==== Front BMC Musculoskelet Disord BMC Musculoskelet Disord BMC Musculoskeletal Disorders 1471-2474 BioMed Central London 37386376 6303 10.1186/s12891-023-06303-2 Research Determination of individual factors associated with hallux valgus using SVM-RFE Nakao Hidetoshi h_nakao@jiu.ac.jp 1 Imaoka Masakazu 2 Hida Mitsumasa 2 Imai Ryota 2 Nakamura Misa 2 Matsumoto Kazuyuki 3 Kita Kenji 3 1 grid.440885.5 0000 0000 9365 1742 Faculty of Social Work Studies, Josai International University, Chiba, Japan 2 grid.449155.8 0000 0004 0641 5733 School of Rehabilitation, Osaka Kawasaki Rehabilitation University, Osaka, Japan 3 grid.267335.6 0000 0001 1092 3579 School of Technology, Industrial and Social Sciences, Tokushima University, Tokushima, Japan 29 6 2023 29 6 2023 2023 24 5349 12 2022 8 3 2023 © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Introduction This cross-sectional study aimed to determine the factors related to hallux valgus (HV) and their importance using support vector machine-recursive feature elimination (SVM-RFE). Methods A total of 864 participants aged ≥ 18 years were enrolled. The Manchester scale was used to determine the presence of HV (summed scores for both feet ≥ 4). The questionnaire included items such as age, sex, height, weight, and foot measurements. These internal factors were analyzed to determine if they are related to HV using SVM-RFE. Results The results of tenfold cross-validation using SVM-RFE revealed that the numbers of feature selections were 10, 10, and 9 for age, sex, and body weight, respectively, and these factors were shown to be related to HV. HV was found to be more common in women than in men (women, 24.9%; men, 7.6%), but the sex difference was not significant in older people. Conclusion Age and sex were found to be important factors associated with HV identified via feature selection using SVM-RFE. Keywords Feature selection Hallux Valgus Manchester Scale SVM-RFE issue-copyright-statement© BioMed Central Ltd., part of Springer Nature 2023 ==== Body pmcIntroduction Hallux valgus (HV) is a joint deformity that occurs in the first metatarsophalangeal joint of the great toe, in which the first metatarsal upon birth turns inward and the great toe turns outward. HV is the most common joint deformity, with an estimated incidence of 21–65% [1, 2]. It increases with age and was reported to occur in 23.0% of individuals aged 15–65 years and in 35.7% of those aged ≥ 65 years [2]. Furthermore, it causes foot pain and is correlated with impaired gait and balance, thereby increasing the risk for falls in older people [3]. HV is caused by the displacement of the first ray in the dorsal–medial direction due to the hypermobility of the first tarsometatarsal joint and foot pronation due to loading of their body weights [4, 5]. In general, HV is quantitatively diagnosed based on the dorsal plantar radiographs of the foot during loading. Furthermore, its presence is confirmed if the angle between the long axis of the first metatarsal and the long axis of the great toe is ≥ 15° [6]. However, owing to the difficulty in performing a radiographic examination in epidemiologic studies, self-reports [7], standardized photographs [8], and line drawings are used [9]. A systematic review of the literature demonstrated a wide variation in HV prevalence estimates due to several factors, such as HV diagnosis method, sex, age, study quality, and sampling method [2]. Previous investigated on self-recognized of HV, there was an error in rate of agreement with the diagnosis using radiologically assessed, and there is a problem that self-recognized cases is more likely to be perceived as less severe than the diagnosed cases by the physician [10]. Thus, a system that can correctly determine HV severity is desirable. Graded retests and inter-rater reliability using the Manchester scale (MS) were found to be excellent [11], and MS scale method can be widely applied in the future. The mean hallux abductus angle, measured using the radiographs of participants with an MS score of 2, whom this study was based on, was approximately 15°, which is the generally accepted minimum value for HV diagnosis [12]. HV can be influenced by external factors, e.g., wearing of high heels [13, 14] and injuries of the medial collateral