of weighting schemes on individual embeddings, we conducted additional analyses to systematically assess how different weighting strategies influence the PERADIGM framework. We compared our original weighting scheme with four alternative strategies: (1) × , (2) , (3) , and (4) . Together with the original approach, these five schemes incorporate varying combinations of disease-association strength (via p-values or effect sizes) and phenotype information content (IC). The additional schemes were designed to disentangle the relative contribution of association strength and information content to the weighting mechanism in PERADIGM. For each scheme, we generated corresponding ICD-10 code weights and evaluated pairwise consistency among them by computing Pearson correlation coefficients across all weighting matrices. This analysis allowed us to assess whether the different formulations capture similar disease-relevant information or emphasize distinct aspects of the phenotype space. In addition, we re-ran the PERADIGM pipeline using each weighting scheme to examine how weighting choice influences downstream gene-level results and overall calibration. The consistency of significant findings across these weighting variants provides an indication of PERADIGM’s robustness to the specific choice of weighting formulation. All the alternative weighting scheme analysis results are provided in the S1 Text, S2 Fig, and S3 Fig.