Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
American Journal of Epidemiology Copyright O 1996 by The Johns Hopkins University School of Hygiene and Public Health All rights reserved Vol. 144, No. 1 Printed In L/.S.A Correlation Between Systolic Blood Pressure and Physical Development in Adolescence Masazumi Akahoshi,1 Midori Soda,1 Randolph L. Carter,2 Eiji Nakashima,2 Katsutaro Shimaoka,1 Shinji Seto,3 and Katsusuke Yano3 Although the close relation between blood pressure and physical development in adolescence has been established in cross-sectional and comparative cross-sectional studies, the entire trend of systolic blood pressure (SBP) during adolescence has not been elucidated in conjunction with physical development in a longitudinal study. Blood pressure (mmHg), body weight (kg), and body height (m) were measured annually for 418 subjects in Hiroshima and Nagasaki, Japan, from age 10 (1955 or 1956) through 18 years (1963 or 1964). The Gompertz growth model was used to determine the velocity of weight increase (VEL) during that age period. The relations between SBP from age 10 to 18 and VEL, weight, height, body mass index (BMI; weight/height2, kg/m2), and the age at which the measurements were made were investigated individually using random-coefficient growth-curve analysis. The SBP trend for the 10- to 18-year age period could be shown by the following prediction equations: for the 163 Hiroshima males, SBP = 82.38 + 0.89 VEL at age 1.15 years prior to the current examination (VEL (age - 1.15)) + 1.40 BMI; for the 57 Nagasaki males, SBP = 92.70 + 1.07 VEL (age - 1.15) + 0.79 BMI; for the 148 Hiroshima females, SBP = 104.88 + 1.63 VEL (age - 1.15) + 0.05 BMI; for the 50 Nagasaki females, SBP = 113.62 + 1.67 VEL (age - 1.15) - 0.59 BMI. VEL 1.15 years prior to the current examination was significantly and positively related to SBP in each city by sex group (p < 0.01), and current BMI was significantly related to SBP for males in Hiroshima (p < 0.01) and nearly so in Nagasaki (p = 0.06), but not for females in either city (p = 0.84 and 0.13, respectively). Because the plot of VEL was a convex curve, SBP peaked approximately 1-2 years after the peak in VEL and then decreased in both sexes. The entire SBP trend during adolescence can be expressed as an equation of VEL and BMI in males and of VEL in females. SBP does not increase linearly with age. Am J Epidemiol 1996; 144:51-8. adolescence; blood pressure; body mass index; body weight; growth Cross-sectional studies have shown that adolescent blood pressure is closely associated with body weight, body mass index (BMI, weight/height2) and standing height (1-6). Comparative cross-sectional studies conducted at intervals of several years to review the relation between intervening changes in blood pressure and changes in weight and BMI have also shown that the rate of weight (7-10) or BMI (11-15) increase is positively related to the rate of blood pressure increase and is predictive of subsequent high blood pressure. Thus, the level of blood pressure is related to body size and the change in blood pressure to the change in body size, suggesting the close relation between adolescent blood pressure and physical development. In many cross-sectional and comparative crosssectional studies, adolescent blood pressure is reported to increase with age (16-20). In spite of the close relation between blood pressure and physical development, however, the trends of blood pressure in these studies were determined by plotting blood pressure level, averaged across individuals, simply as a function of age without taking physical development into consideration. Therefore, the question of whether or not the blood pressure increase with age represents the actual blood pressure trend naturally arises because the degree of physical development and the age at spurt of physical development differ among individuals (21). To elucidate the blood pressure trend in view of individual degree and trend of physical development, we studied whether the entire blood pressure trend during adolescence in individuals can be expressed as Received for publication April 17, 1995, and accepted for publication October 25, 1995. Abbreviations: BMI, body mass index; DBP, diastolic blood pressure; SBP, systolic blood pressure; VEL, velocity of weight increase. 1 Department of Clinical Studies, Radiation Effects Research Foundation, Nagasaki, Japan. 2 Department of Statistics, Radiation Effects Research Foundation, Hiroshima, Japan. 