ligament of the first metatarsophalangeal joint [15], and internal factors, e.g., genetic predisposition, sex, age, and flat feet [14]. Thus, HV is caused by a combination of factors, which indicates the importance to rank the relevant factors. However, to the best of our knowledge, studies investigating the factors related with HV using MS are scarce. Support vector machine (SVM) is a machine learning-based classification method that can be applied to pattern recognition and regression analysis [16]. In the 1990s, the application of SVM was extended to nonlinear discriminant methods combined with kernel methods. SVM, which has been used to construct nonlinear discriminant functions by kernel tricks, is currently the best learning method for pattern recognition. In general, many features are used for pattern recognition and discrimination, and features are identified using feature selection methods, e.g., recursive feature elimination (RFE) [17]. SVM-RFE is one of the most widely used feature selection methods owing to its flexibility and simplicity. It can be applied to any model and produces the optimal set of features to achieve the best performance. In this study, we used SVM-RFE to analyze HV-related factors. Studies have applied this two-class classification algorithms using SVM and reported that the use of evaluation and diagnosis systems in the medical field has increased in recent years [18]. The RFE algorithm for nonlinear kernel allows ranking of variables but not comparison of the performance of all variables in a specific iteration. Therefore, this study aimed to demonstrate the importance of HV-related factors via feature selection using SVM-RFE. Foot alignment was added to the basic items of age, sex, weight, and body mass index (BMI), and HV-related factors were analyzed via SVM-RFE. Methods Research design This cross-sectional study included 928 participants aged ≥ 18 years. The participants were examined as a part of a foot health survey at sports and local health events, and a corporate health project was held in Osaka Prefecture in 2018–2020. The inclusion criteria were no pain or slight foot pain during loading and ability to walk. Among the participants, 48 for whom the date the photograph was taken was unclear and 16 for whom both feet could not be photographed were excluded. As a result, only 864 participants (353 males) were finally included in the analysis. The collected data were analyzed to evaluate the accuracy of the extraction method for HV-related factors and feature selection via SVM-RFE using machine learning. The causal relationship between HV and the selected features was statistically investigated. The study protocol was approved by the Research Ethics Review Committee of Osaka Kawasaki Rehabilitation University (approval no. OKRU29-A019). Furthermore, the study was conducted in accordance with the principles of the Declaration of Helsinki. The purpose and methods of the study were fully explained in advance to the participants, and measurements were performed after obtaining written informed consent. In addition, this study has been reported according to the STROBE guideline [19]. Evaluation using the MS and foot measurements The summed scores of the MS on the horizontal image of the forefoot body surface were used to evaluate the presence or absence of HV [8]. A digital camera (RX-0, SONY, Tokyo, Japan) was used to capture foot images for MS. A horizontal image of the forefoot was taken to confirm that the second toe was in the middle position of adduction and abduction as much as possible. All participants were evaluated for HV using the MS by one examiner, a physiotherapist with 21 years of general physiotherapy clinical experience. The criteria for the presence of HV were based on the grade classification of HV in MS: 0, no deformity; 1, mild deformity; 2, moderate deformity; and 3, severe deformity　(Fig. 1) [11]. If the summed score of the right and left MS was ≥ 4, the patient was considered as having HV. In this study, the standard value indicating the presence of HV was 2 points on both sides or ≥ 3 points on one side, and a total of ≥ 4 points. Fig. 1 Evaluation of hallux valgus using the Manchester scale score. (A) No deformity (score = 0), (B) mild deformity (score = 1), (C) moderate