AMERICAN JOURNAL OF HUMAN BIOLOGY 13:316–322 (2001) Prediction of Adult Stature for Japanese Population: A Stepwise Regression Approach MD. AYUB ALI AND FUMIO OHTSUKI* Laboratory of Human Morphology, Graduate School of Science, Tokyo Metropolitan University, Tokyo, Japan ABSTRACT The longitudinal growth in stature for 509 males and 311 females was characterized from early childhood to adulthood. A triphasic generalized logistic (BTT) model (Bock et al. [1994] Chicago: SSI) was used through the AUXAL software program. Growth parameters were derived from the estimated distance and velocity curves for each individual. A set of estimated growth parameters, including adult stature, was selected to develop equations, through the forward stepwise regression method, for the prediction of adult stature for Japanese boys and girls. Am. J. Hum. Biol. 13:316–322, 2001. © 2001 Wiley-Liss, Inc. The orderly growth of children in stature and weight is an important indicator of general health and thriving. Because of its greater stability, stature is more valuable than body weight in this role. Pediatricians, clinicians, endocrinologists, and orthopedic surgeons are among those most concerned with evaluating the present growth status of children and estimating future growth potential. In many families, there is at least passing interest in the adult stature of individual children. In other families, however, there is concern that a child with unusual stature will be a short adult. Family concern with present and future stature can have adverse psychological effects, especially near the usual age of puberty when the statures of many short or tall children become increasingly deviant. The management of such children should begin with assessments of present size and maturity, and be directed toward diagnosis. Their medical and psychological management may be improved if the final stature of children could be predicted with known reliability. Accurate predictions of adult stature help pediatricians to decide what is the appropriate medical treatment, especially for short children. They are also of interest to officials in some sports to detect potentially talented youth. Many researchers have proposed methods to predict adult stature from childhood data (Bayley and Pinneau,1952; Khamis and Guo, 1993; Khamis and Roche, 1994; Onat, 1975; Roche et al., 1975a,b; Wainer et al., 1978). Most protocols include skeletal age as a predictor variable. In the present study, equations were developed to predict the © 2001 Wiley-Liss, Inc. PROD #M20031R2 adult stature through asymptotic curve fitting to longitudinal stature data. The biological parameters of growth curves can be estimated from parametric and nonparametric models. Fitting curves to serial stature data for individuals permits the extraction of a maximum amount of information about the child’s growth, and, of course, individual curves can be compared and contrasted. When fitted growthcurve parameters are available for many children, means and the variation around them are a convenient way to summarize a large amount of data for comparison of growth patterns between sexes or among populations (Thissen et al., 1976). Therefore, fitting curves provides a convenient means of characterizing individual or group differences in growth patterns. Many growth models have been developed that can be compared for goodness of fit and for their ability to provide estimates of important features of the growth curve (Ali and Ohtsuki, in press; Berkey and Reed, 1987; Bock et al., 1973; Count, 1943; Jolicoeur et al., 1988; Jolicoeur et al., 1992; Karlberg, 1989; Preece and Baines, 1978). However, for a good prediction, it is necessary to select a good model. Jolicoeur et al. (1992) declared that the JPA-2 model had, at the time, the best fit compared with other structural growth models. Recently, Ali and *Correspondence to: Fumio Ohtsuki, Laboratory of Human Morphology, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minamiohsawa, Hachiojishi, Tokyo 192-0397, Japan. E-mail: ohfumi@comp.metro-u.ac.jp Received 2 May 2000; Revision received 1 August 2000; Accepted 4 August 2000 PREDICTION OF ADULT STATURE Ohtsuki (in press) showed that the average root mean square error of the estimate for the triphasic generalized logistic (BTT) model was smaller than that for JPA-2 model. Furthermore, the JPA-2 model cannot estimate the mid-growth spurt, whereas the BTT model can do so. The purpose of the present study was to apply the BTT model to longitudinal data for stature of Japanese boys and girls, and to use the estimated growth parameters for individuals to develop equations to predict adult stature. DATA AND METHODS Data Longitudinal data for 820 Japanese children, 509 males and 311 females, from birth to 