3 The Third Department of Internal Medicine, Nagasaki University School of Medicine, Nagasaki, Japan. Reprint requests to Dr. Masazumi Akahoshi, Department of Clinical Studies, Fiadiation Effects Research Foundation, 8-6 Nakagawa 1-chome, Nagasaki 850, Japan. 51 52 Akahoshi et a). a function of weight, height, the BMI, and the velocity of the weight increase (VEL) as an index of weight increase in a longitudinal follow-up study. For this purpose, we selected subjects whose blood pressure, weight, and height had been measured annually from ages 10 to 18 years and determined the individual VEL for that period using the Gompertz growth model. We then investigated the relation of blood pressure to VEL, weight, height, BMI, and age individually and annually from age 10 to 18 years by randomcoefficient growth-curve analysis and determined the blood pressure trend using the prediction equation obtained. MATERIALS AND METHODS The subjects were 509 individuals born in Hiroshima or Nagasaki between August 6, 1945 (Hiroshima) (or August 9, 1945 (Nagasaki)), and May 31, 1946, who were considered to have suffered no effects of atomic bomb exposure because their mothers were not in the city at the time of the bombing. The subjects were examined at the Hiroshima or Nagasaki Radiation Effects Research Foundation (formerly the Atomic Bomb Casualty Commission) annually on or about their birthday starting at age 9 (1954 or 1955) up to age 18 (1963 or 1964). Only data from age 10, obtained after the subjects had become familiar with the site and the examination procedure, were used. Measurements of blood pressure, height, and weight were included in the examination. Standing height (m) was measured without stockings, and body weight (kg), with underwear. Blood pressure (mmHg) was measured with a standard mercury sphygmomanometer (left arm, subject sitting). One of two kinds of cuff was used depending on the size of the upper arm. The first Korotkoff phase was used for the systolic blood pressure (SBP). The following steps were taken at each examination to minimize the effects of the subject's emotional state and to obtain basal blood pressure with the subject in a relaxed state: 1. Subjects were transported to and from the clinic by automobile. 2. They were examined in the same, quiet outpatient clinic each time, after a sufficient period of sedentary waiting (at least 10-15 minutes after arrival). 3. Blood pressure was measured by a pediatrician with subjects in the sitting position after at least 5 minutes of rest. 4. The pediatrician assumed a calm attitude, which helped the subject to relax. Data for 422 subjects, who were examined four times or more during the 9-year period, were analyzed. STATISTICAL METHODS We used a double-exponential Gompertz model (table 1) for each of these 422 individuals to describe mean weight as a function of age (22). The growth dynamics of the model for a typical individual are shown in figure 1. The first and second derivatives of the resulting prediction equations were used to calculate the predicted velocity and acceleration of weight increase at each age of measurement and at the lagged ages. The nonlinear least squares procedure used to estimate weight as a function of age failed to converge for two individuals. Data for the remaining 420 individuals were used in random-coefficient growth-curve analyses (23) to relate SBP to VEL, weight, height, BMI, and chronologic age. Details for randomcoefficient growth-curve analyses are shown in the Appendix. Because random-coefficient growth-curve analysis fit 418 of the 420 subjects, the analysis was based on the data for 418 subjects. In figures 2-5, the correspondence between growth dynamics and change in SBP during adolescence is shown. The velocity and weight curves therein were obtained from data pooled across individuals within city by sex group. These pooled data were used in a nonlinear regression analysis that ignored dependence among within-individual observations to obtain a Gompertz growth curve that described growth for a typical individual in each group (figures 2-5). For our purposes, least squares nonlinear regression analyses by city and sex group were adequate. TABLE 1. Gompertz growth model* Growth w = ft + &-*** Velocity dw — Acceleration d2w — _ da1 _ -, Zero at a = - / the age of the maximum velocity of weight increase. Third derivative _ n _ Zeroes at a = (0.96 - ft^fe and a = (-0.96 the ages of maximum and