deformity (score = 2), (D) severe deformity (score = 3). Diagram adapted from Garrow et al [8] Furthermore, dorsal height (DH), foot length (FL), and arch height ratio (AHR) were evaluated [20]. In this study, the DH/truncated FL (TFL) was defined as the AHR. DH, FL, and TFL were measured using a foot arch height-measuring instrument (Takei Corp, Niigata, Japan). The mean of both feet measurements was used for SVM-RFE analysis. Discriminant evaluation using SVM-RFE SVM is a machine learning-based classification method that can be applied to pattern recognition and regression analysis. SVM-RFE was implemented using the RFE class in the feature selection module of scikit-learn. The SVM-RFE inputs were age, height, weight, BMI, average left–right FL, average DH, and average left–right AHR, all of which are numerical data. However, because the mean and scale of all items are different, the data were first standardized, and the mean and variance were set to 0 and 1, respectively. Then, we input the binary data of sex, history of foot injury, foot pain, and exercise habits and performed feature selection. In this study, the linear function was used as the kernel function for feature selection. The value of the cost parameter (C), which determines tolerance for misclassification, needs to be determined and the accuracy of the prediction model needs to be evaluated. In the evaluation experiment, the fit rate, reproducibility, and accuracy of the model when C = 1.0 were obtained via a tenfold cross-validation. Statistical examination In this study, the HV-related factors were extracted via feature selection using SVM-RFE, and their accuracy was evaluated. The SVM-RFE classification was implemented at the Tokushima University. The extracted factors were statistically processed, and normality of the explanatory variables was confirmed using the Shapiro–Wilk test. Comparison of the basic attributes between male and female participants was performed using the unpaired t-test or Mann–Whitney U test. The χ2 test or Fisher’s exact test was used for analyzing the sex-related difference in participants with and without HV. Pearson’s or Spearman’s correlation coefficients were used to examine the correlation between MS score and each explanatory variable in female participants with HV. Statistical analysis was conducted using IBM SPSS Statistics version 28.0 (IBM Corp., Armonk, NY, USA) with a significance level of 5%. Results Comparison of sex differences in basic attributes and foot measurements of the participants Data were collected from 928 participants aged 18–96 years, including university students, workers, citizen athletes, and community-dwelling older people. Among them, 48 participants with unclear imaging data and 16 whose feet could not be photographed were excluded. As a result, data from 864 participants (353 men and 511 women) were used in the final analysis. The questionnaire was self-administered and contained the items age, sex, height, and weight. Comparison of the basic attributes and foot measurements between the male and female participants is demonstrated in Table 1. The results indicated that the male participants had significantly higher height, weight, BMI, FL, DH, AHR, and total MS score than the female participants. Female participants were significantly older than male participants. Table 1 Basic attributes and foot measurements of the subjects Male (n = 353) Female (n = 561) Mean ± SD Mean ± SD  p-value Age (y) 44.6 ± 21.2 56.7 ± 21.1 < 0.001 Height(cm) 169.9 ± 7.6 154.6 ± 6.4 < 0.001 Weight (kg) 66.5 ± 9.9 52.1 ± 8.0 < 0.001 BMI (kg/m2) 23.0 ± 3.0 21.7 ± 3.0 < 0.001 FL(mm) 247.6 ± 12.4 224.4 ± 4.6 < 0.001 DH (mm) 63.4 ± 5.2 56.0 ± 4.6 < 0.001 AHR (%) 25.6 ±2.2 25.0 ±2.1 < 0.001 MS Total Score 2.3 ± 1.8 1.4 ± 1.4 < 0.001 BMI, Body mass index; DH, Dorsal height; FL, Foot length; TFL, Truncated foot length; MS, Manchester scale *: statistically significant, P < 0.05 Predictive model accuracy evaluation of feature selection using SVM-RFE The results of the tenfold cross-validation using SVM-RFE are presented in Table 2. The features selected by training the prediction model were age, sex, weight, and mean DH, with the number of features selected for the parameters being 10, 10, 9, and 1, respectively. Age, sex, and