20 years of age, who were born between 1967 and 1977, were analyzed. Several universities from the Kanto District of Japan were selected and all students with complete information from several classes of the selected universities were included. The sample provides individual information applicable to all of Japan because the universities that were included do not have entrance criteria based on place of residence. The present sample included children from every prefecture of Japan, but the Kanto region is better represented than other regions. The sample includes 24 from the Hokkaido area, 29 from Touhoku, 466 from Kanto, 87 from Chubu, 37 from Hokuriku, 69 from Kinki, 31 from Chugoku, 17 from Shikoku, 41 from Kyushu, and 19 from other areas. Every year, physical examinations of school children were made from April to June in Japan from kindergarten to university. It was possible to collect longitudinal growth information (including stature), but not the exact dates of all the examinations. Using birth dates, ages at examinations were calculated by taking the date of examination as May 1 (median of April to June) for each year. Methods To estimate the growth parameters, the BTT model was applied to the individual longitudinal data of stature as previously described by Ali and Ohtsuki (in press). The growth parameters were age at early childhood minimum (AECM), stature at early childhood minimum (SECM), velocity at early childhood minimum (VECM), age at 317 mid-childhood maximum (AMC), stature at mid-childhood maximum (SMC), velocity at mid-childhood maximum (VMC), age at takeoff (ATO), stature at takeoff (STO), velocity at takeoff (VTO), age at peak height velocity (APHV), stature at peak height velocity (SPHV), peak height velocity (PHV), and predicted adult stature (PAS). According to the Bock et al. (1994), adult stature was considered in this study as stature at age 25 years for each individual. The definition of age at adult stature, however, varies (Kato et al., 1998). The adult stature of an individual is determined by the growth pattern including aspects that describe size and timing. The relationships, either linear or nonlinear, between adult stature and biological parameters of the growth curve should be considered in the development of an equation to predict adult stature. This can be easily shown from the correlation matrix plot (Figs. 1 and 2). The figures show that the relationships between PAS and growth parameters are linear. Considering the goal to predict adult stature from biological parameters and, because the relationships between adult stature and some biological parameters are linear, multiple linear regressions of adult stature on biological parameters can be considered. The problem is to determine how many explanatory variables are needed to explain the maximum percentage of variation in the dependent variable, adult stature. In other words, an objective method is needed to exclude predictors that are not useful. The screening procedure is forward stepwise regression analysis (Draper and Smith, 1966, pp. 169–171). The STATISTICA software was used. It is sometimes necessary to specify a regression equation without an intercept (intercept forced to zero, regression through the origin). In some applications, particularly, in the social and natural sciences, variables of interest are measured on more or less arbitrary scales where the zero points have no special meaning. For example, if PAS is considered a function of different height growth parameters, e.g., SPHV, APHV, PHV, ATO, STO, etc., the intercept term is meaningless because one cannot consider PAS when the growth parameters are zero. In such a situation, inclusion of intercept term results in a low value of R2. 318 M.A. ALI AND F. OHTSUKI Fig. 1. Correlation matrix plot between PAS and growth parameters for Japanese boys. The parameters were drawn from the estimated distance and velocity curves of the BTT model. The growth parameters were age at takeoff (ATO), stature at takeoff (STO), velocity at takeoff (VTO), age at peak height velocity (APHV), stature at peak height velocity (SPHV), peak height velocity (PHV), and predicted adult stature (PAS). In every element in the matrix, the x-axis is for PAS. Only the pattern, either linear or nonlinear, is of concern. No scales are shown here. Because multiple regression is a mathematical maximization procedure, it can be very sensitive to outliers and influential points. There are various statistics for identifying outliers on the dependent variable and influential data points. Two are considered in this study, i.e., Mahalanobis distance (Stevens, 1996) and Cook’s distance (Cook, 1977). Cook and Weisberg (1982) indicated that a Cook distance >1 would generally be considered large, implying