minimum accelerations of weight increase. * w, weight; a, age. Am J Epidemiol Vol. 144, No. 1, 1996 Adolescent Growth and Blood Pressure 53 Hiroshima Female 10 12 14 16 111 Age (years) FIGURE 1. Weight (upper panel), velocity of weight Increase (middle panel), and acceleration of weight increase (lower panel) from ages 10 through 18 years for a typical Individual, as determined by the Gompertz growth model. The ages of the maximum velocity of weight increase and maximum and minimum accelerations of weight increase are shown. RESULTS Patterns of adolescent physical development and changes in SBP for typical individuals in each city by sex group are described by the equations in table 2. VEL at age minus 1.15 years, VEL (a — 1.15), was significantly positively related to SBP in each city by sex group (p ^ 0.01). The BMI was significantly related to SBP for males in Hiroshima (p - 0.0001) and nearly significant in Nagasaki (p = 0.06), but was not significant for females in either city (p = 0.84 and 0.13, respectively). SBP curves varied significantly with the city by sex group. Significant main effects of city (p = 0.0004) and sex (p = 0.0001) on SBP curves were found overall. The city effect was due primarily to the higher initial SBP in Nagasaki. The sex effect was due primarily to a difference in the initial SBP levels and to a difference in the effect of BMI on SBP (p = 0.0001). The effects of lagged VEL on SBP for Am J Epidemiol Vol. 144, No. 1, 1996 FIGURE 2. Trends in systolic blood pressure (SBP) (upper panel), velocity of weight increase (middle panel), and body mass index (lower panel) from ages 10 through 18 years for a typical Hiroshima female. The age of maximum velocity of weight increase is indicated. The SBP peaks approximately 1-2 years after the peak In velocity of weight increase. males and females differed only marginally (p = 0.06). The effect of VEL on changes in SBP during adolescence appears to be relatively consistent across the city-by-sex groups. The city-by-sex-interaction effects on the SBP curves were not significant (p > 0.23). The relation between SBP and VEL during adolescence is illustrated by the city-by-sex groups in figures 2-5. The ages at which maximum VEL occurred for a typical individual in each group are indicated. Because BMI also affects change in the SBP, although not significantly in females, the SBP peak is not exactly 1.15 years after the VEL peak; it is later than 1.15 years in males and in Hiroshima females because the coefficient for BMI is positive, whereas, it is earlier than 1.15 years in Nagasaki females because the coefficient is negative. In any case, SBP increases with VEL, peaks approximately 1-2 years after the peak of 54 Akahoshi et al. 12 14 Age ( years ) Age (years ) FIGURE 3. Trends in systolic blood pressure (SBP) (upper panel), velocity of weight increase (middle panel), and body mass index (tower panel) from ages 10 through 18 years for a typical Hiroshima male. The age of maximum velocity of weight increase is indicated. The SBP peaks approximately 1-2 years after the peak in velocity of weight increase. FIGURE 4. Trends In systolic blood pressure (SBP) (upper panel), velocity of weight increase (middle panel), and body mass index (lower panel) from ages 10 through 18 years for a typical Nagasaki female. The age of maximum velocity of weight increase Is Indicated. The SBP peaks approximately 1-2 years after the peak in velocity of weight Increase. VEL, and decreases thereafter. The decrease is greater in females than in males, but this merely reflects the influence of increasing BMI with age. Acceleration of weight increase was not significantly related to SBP, regardless of VEL. Thus, it appears that among the potential explanatory variables studied, VEL 1.15 years prior to and BMI at the time of examination are the most important factors related to changes in SBP during adolescence. consistent with the research results reported to date. A number of cross-sectional and comparative crosssectional studies have shown that in adolescence levels of weight and habitus are related to blood pressure levels (1-4, 16), that changes in weight or habitus are related to changes in blood pressure (7-14), but that height was not related to blood pressure when weight was taken into consideration (16, 24), and that age is not a determinant of blood pressure in adolescence even though blood pressure increases with age (7-11, 14). Puberty is an important factor when discussing