weight were mainly related to HV. Table 2 Feature selection of hallux valgus-related factors using SVM-RFE Selected features Number of choices Age 10 Sex 10 Weight 9 Dorsal height 1 SVM-RFE, support vector machine-recursive feature elimination The accuracy evaluation results of the prediction model are presented in Table 3. The fit, repeatability, and accuracy of the model were determined via a tenfold cross-validation, with the results being 30%, 73%, and 43%, respectively. Table 3 Accuracy evaluation using SVM-RFE Precision ratio Recall Accuracy With HV 30% 73% 43% Without HV 92% 64% 75% HV, hallux valgus; SVM-RFE, support vector machine-recursive feature elimination Sex difference in the HV rate Table 4 presents the HV rates by sex as an associated factor, with 24.9% of the female participants having HV compared with 7.6% of the male participants. Table 4 Comparison of sex differences in hallux valgus Male Female p-value n (%) n (%) With HV 27 (7.6) 127 (24.9) p < 0.001 Without HV 326 (92.4) 384 (75.1) HV, hallux valgus χ2test Comparison of the percentage of male and female participants with HV based on their age group The proportion of the participants by age group is presented in Table 5. The age groups were classified based on the life stages (adolescence, adulthood, and old age) presented in Health Japan 21, a guideline issued by the Ministry of Health, Labor and Welfare. Table 5 Comparison of the percentage of men and women with HV by age group Female Male With HV Without HV With HV Without HV Age group n (%) Expected number n (%) Expected number n (%) Expected number n (%) Expected number p-value 18–29 8 (9.1) 21.9 80 (90.9) 66.1 1 (0.8) 9.8 127 (99.2) 118.2 <0.01 30–44 10 (13.3) 18.6 65 (86.7) 56.4 0 (0) 3.8 50 (100) 46.2 <0.01 45–64 20 (23.3) 21.4 66 (76.7) 64.6 7 (7.4) 7.3 88 (92.6) 87.7 <0.01 ≥65 89 (34.0) 65.1 173 (66.0) 196.9 19 (23.7) 6.1 61 (76.3) 73.9 0.08 The proportion of female participants with HV increased with increasing age, with 89 (34%) participants aged ≥ 65 years, followed by 20 (23.3%) aged 45–64 years, and 10 (13.3%) aged 30–44 years. Similarly, the proportion of male participants with HV increased with increasing age, with 19 (23.7%) participants aged ≥ 65 years, followed by 7 (7.4%) aged 45–64 years. The proportion of female participants aged ≥ 65 years was higher than that of male participants. In the comparison of sex differences by age, significant differences were observed in the proportion of women with HV in the age groups of 18–29, 30–44, and 45–64 years but not in the age group of ≥ 65 years. Correlation between HV explanatory variables and total MS score The correlations between HV explanatory variables and total MS score for female participants with a high prevalence of HV are presented in Table 6, and significant correlations were observed for age (r = 0.343), height (r = − 0.324), and FL (r = − 0.216) in female participants with HV in all age groups. In the significant correlation analysis were found for age (r = 0.478), height (r = − 0.483) in female participants with HV MS score in the age group of 45–64 years. No item showed a significant difference in female participants aged ≥ 65 years. Table 6 Correlation between HV explanatory variables and MS score in females Age group Age (y) Height (cm) Weight (kg) BMI (kg/m2) FL (mm) DH(mm) AHR (%) r r r r r r r All age (n = 127) 0.343* −0.324* −0.082 0.072 −0.216* −0.019 0.080 18–29 (n = 8) 0.516 −0.126 −0.191 −0.126 −0.258 0.252 0.127 30–44 (n = 10) −0.28 0.114 −0.309 −0.572 −0.076 0.038 0.076 45–64 (n = 20) 0.478* −0.483* −0.048 0.127 −0.142 −0.037 0.087 ≥65 (n = 89) −0.022 −0.153 −0.085 0.049 −0.085 −0.114 −0.072 BMI, Body mass index; FL, Foot length; DH, Dorsal height; AHR, Arch height ratio Pearson’s or Spearman’s correlation. Statistically significant, * P < 0.05 Discussion To date, few studies have used machine learning to analyze joint deformities, and to the best of our knowledge, SVM-RFE has only been used for Kashin–Back disease, which involves alteration of hands [21]. In the present study, a feature selection algorithm was used to analyze HV-related factors using SVM-RFE. The fit rate, reproducibility, and accuracy of the HV prediction model in this study were 30%, 73%, and 43%, respectively. This indicates that the explanatory variables of age, sex, weight, and DH were significantly related in 30% of the participants with HV but not in 73% of those without HV. The final output of the SVM-RFE algorithm is a list of variables ranked according to their relevance. SVM-RFE is essentially a backward elimination method. However, the top-ranked variables are not necessarily the most relevant variables under the most relevant conditional on the specific ranked subset in the model [18]. Thus, the importance of HV-related factors depends on the number of variables. SVM-RFE algorithm allows the classification and ranking of variables but not the comparison of the performance of all variables, In other words, it is important to interpret the results in terms of their relationship to the response variable and other variables and the magnitude of the relationship. Therefore, in this study, statistical analyses were performed for HV-related factors. Regarding feature-selected factors of HV, age, sex, weight, and DH were selected in that order. Statistical analysis of the selected factors revealed that women were predominant in terms of the sex ratio for HV. In this study, 24.9% of the female participants had HV compared with 7.6% of the male participants. In a questionnaire survey of 4,249 cases in the UK, HV was detected in 28.4% cases, with an odds ratio of 2.64, which was higher in men than in women [9]. In a study conducted on Japanese participants, the incidence rate of definite radiographic HV was 29.8%. Female sex was significantly associated with increased risk for HV (odds ratio, 1.71) [22]. A similar trend was observed in this study. The mean age was higher in female participants with HV than in those without HV, and total MS score was found to be positively correlated with age (r = 0.478) in the age group of 45–64 years, suggesting that prime age is an important factor related to HV. Regarding age group, the proportion of HV was the highest in the older age group (aged ≥ 65 years) for both sexes but decreased in the younger age groups. In adolescents, HV was more common in female participants than in male participants, but sex difference was not observed in the age group of ≥ 65 years. As for the relationship between age and sex and HV onset, HV began to develop in female participants when they were in primary and secondary schools [2]. These findings are similar to the findings of the present study; however, in the present study, the incidence rate of HV was not different between older men and women. In an analytical study of 11,714 Japanese individuals aged 60–79 years, the incidence of HV increased with age in both men and women, with a significant increase observed between the age groups of 40–50 years and 50–60 years [23]. To prevent worsening of HV in women, it is important to inform them of appropriate shoe selection and preventive exercises for HV, especially for those aged ≥ 45 years. The next most frequently extracted item in feature selection was weight, which did not show a valid statistical relationship with HV. In addition to weight, age, sex, obesity, inappropriate shoes, and physical activity were reported as risk factors for foot problems [13]. Studies have demonstrated that obesity is associated with reduced foot arches [24, 25]. Thus, obesity was reported to be associated with foot problems; however, in the present study, no correlation was observed between body weight and HV. Foot height, which was extracted less frequently in feature selection, was not found to have the same trend as body weight in the statistical analysis. Foot height was related to arch deformities, such as flat feet and high arches, and previous studies have demonstrated that HV and flat feet are related [14]. However, some studies reported that HV was not related to flatfoot [26], and the correlation between foot arch reduction and HV development is still under debate. Furthermore, height was not correlated with HV in women aged 45–64 years, and it was not extracted in feature selection. This association between height reduction and HV may be due to fact that risk of spinal degeneration increases in HV (odds ratio1.75) [27], and not only the HV but also the alignment of other body parts tend to change in older age. This study had some