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method5), and the measurement method6). The numerical method counts the number of ossification centers on the hand. The qualitative method compares the shape of the ossification centers on hands to a standard chart, and the measurement method measures the area and aspect ratio of the ossifica-tion centers on the hand. For the Japanese popula-tion, Murata et al. standardized the Tanner White-house 2 (TW2) method, a qualitative method7).The Growth Potential method8) and the Bayley- Pinneau method9) have been used to predict final height using bone age, and a prediction formula for Japanese children was developed by Matsuoka et al. in 1994.10, 11). As an alternative, Ogata et al. devel-oped the target height method, which calculates the predicted height of Japanese children based on their parents’ height rather than using bone age12).In clinical practice, bone age is usually used for differential diagnosis or follow-up of growth disor-ders in children. Its use to predict the future height of athletes might therefore be challenging, because it requires radiography, and not many athletes have access to this. Estimates based on parental height are therefore often used. Previous studies have suggested several models to predict future height, but it is not known which formula is accu-rate and whether the model fits athletes. This study therefore aimed to compare the accuracy of the prediction formulas, and to develop a new prediction formula for athletes.Materials and MethodsThis study was approved by the ethical committee of Juntendo University (No.2021-12) and was carried out from June to October 2021. Consent forms were sent to potential participants and we enrolled any who agreed to participate and provided written consent. The participants were elite academy football players who belonged to a football club linked to the Japan Football Associa-tion. They were all dormitory lives and had a similar lifestyle of eating, sleeping and practicing for 6 years. The participants had all belonged to the football club for six years from the age of 12 to 18 (from 2006 to 2019). We collected data in October of their 6th grade of primary school (11 to 12 years old) with agreement of their parents (the fiscal year starts in April and ends in March in Japan) and then at the age of 20 to 28. In 6th grade of primary school, we obtained participants’ height, weight, parents’ height, and hand x-rays. X-rays were taken at a nearby clinic. At the age of 20-28, we obtained participants’ current height, weight and age. Height measured after 20 years old was defined as final height and was self-reported by participants to the investigator. We excluded those who were less than 20 years old in 2021.Estimated bone ageWe used the TW2 method5) to calculate bone age. This has three types of evaluation methods: RUS (radius, ulna and short bone), carpal and 20Bone. The RUS method evaluates 13 nuclei; the carpal method evaluates seven nuclei (carpal bone); and the 20bone method evaluates 20 nuclei (both RUS and carpal). We used the RUS method, which was reported to have a high correlation with final height11), to calculate the bone age.Models predicting future heightFirst, we compared two conventional models. The first model (Model 1) was reported by Matsuoka et al. in 199411). The formula was devel-oped using actual measured height, calendar age and bone age, and the equation was Y = a × actual measured height + b × calendar age + c × bone age + d. In the model, a, b, c and d change depending on the calendar age. In this study, for those with a calendar age of 11.5 to 12 years, we used Y = 0.639 × actual measured height − 9.221 × calendar age − 3.567 × bone age + 230.39. We used Y = 0.557 × actual measured height + 7.809 × calendar age − 3.413 × bone age + 36.161 for those with a calendar age of 12 to 12.5 years, and Y = 0.288 × actual measured height + 6.475 × calendar age − 1.825 × bone age + 36.161 for those aged 12.5 to 13 years. Actual measured heights at 6th grade of primary school were measured on the day of the hand X-ray. We measured the left hand12) unless it had previously been broken. The second model (Model 2) was the target height method developed by Ogata et al. in 199013). The formula uses parents’ height and the equation was (father’s height + mother’s height + 13)/2.After assessing Models 1 and 2, we created new height prediction models, Models 3 and 4. We conducted a multiple regression analysis using the 223