blood pressure in adolescence. There is one report that blood pressure is unrelated to sexual maturation or menarche (25). However, Tell (26) reported that blood pressure in both sexes is underestimated at ages 11-12 and overestimated at ages 15-16 if age is not corrected DISCUSSION By evaluating the relation between SBP and VEL, weight, height, BMI, and age individually and annually for the ages of 10-18, we have shown for the first time that the entire SBP trend for this age period is expressible as an equation of VEL (a — 1.15) and BMI in males and VEL (a — 1.15) in females. This is Am J Epidemiol Vol. 144, No. 1, 1996 Adolescent Growth and Blood Pressure Nagasaki Male 21 20 it u 10 12 14 16 IS Age ( y e a r s ) FIGURE 5. Trends in systolic blood pressure (SBP) (upper pane)), velocity of weight Increase (middle panel), and body mass index (lower panel) from ages 10 through 18 years for a typical Nagasaki male. The age of maximum velocity of weight increase is indicated. The SBP peaks approximately 1-2 years after the peak In velocity of weight increase. for the sexual maturation stage. She recommended that developmental age, assessed by the sex-maturity ratings formulated by Tanner, rather than chronologic age, be used in epidemiologic studies of blood pressure in adolescence. Heredity also plays an important role in adolescent blood pressure inasmuch as children of parents with high blood pressure also have high blood pressure (27-29). Neither puberty nor parental blood pressure was included in die analysis reported here, but these factors should be included in future studies. Another important finding in our study is that SBP in adolescence does not increase linearly with age but rather has a convex curve with a peak approximately 1-2 years after the peak of VEL. Many studies have indicated that blood pressure in adolescence increases with chronologic age (6, 16, 17, 30-33). This result, however, comes mainly from cross-sectional studies Am J Epidemiol Vol. 144, No. 1, 1996 55 (6, 16, 32, 33) or comparative cross-sectional studies (17, 30, 31) in which SBP levels, averaged across individuals, were plotted as a function of age without taking physical development into consideration, in spite of the close relation between adolescent blood pressure and physical development. However, Voors et al. (4) reported the absence of an increase in SBP with age when height was adjusted. Prineas et al. (5) and Voors et al. (6) also reported that there is no relation between blood pressure and age when BMI and height are considered. Using the prediction equation obtained by evaluating the relation between SBP and physical development individually, we demonstrated for the first time that SBP in adolescence does not increase linearly with age but instead exhibits a convex curve. Because VEL contributed closely to the convex curve of SBP, the biologic significance of SBP trend observed in this study depends on the biologic significance of the VEL estimated by the Gompertz model. VEL for females was 1.0-2.0 kg/year at 10 years old, reached a maximum (5.0 kg/year) at 12.23 years old in Hiroshima and at 12.36 years in Nagasaki, and decreased to 1.0 kg/year at 18 years old. VEL for males was 0.5 kg/year at 10 years old, reached a maximum (6.0 kg/year) at 13.35 years old in Hiroshima and at 13.57 years old in Nagasaki, and decreased to 1.0-1.5 kg/year at 18 years old. These results did not differ from the trends of VEL reported to date: VEL for females was 2.0-3.0 kg/year at 10 years old, reached a maximum (5.0-6.0 kg/year) at 12.0-13.0 years old, and decreased to 1.0-2.0 kg/year at 18 years old; and VEL for males was 2.0 kg/year at 10 years old, reached a maximum (6.0-7.0 kg/year) at 14.0-14.5 years old, and decreased to 1.0 kg/year at 18 years old (34, 35). We consider, therefore, that the trends of both VEL and SBP in this study have biologic significance. Even if the SBP trend was determined in conjunction with physical development, we would not have obtained the present results if the raw data of SBP used for analysis had increased linearly with age. Shock (36), who measured the blood pressure of 50 boys and 50 girls semiannually from age 11.5 to 17.5 years, reported that SBP increased with age up to 14 years, but not from age 14 to 16.5 in boys, and that it decreased from age 14 to 15.5 in girls. His results are consistent with ours in that they show that SBP does not necessarily increase with age. Shock's study and ours differ from other studies reported in the literature in the following ways: 1) a fixed population was followed for a long period, 2) blood pressure always was measured at the same clinic, and 3) subjects were brought to the clinic by automobile. It is important to alleviate anxiety and to provide peace of mind when 56 Akahoshi et al. TABLE 2. Prediction equations for systolic blood pressure based on data from 10-18 year olds* Standard deviation Subjects Equation V E L ( a g e - 1.15) Hiroshima females (n = 148) Weight (kg) SBP (mm Hg) 24.20 + e 3 ^ 104.88 + 1.63 VELfage - 1.15) + 0.05(q) 0.26 0.23 Hiroshima males (n = 163) Weight (kg) SBP (mm Hg) 26.08 + a * 82.38 + 0.89 VEL{age - 1.15) + 1.40(q) 0.25 0.24 Nagasaki females (n = 50) Weight (kg) SBP (mm Hg) 24.48 + e ^ 3 113.62 + 1.67 VEL(age - 1.15) - 0.59(g) 0.45 0.39 Nagasaki males (n = 57) Weight (kg) SBP (mm Hg) 26.79 + e 3 - 5 3 - " - 0 4 " 8 * 92.70 + 1.07 VEL(age - 1.15) + 0.79(q) 0.42 0.41 • SBP, systolic blood pressure; VEL{age - 1.15), velocity of weight increase 1.15 years prior to examination; q, body mass index at the time of examination. measuring the blood pressure of children (18), and the conditions that exist prior to blood pressure measurement should be uniform in the population and cohort study. We believe that the facts that the subjects were familiar with the site and examination procedure and that physical activity before blood pressure measurement was calm and uniform also contributed to the reliability of the data obtained. The reported research results based on comparative cross-sectional studies have shown consistently that weight change is related to change in blood pressure; a weight increase is associated with a blood pressure increase and vice versa (7-14). Our results, however, showed that SBP decreased even when weight increased, a possibility suggested by results of the longitudinal follow-up program of the Muscatine Study in which 4,313 children were examined on three to six occasions between 1970 and 1981 (13). Values for blood pressure and body size (weight, relative weight, height, and triceps skinfold thickness) were expressed as percentile ranks, with a line describing changes in the percentiles over time being calculated and the slope of that line being defined as a trend. The authors found a correlation between the average blood pressure rank and average body size rank, as well as between the blood pressure trend and body size trend percentiles, and suggested the importance of the relative rate of growth in establishing the rank order of blood pressure. Although the authors did not discuss absolute values, the possibility exists that blood pressure decreases with the decrease in percentile rank of weight and that it exceeds the blood pressure increase associated with the weight increase in cases in which the absolute value of weight increases with age but the percentile weight rank decreases. Although not shown in Results, diastolic blood pressure (DBP) trends during adolescence could not be expressed as an equation of VEL and BMI in males and females in either city. In the present study, however, we encountered the following problem in DBP measurements. Although the difference between mean Korotkoff fourth phase (K4) and fifth phase (K5) DBP is from 6.5 to 9.2 mmHg depending on the age of children (37), from the beginning of the study it was left to the discretion of the pediatrician whether to use K4 or K5 as the indicator for DBP. It was reported recently that reliable and repeatable blood pressure measurements in childhood are best achieved with K5 as the indicator for DBP (37). Therefore, the evaluation of the relation between the entire DBP trend during adolescence and physical development are left for future studies using K5 as DBP. In conclusion, the evolution of SBP in adolescence, from 10 to 18 years of age, was determined from the velocity of weight increase 1.15 years prior to current measurement and the current BMI in males and by the velocity of weight increase 1.15 years prior to current measurement in females. In both sexes, SBP increased approximately 1-2 years after the peak in velocity of weight increase and decreased thereafter. ACKNOWLEDGMENTS This research was conducted at the Radiation Effects Research Foundation (RERF), Hiroshima and Nagasaki, Japan. RERF is a private foundation funded equally by the Japanese Ministry of Health and Welfare and the US Department of Energy through the National Academy of Sciences. Am J Epidemiol Vol. 144, No. 1, 1996 Adolescent Growth and Blood Pressure REFERENCES 1. Kotchen JM, Kotchen TA, Schwertman NC, et al. Blood pressure distributions of urban adolescents. Am J Hygiene 1974;99:315-24. 