limitations. First, we used a cross-sectional design, and the causal relationship with HV onset cannot be fully explained. To conduct a more accurate analysis of HV-related factors, more specific models focusing on the severity of the deformity using a large dataset should be developed. Second, there were no data on the shoes used, such as high heels, which are considered to be related to HV, or on heredity. If these data were available, the accuracy and precision of the fit would further improve. Because HV is often treated with surgery when foot pain is severe and affects the patient’s quality of life, the factors associated with HV and foot pain should be examined in the future. Conclusion The results of this study indicated that age, sex, and weight were the most frequently extracted features; however, age and sex showed significant differences in the subsequent statistical analysis. Although SVM-RFE is an effective method for feature selection, further analysis using a large dataset is needed to show the causal relationship between feature selection and weight. Acknowledgements We would like to thank the individuals who participated in data collection and data entry and the many students at Osaka Kawasaki Rehabilitation University for their assistance with examinations and measurements. Author contributions Conceptualization: Hidetoshi Nakao. Data curation: Hidetoshi Nakao, Imaoka Masakazu, Mitsumasa Hida. Formal analysis: Hidetoshi Nakao. Data analysis and interpretation: Hidetoshi Nakao, Kenji Kita, Kazuyuki Matsumoto. Methodology: Hidetoshi Nakao, Mitsumasa Hida, Kenji Kita. Investigation: Hidetoshi Nakao, Masakazu Imaoka, Ryota Imai, Mitsumasa Hida, Misa Nakamura. Project administration: Masakazu Imaoka, Misa Nakamura. Writing-original draft: Hidetoshi Nakao. Writing-review & editing: All authors. Funding This work was supported by the Research Foundation of Josai International University presidents. The funding agencies had no role in the design of study and analysis, interpretation of data, and in writing of the manuscript. Availability of date and materials The dataset used and analyzed during the current study is available from the corresponding author on reasonable request. Declarations Ethics approval and consent to participant This study was conducted after obtaining approval from the Research Ethics Review Committee of Osaka Kawasaki Rehabilitation University (Approval no. OKRU29-A019) and was performed in accordance with the Declaration of Helsinki. All participants provided written, informed consent for data collection and storage. Competing interests The authors declare that they have no competing interests. Consent of publication Not applicable. Abbreviations SVM-RFE Support Vector Machine-Recursive Feature Elimination HV Hallux Valgus BMI Body Mass Index DH Dorsal Height FL Foot Length AHR Arch Height Ratio TFL Truncated Foot Length MS Manchester Scale Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ==== Refs References 1. Menz HB Roddy E Thomas E Croft PR Impact of hallux valgus severity on general and foot-specific health-related quality of life Arthritis Care Res 2011 63 3 396 404 2. Nix S Smith M Vicenzino B Prevalence of hallux valgus in the general population: a systematic review and meta-analysis J Foot Ankle Res 2010 3 21 10.1186/1757-1146-3-21 20868524 3. Menz HB Auhl M Spink MJ Foot problems as a risk factor for falls in community-dwelling older people: a systematic review and meta-analysis Maturitas 2018 118 7 14 10.1016/j.maturitas.2018.10.001 30415759 4. Biz C Favero L Stecco C Aldegheri R Hypermobility of the first ray in ballet dancer Muscles ligaments and tendons journal 2012 2 4 282 8 23738311 5. Singh D Biz C Corradin M Favero L Comparison of dorsal and dorsomedial displacement in evaluation of first ray hypermobility in feet with and without hallux valgus Foot and ankle surgery: official journal of the European Society of Foot and Ankle Surgeons 2016 22 2 120 4 10.1016/j.fas.2015.05.014 27301732 6. Hecht PJ Lin TJ Hallux valgus Med Clin N Am 2014 98 2 227 32 10.1016/j.mcna.2013.10.007 24559871 7. Roddy E Zhang W Doherty M Validation of a self-report instrument for assessment of hallux valgus Osteoarthr Cartil 2007 15 9 1008 12 10.1016/j.joca.2007.02.016 8. Garrow AP Papageorgiou A Silman