an influential point. Particularly with small samples (<100), multiple regression estimates are not very stable. In other words, extreme observations can greatly influence final estimates. Therefore, it is advisable to use formal statistical procedures to identify outliers, and to repeat the analyses after omitting any outliers. Another alternative is to repeat the analyses using absolute deviations rather than least squares regression, thereby reducing the effects of outliers. RESULTS The BTT model was run on the individual longitudinal data for stature to estimate the individual growth parameters for each distance and velocity curve. Using forward stepwise regression, only two parameter variables explain the maximum percentage of variation in the dependent variable, adult stature. The model is PAS= b1(SPHV) + b2(STO) + « where b1 and b2, are the partial regression coefficients, and « is the random error term assumed to be normally distributed with mean zero and variance unity. A summary of the stepwise regression of the dependent variable PAS for different cases is shown in Table 1. Case 1, case 2, and case 3 refer to analyses based on the whole sample, those with a mid-growth spurt, and those without a mid-growth spurt, respectively. The regression coefficients are highly significant and the standard errors of the estimates are small. This table also shows that for the three-variable regression equation, maximum R2 is attained in case 2. Also, the average standard errors of the estimated coefficients in case 2 are smaller than those in case 3. It should be noted that, although the 319 PREDICTION OF ADULT STATURE Fig. 2. Correlation matrix plot between PAS and growth parameters for Japanese girls. The parameters were drawn from the estimated distance and velocity curves of the BTT model. The growth parameters were; age at takeoff (ATO), stature at takeoff (STO), velocity at takeoff (VTO), age at peak height velocity (APHV), stature at peak height velocity (SPHV), peak height velocity (PHV), and predicted adult stature (PAS). In every element in the matrix, the x-axis is for PAS. Only the pattern, either linear or nonlinear, is of concern. No scales are shown here. TABLE 1. Summary of the stepwise regression for the dependent variable, predicted adult stature* Cases Sample size Boys Case 1 415 Case 2 213 Case 3 197 Girls Case 1 234 Case 2 96 Case 3 136 Variable Step +in Coefficient Standard error F—to enter/remove R2 Variables included SPHV STO SPHV STO SPHV STO 1 2 1 2 1 2 1.534135 −0.483147 1.539818 −0.498201 1.558884 −0.503437 0.031135 0.035777 0.017258 0.019778 0.050298 0.058064 1170799.0 182.0 2202710.0 635.0 391888.3 75.2 0.99964 0.99976 0.99990 0.99998 0.99950 0.99964 1 2 1 2 1 2 SPHV STO SPHV STO SPHV STO 1 2 1 2 1 2 1.628559 −0.580845 1.488222 −0.431707 1.592562 −0.534061 0.038572 0.043748 0.046936 0.052431 0.057328 0.065738 394039.4 176.3 367055.8 67.8 220941.4 66.0 0.99941 0.99967 0.99974 0.99985 0.99939 0.99959 1 2 1 2 1 2 *Case 1, case 2, and case 3 refer to the analysis based on whole sample, individuals who have the mid-growth spurt, and who do not have the mid-growth spurt, respectively. The classifications of Case 2 and case 3 are considered here for each individual on the results of BTT model on AUXAL. The sample sizes among three cases are not consistent because the outliers were omitted. present study started with a sample of 820 individuals, some were excluded. For some individuals, the AUXAL software (Bock et al., 1994) did not converge because of outliers or missing observations. Other individuals were excluded to discard outliers and influential data points. Thus, the results are free from the problem of inclusion of outlier and influential data points. Analyses of residuals for individual cases help us to understand the precision of the prediction for the adult stature. Average values of observed adult stature, PAS, and the residuals are shown in Table 2. The re- 320 M.A. ALI AND F. OHTSUKI TABLE 2. Averages of the observed, predicted, residual, 90% confidence bounds of residuals, and standard errors (SE) of prediction equations of adult stature based on growth parameter-variables for different cases* Cases Boys Case 1 Case 2 Case 3 Girls Case 1 Case 2 Case 3 Residual (cm) 90% Confidence bounds of residuals Mean SD Lower (cm) Upper (cm) SE of prediction (cm) 172.37 171.72 173.37 0.026 0.002 −0.264 2.70 0.84 2.71 −1.896 −0.830 −2.618 3.530 0.874 4.342 0.18 0.08 0.31 159.02 157.84 159.79 0.030 0.022 0.034 2.92 1.94 3.25 −2.651 −1.855 −3.304 4.449 2.054 4.987 0.26 0.27 0.38 Sample size Observed stature (cm) Predicted stature (cm) 415 213 197 172.40 171.72 173.10 234 96 136 159.05 157.86 159.82 *Categories of Cases 1–3 are the same as in Table 1. The sample sizes among three cases are