2. Lauer RM, Filer LJ Jr, Reiter MA, et al. Blood pressure, salt preference, salt threshold, and relative weight. Am J Dis Child 1976; 130:493-7. 3. Florey C du V, Uppal S, Lowy C. Relation between blood pressure, weight, and plasma sugar and serum insulin levels in schoolchildren aged 9-12 years in Westland, Holland. Br Med J 1976;1:1368-71. 4. Voors AW, Webber LS, Frerichs RR, et al. Body weight and body mass as determinants of basal blood pressure in children—the Bogalusa Heart Study. Am J Epidemiol 1977; 106:101-8. 5. Prineas RJ, Gillum RF, Horibe H, et al. The Minneapolis Children's Blood Pressure Study part 2: multiple determinants of children's blood pressure. Hypertension 1980;2(Suppl I):I25-8. 6. Voors AW, Foster TA, Frerichs RR, et al. Study of blood pressure in children, ages 5-14 years, in a total biracial community—the Bogalusa Heart Study. Circulation 1976;54: 319-27. 7. Miall WE, Bell RA, Lovell HG. Relation between change in blood pressure and weight. Br J Prev Soc Med 1968;22: 73-80. 8. Heyden S, Bartel AG, Hames CG, et al. Elevated blood pressure levels in adolescents, Evans County, Georgia, sevenyear follow-up of 30 patients and 30 controls. JAMA 1969; 209:1683-9. 9. Kuller LH, Crook M, Almes MI, et al. Dormont High School (Pittsburgh, Pennsylvania) blood pressure study. Hypertension 1980;2(Suppl I):I-109-16. 10. Visser MC, Grobbee DE, Hofman A. Determinants of rise in blood pressure in normotensive children. J Hypertens 1987;5: 367-70. 11. Clarke WR, Woolson RF, Lauer RM. Changes in ponderosity and blood pressure in childhood: the Muscatine Study. Am J Epidemiol 1986; 124:195-206. 12. Mahoney LT, Clarke WR, Burns TL, et al. Childhood predictors of high blood pressure. Am J Hypertens 1991 ;4: 6O8S-1OS. 13. Lauer RM, Clarke WR, Beaglehole R. Level, trend, and variability of blood pressure during childhood: the Muscatine Study. Circulation 1984;69:242-9. 14. Higgins MW, Keller JB, Metzner HL, et al. Studies of blood pressure in Tecumseh, Michigan. II. Antecedents in childhood of high blood pressure in young adults. Hypertension 1980; 2(SupplI):I-l 17-23. 15. Lauer RM, Burns TL, Clarke WR, et al. Childhood predictors of future blood pressure. Hypertension 1991 ;I8(Suppl I):I74-81. 16. Londe S. Blood pressure in children as determined under office conditions. Clin Pediatr 1966;5:71-8. 17. Zinner SH, Margolius HS, Rosner B, et al. Stability of blood pressure rank and urinary kallikrein concentration in childhood: an eight-year follow-up. Circulation 1978;58: 908-15. 18. Task force on blood pressure in children. Report of the second task force on blood pressure control in children. Pediatrics 1987,79:1-25. 19. Uhari M, Nuutinen EM, Turtinen J, et al. Blood pressure in children, adolescents and young adults. Ann Med 1991 ;23: 47-51. 20. Sanchez RG, Labarth DR, Forthofer RN, et al. National standards of blood pressure for children and adolescents in Spain: international comparisons. Int J Epidemiol 1992;21:478-87. 21. Tanner JM. Growth at adolescence. 2nd ed. London, England: Blackwell Scientific Publications, 1962. 22. Deming J. Application of the Gompertz curve to the observed pattern of growth in length of 48 individual boys and girls Am J Epidemiol Vol. 144, No. 1, 1996 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 57 during adolescent cycle of growth. Hum Biol 1957;29: 83-122. Vonesh EF, Carter RL. Efficient inference for randomcoefficient growth curve models with unbalanced data. Biometrics 1987;43:617-28. Hofman A, Valkenburg HA. Determinants of change in blood pressure during childhood. Am J Epidemiol 1983;117: 735-43. Londe S, Johanson A, Kronemer NS, et al. Blood pressure and puberty. J Pediatr 1975;87:896-9O0. Tell GS. Cardiovascular disease risk factors related to sexual maturation: the Oslo Youth Study. J Chron Dis 1985;38: 638-42. Beresford SAA, Holland WW. Levels of blood pressure in children: a family study. Proc R Soc Med 1973;66:1009-11. Brandao AP, BrandiSo AA, Araujo EM. The significance of physical development on the blood pressure curve of children between 6 and 9 years of age and its relationship with familial aggregation. J Hypertens 1989;7(Suppl I):S37-9. Grobbee DE. Predicting hypertension in childhood: value of blood pressure measurement and family history. J Am