AJ Thomas E Jayson MI Macfarlane GJ The grading of hallux valgus. The Manchester Scale J Am Podiatr Med Assoc 2001 91 2 74 8 10.7547/87507315-91-2-74 11266481 9. Roddy E Zhang W Doherty M Prevalence and associations of hallux valgus in a primary care population Arthritis Rheum 2008 59 6 857 62 10.1002/art.23709 18512715 10. Matsumoto T Higuchi J Maenohara Y Chang SH Iidaka T Horii C Oka H Muraki S Hashizume H Yamada H The discrepancy between radiographically-assessed and self-recognized hallux valgus in a large population-based cohort BMC Musculoskelet Disord 2022 23 1 31 10.1186/s12891-021-04978-z 34983473 11. Menz HB Fotoohabadi MR Wee E Spink MJ Validity of self-assessment of hallux valgus using the manchester scale BMC Musculoskelet Disord 2010 11 215 10.1186/1471-2474-11-215 20854678 12. Menz HB Munteanu SE Radiographic validation of the Manchester scale for the classification of hallux valgus deformity Rheumatology (Oxford) 2005 44 8 1061 6 10.1093/rheumatology/keh687 15901901 13. Menz HB Roddy E Marshall M Thomas MJ Rathod T Peat GM Croft PR Epidemiology of shoe wearing patterns over time in older women: associations with foot pain and hallux valgus The journals of gerontology Series A Biological sciences and medical sciences 2016 71 12 1682 7 10.1093/gerona/glw004 26834078 14. Nguyen US Hillstrom HJ Li W Dufour AB Kiel DP Procter-Gray E Gagnon MM Hannan MT Factors associated with hallux valgus in a population-based study of older women and men: the MOBILIZE Boston Study Osteoarthr Cartil 2010 18 1 41 6 10.1016/j.joca.2009.07.008 15. Fabeck LG Zekhnini C Farrokh D Descamps PY Delincé PE Traumatic hallux valgus following rupture of the medial collateral ligament of the first metatarsophalangeal joint: a case report J foot ankle surgery: official publication Am Coll Foot Ankle Surg 2002 41 2 125 8 10.1016/S1067-2516(02)80037-0 16. Cortes C Vapnik V Support-vector networks Mach Learn 1995 20 3 273 97 10.1007/BF00994018 17. Miao J Niu L A survey on feature selection Procedia Comput Sci 2016 91 919 26 10.1016/j.procs.2016.07.111 18. Sanz H Valim C Vegas E Oller JM Reverter F SVM-RFE: selection and visualization of the most relevant features through non-linear kernels BMC Bioinformatics 2018 19 1 432 10.1186/s12859-018-2451-4 30453885 19. van der Noord R Paap D van Wilgen CP Convergent validity and clinically relevant categories for the Dutch Central Sensitization Inventory in patients with chronic pain J Appl Biobehavioral Res 2018 23 2 e12119 10.1111/jabr.12119 20. Nakao H Imaoka M Hida M Imai R Tazaki F Morifuji T Hashimoto M Nakamura M Correlation of medial longitudinal arch morphology with body characteristics and locomotive function in community-dwelling older women: a cross-sectional study J Orthop Surg 2021 29 2 23094990211015504 10.1177/23094990211015504 21. Zhang Y Wei X Cao C Yu F Li W Zhao G Wei H Zhang F Meng P Sun S Identifying discriminative features for diagnosis of Kashin-Beck disease among adolescents BMC Musculoskelet Disord 2021 22 1 801 10.1186/s12891-021-04514-z 34537022 22. Nishimura A Fukuda A Nakazora S Uchida A Sudo A Kato K Yamada T Prevalence of hallux valgus and risk factors among japanese community dwellers J Orthop science: official J Japanese Orthop Association 2014 19 2 257 62 10.1007/s00776-013-0513-z 23. Sakou S Sugiura H Enishi K Inaba R Gender difference in first phalangeal angle after age 40 Japanese Soc Med Study Footwear 2011 25 2 150 4 24. Aurichio TR Rebelatto JR de Castro AP The relationship between the body mass index (BMI) and foot posture in elderly people Arch Gerontol Geriatr 2011 52 2 e89 92 10.1016/j.archger.2010.06.014 20678817 25. Faria A Gabriel R Abrantes J Bras R Moreira H The relationship of body mass index, age and triceps-surae musculotendinous stiffness with the foot arch structure of postmenopausal women Clin Biomech (Bristol Avon) 2010 25 6 588 93 10.1016/j.clinbiomech.2010.02.014 20398984 26. Coughlin MJ Jones CP Hallux valgus: demographics, etiology, and radiographic assessment Foot Ankle Int 2007 28 7 759 77 10.3113/FAI.2007.0759 17666168 27. Hsu TL, Lee YH, Wang YH, Chang R, Wei JC. Association of hallux valgus with degenerative spinal diseases: a population-based cohort study. International journal of environmental research and public health 2023, 20(2).