not consistent because the outliers were omitted. siduals in case 2 are smaller than those in cases 1 and 3 for both boys and girls. Also, the predictions of adult stature, on average, were underestimated approximately by 0.03 cm in case 1, overestimated by 0.26 cm in case 3, but asymptotically unbiased in case 2 for boys. For girls, predictions, on average, were underestimated by 0.03 cm in cases 1 and 3, but underestimated by only 0.002 cm in case 2. This implies, on average, that the prediction of adult stature is slightly better in those individuals who have a mid-growth spurt than in those individuals who do not have this spurt. Thus, this study postulates that the BTT model gives the asymptotically unbiased estimate of the growth parameters for those individuals who have the mid-growth spurt, and gives biased estimate (although the bias is small) of the growth parameters for individuals who do not have the mid-growth spurt; the reason may be the triphasic function itself. DISCUSSION To predict adult stature from the present study, it is necessary to determine STO and SPHV that are possible after 12 years in girls and 14 years in boys. For clinical purpose, it would be better to predict adult stature near the onset of adolescent growth using the protocols reported by others, which use skeletal age (Bayley and Pinneau, 1952; Khamis and Guo, 1993; Onat, 1975, 1983; Roche et al., 1975a,b; Wainer et al., 1978). The advantage of the present method is that it removes the problem of X-ray exposure to the subject, even though it is essential to estimate the skeletal age for clinical purposes or pediatric treatment for short stature children. Predicting adult stature without skeletal age is applicable, for example, not only for the purpose of sport talent detection and selection based on PAS, but also for giving advice for choosing a more suitable sport event and position from the viewpoint of PAS. During the past two or three decades, considerable literature on the growing child in competitive sports has accumulated (Malina, 1994, 1998). Many reports indicate that physical performance is higher in those who are more biologically mature, especially among boys (Malina and Bouchard, 1991). The relationship between physical performance and biological age or skeletal age is well established, although there are many conflicting reports under some conditions (Beunen et al., 1978a,b, 1981, 1997; Bouchard and Malina, 1977; Bouchard et al., 1976, 1978; Carron and Bailey, 1974; Ohtsuki et al., 1994). The mean residuals of PAS in the present study (Table 2) are smaller compared with those reported by others (Bayley and Pinneau,1952; Khamis and Guo, 1993; Khamis and Roche, 1994; Roche et al., 1975a,b; Wainer et al., 1978). Average prediction failure, i.e., residual >4.0 cm, was reported by Khamis and Guo (1993) as about 10% for boys and 8% for girls. In the present study, failure did not occur for boys, except for case 3, but only 4% occurred for girls in case 2. Case 3 and a part of case 1 (i.e., sample without mid-growth spurt) are affected by the triphasic BTT model itself. Standard errors of PAS in the present study (Table 2) are smaller than those of some other studies (Onat, 1975, 1983). Comparing the 90% confidence bounds for residuals, the present PREDICTION OF ADULT STATURE study (Table 2) shows better prediction than those of some others (Khamis and Roche, 1994; Roche et al., 1975a; Wainer et al., 1978). The proposed equations of predicting final stature for the Japanese are as follows: For boys (whole sample): PAS 4 1.534135 (SPHV) − 0.483147(STO); For boys (with mid-growth spurt): PAS 4 1.539818(SPVH) − 0.498201(STO); For boys (without mid-growth spurt): PAS 4 1.558884(SPVH) − 0.503437(STO); For girls (whole sample): PAS 4 1.628559(SPVH) − 0.580845(STO); For girls (with mid-growth spurt): PAS 4 1.488222(SPVH) − 0.431707(STO); and For girls (without mid-growth spurt): PAS 4 1.592562(SPVH) − 0.534061(STO). ACKNOWLEDGMENTS We are grateful to Alex F. Roche, Professor Emeritus, Wright State University, for reading our manuscript and giving us many valuable suggestions and comments. Our thanks extend to the anonymous reviewers and Professor Robert M. Malina, Editor-inChief, American Journal of Human Biology, for their criticism on earlier versions of this paper and for their helpful suggestions. LITERATURE CITED Ali MA, Ohtsuki F. In press. Application of the BTT model to longitudinal growth data of Japanese boys and girls. Am J Hum Biol. Bayley N, Pinneau SR. 1952. Tables for predicting adult height from skeletal age: Revised for use with Greulich-Pyle hand standards. J Pediatr 40:423–441. Beunen G, Oystyn M, Simons J, Van Gerven D, Swalus P, de Beul G. 1978a. A correlation analysis of skeletal maturity, anthropometric