Coll Nutr 1992;ll:S55-9. Oberman A, Lane NE, Harlan WR, et al. Trends in systolic blood pressure in the thousand aviator cohort over a twentyfour-year period. Circulation 1967;36:812-22. Beaglehole R, Salmond CE, Eyles EF. A longitudinal study of blood pressure in Polynesian children. Am J Epidemiol 1977; 105:87-9. Szklo M. Epidemiologic patterns of blood pressure in children. Epidemiol Rev 1979; 1:143-69. de Man SA, Andre1 JL, Bachmann H, et al. Blood pressure in childhood: pooled findings of six European studies. J Hypertens 1991;9:109-14. Tanner JM. Use Aid abuse of growth standards. In: Falkner F, Tanner JM, eds. Human growth. Vol 3, 2nd ed. New York, NY: Plenum Press, 1986:95-109. Roche AF, Himes JH. Incremental growth charts. Am J Clin Nutr 1980;33:2041-52. Shock NW. Basal blood pressure and pulse rate in adolescents. Am J Dis Child 1944;68:16-24. Uhari M, Nuutinen M, Turtinen J, et al. Pulse sounds and measurement of diastolic blood pressure in children. Lancet 1991;338:159-61. APPENDIX The random-coefficient growth-curve model is a two-stage model. One stage describes responses (e.g., SBP) within an individual as a function of withinsubject covariates (e.g., velocity of weight increase and BMI), and the other relates the coefficients of the first stage to between-subject variables (e.g., city, sex). Written in general form, the two stages are = X.7; + eh (1) and (2) where y,- is the vector of repeated observations of the response variable from the j 0 1 individual; X,, the matrix of observations of the within-subject explanatory variables from the Ith individual; -y,, a column vector of coefficients that relates the response to the explanatory 58 Akahoshi et a). variables; y\, the row vector formed from y,\ Z'iy a row vector of observations of the between-subject explanatory variables; A, the matrix of the parameters that relate the random-coefficient vectors, y,., to the between-subject variables, Z,; and et, and £, are random-error variables. We assume that et are independently and identically distributed with a mean of 0 and a variance matrix of <x2/ and that £, are independently and identically distributed with a mean of 0 and a variance matrix of ip. The primary objective is to estimate A, the matrix of parameters that relate the mean of the random coefficients, yt, to the between subject covariates, Z,, by use of a two-stage estimation procedure. First, ordinary least-squares regressions of yt on X; are performed separately for each individual to estimate y, and of for each i. Then, a2 is estimated as a pooled estimate from &? and 4> from the individual estimates of y,. Next, A is estimated by the multivariate linear regression technique using & and \\i. The prediction equation for y{ is given by Si = x,A r z,, (3) Initially, single-variable random-coefficient growthcurve models are fitted. (See Equations 1 and 2 for the general definition of such models.) The X, matrices are formed by concatenating a column of ones with a column of weights, heights, BMIs, ages, VEL, and VEL evaluated at 8 lagged ages chosen to determine the best lag, 8. Of all the fits, the VEL evaluated at age minus 1.15 produced the smallest pooled estimate of a 2 (d-2 = 65.28); therefore, the VEL evaluated at age minus 1.15 years was used in Equation 1. We do not show the confidence interval of this lagged estimate because there is no goodness of fit statistic (e.g., likelihood) for our method. Random-coefficient models with two variables were fit next for six choices of X, formed by [1, VEL (a), q], [1, VEL (a - 1.15), q], [1, VEL (a - 1.15), h], [1, VEL (a - 1.15), w], [1, VEL (a - 1.15), a], and (1, a, a2), where 1 denotes a column of ones; VEL (x), a column of VEL values evaluated at x; q, a column of values of BMI; h, a column of heights; w, a column of weights; and a, a column of ages at which the Ith subject was observed. Models involving VEL (a — 1.15) all produced smaller pooled estimates for a2 than the two models without VEL (a - 1.15). The mean coefficient on VEL (a — 1.15) in each of these models was significant (p < 0.05) for each city by sex group, but the coefficient of the third variable was only significant in at least one city by sex group when the third variable was BMI. Further model fitting showed that no additional, fourth, variable was significant. We therefore fit the three-variable model with X, = [1, VEL (a - 1.15), q] in the final analysis. This model yielded d 2 = 59.19. Am J Epidemiol Vol. 144, No. 1, 1996