measures and motor fitness among boys 12 through 16. In: Landry F, Orban WAR, editors. Biomechanics of sports and kinanthropometry. Miami: Symposia Specialists. p 343–350. Beunen G, Oystyn M, Renson R, Simons J, Van Gerven D. 1978b. Motor performance as related to age and maturation. In: Shephard RJ, Lavallee H, editors. Physical fitness assessment. Principles, practice and applications. Springfield, IL: CC Thomas. p 229–237. Beunen G, Oysty M, Simons J, Renson R, Van Gerven D. 1981. Chronological age and biological age as related to physical fitness in boys 12 to 19 years. Ann Hum Biol 4:321–331. Beunen G, Malina RM, Lefevre J, Claessens AL, Renson R, Eynde BK, Vanreusel B, Simons J. 1997. Skeletal maturation, somatic growth and physical fitness in girls 6–16 years of age. Int J Sports Med 18:413–419. Berkey CS, Reed RB. 1987. A model for describing normal and abnormal growth in early childhood. Hum Biol 49:973–987. Bock RD, Wainer H, Petersen A, Thissen D, Murray J, 321 Roche AF. 1973. A parameterization for individual human growth curves. Hum Biol 45:63–80. Bock RD, du Toit SHC, Thissen D. 1994. AUXAL: Auxological analysis of longitudinal measurements of human stature. Chicago: SSI. Bouchard C, Malina RM. 1977. Skeletal maturity in a Pan American Canadian team. Can J Appl Sport Sci 2:109–114. Bouchard C, Malina RM, Hollmann W. Leblanc C. 1976. Relationship between skeletal maturity and submaximal working capacity in boys 8 to 18 years. Med Sci Sports 8:186–190. Bouchard C, Malina RM, Hollmann W. 1978. Skeletal age and submaximal working capacity in boys. Ann Hum Biol 5:75–78. Carron AV, Bayley DA. 1974. Strength development in boys from 10 through 16 years. Monogr Soc Res Child Develop Serial No. 157. Cook RD. 1977. Detection of influential observations in linear regression. Technometrics 19:15–18. Cook RD, Weisberg S. 1982. Residuals and influence in regression. New York: Chapman and Hall. Count EW. 1943. Growth patterns of human physique: An approach to kinetic anthropometry. Hum Biol 15: 1–32. Draper NR, Smith H. 1966. Applied regression analysis. New York: Wiley & Sons. Jolicoeur P, Pontier J, Pernin M-O, Sempe M. 1988. A lifetime asymptotic growth curve for human height. Biometrics 44:995–1003. Jolicoeur P, Pontier J, Abidi H. 1992. Asymptotic models for the longitudinal growth of human stature. Am J Hum Biol 4:461–468. Kato S, Ashizawa K, Satoh K. 1998. An examination of the definition ‘final height’ for practical use. Ann Hum Biol 25:263–270. Karlberg J. 1989. A biologically-oriented mathematical model (ICP) for human growth. Acta Paediatr Suppl 350:70–94. Khamis HJ, Guo S. 1993. Improvement in the RocheWainer-Thissen stature prediction model: A comparative study. Am J Hum Biol 5:669–679. Khamis H, Roche AF. 1994. Predicting adult stature without using skeletal age: The Khamis-Roche method. Pediatrics 94:504–507. Ledford AW, Cole TJ. 1998. Mathematical models of growth in stature throughout childhood. Ann Hum Biol 25:101–115. Malina RM. 1994. Physical growth and biological maturation of young athletes. Exerc Sports Sci Rev 22:389– 433. Malina RM. 1998. Growth and maturation of young athletes—Is training a factor? In: Chan K-M, Micheli LJ, editors. Sports and children. Hong Kong: Williams and Wilkins. p 133–161. Malina RM, Bouchard C. 1991. Growth, maturation and physical activity. Champaign, IL: Human Kinetics. p 171–186. Ohtsuki F, Kita I, Uetake T, Miyamoto T, Tsukagoshi T, Asami T, Matsui H. 1994. Physical fitness of Chinese and Japanese junior track runners—Can skeletal age and stature be useful for talent detection? Jpn J Phys Fitness Sports Med 43:162–174. Onat T. 1975. Prediction of adult height of girls based on the percentage of adult height at onset of secondary sexual characteristics, at chronological age, and skeletal age. Hum Biol 47:117–130. Onat T. 1983. Multifactorial prediction of adult height of girls during early adolescence allowing for genetic potential, skeletal and sexual maturity. Hum Biol 55: 443–461. 322 M.A. ALI AND F. OHTSUKI Preece MA, Baines MJ. 1978. A new family of mathematical models describing the human growth curve. Ann Hum Biol 5:1–24. Roche AF, Wainer H, Thissen D. 1975a. The RWT method for the prediction of adult stature. Pediatrics 56:1026–1033. Roche AF, Wainer H, Thissen D. 1975b. Predicting adult stature for individuals. In: Monograph in paediatrics, 3. Basel: Karger. Stevens J. 1996. Applied multivariate statistics for the social sciences, 3rd edition. New Jersey: Erlbaum Associates. Thissen D, Bock RD, Wainer H, Roche AF. 1976. Individual growth in stature: A comparison of four growth studies in the U.S.A. Ann Hum Biol 3:529–542. Wainer H, Roche AF, Bell S. 1978. Predicting adult stature without skeletal age and without paternal data. Pediatrics 61:569–572.