How Much Do Children s BMIs Change over Intervals of 6-12 Months? Statistics from Before and During the Obesity Epidemic

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1 This is the accepted version. For the 01published version, see Pediatric Obesity at How Much Do Children s BMIs Change over Intervals of -1 Months? Statistics from Before and During the Obesity Epidemic by Paul T. von Hippel (University of Texas, Austin) 1 Ramzi W. Nahhas (Wright State University) Stefan A. Czerwinski (Wright State University) 1 Corresponding author: LBJ School of Public Affairs, University of Texas at Austin, 1 Red River, Box Y, Austin, TX 1 (paulvonhippel@austin.utexas.edu), phone (1) -, fax (1) -0. Division of Morphological Sciences and Biostatistics, Lifespan Health Research Center, Department of Community Health, Boonshoft School of Medicine, Wright State University, 11 Research Boulevard, Kettering OH 0-01 (ramzi.nahhas@wright.edu). Division of Epidemiology, Lifespan Health Research Center, Department of Community Health, Boonshoft School of Medicine, Wright State University, 11 Research Boulevard, Kettering OH 0-01 (stefan.czerwinski@wright.edu). Running head: - and 1-month Change in BMI Keywords: BMI, obesity, overweight, increments, growth, change, sample size, power Abbreviations: BMI (body mass index), y (years), kg (kilograms), m (meters), lb (pounds), in (inches) Word count: 0 words excluding abstract, captions, and references. Financial disclosures: Nahhas and Czerwinski were supported by NIH grant R01- HD01. Conflict of interest: Nahhas and Czerwinski report grants from the National Institutes of Health during the conduct of the study. Von Hippel has nothing to disclose. Contributors: Von Hippel conceived the study and led the writing, Nahhas led the data analysis and Czerwinski was responsible for data acquisition. All authors participated in interpretation of the data, writing and final approval of the manuscript. Nahhas had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

2 What is already known about this subject Researchers need to anticipate and evaluate changes in children s BMI over periods of or 1 months, yet reference statistics are limited for change in BMI. It can be misleading to evaluate change in BMI over time using cross-sectional references designed to evaluate BMI at a particular age. What this study adds 1 We estimate the percentiles of - and 1-month BMI changes among two cohorts of children in the Fels Longitudinal Study: an older cohort born 1-10, and a recent cohort born Percentiles of BMI change are highly dispersed, especially for girls and especially in adolescence. Large BMI gains are common in adolescence, and BMI losses are not uncommon at any age. In the more recent cohort, the adiposity rebound is earlier and BMI gains are larger, especially at higher percentiles. 1 - and 1-month Change in BMI

3 Abstract Background. Researchers need to evaluate changes in children s BMI over periods of or 1 months, yet reference statistics are limited for change in BMI. Objectives. We aim to estimate the distribution of changes in children s BMI over periods of and 1-months. Methods. We analyze data on two cohorts of children in the Fels Longitudinal Study: an older cohort born 1-10, and a recent cohort born Between ages and 1y, we calculate changes in BMI over intervals of and 1 months. For each age, sex, and cohort, we estimate the mean, standard deviation, skewness, kurtosis, and percentiles of change in BMI. Results. Median BMI growth peaks around age 1-1y for girls and 1-1y for boys. Large BMI gains are common in adolescence, and BMI losses are not uncommon at any age. Percentiles of BMI change are quite dispersed, especially for girls and especially in adolescence. In the recent cohort, the adiposity rebound is earlier and BMI gains are larger, especially at the high percentiles. Conclusions. Researchers can use these estimates to evaluate data quality, evaluate effect sizes, and calculate the sample size needed to detect an effect. 1 - and 1-month Change in BMI

4 Introduction The epidemic of pediatric obesity has increased the importance of longitudinal studies estimating the impact of different environments and interventions on children s body mass index (BMI, kg/m ). Evaluations of the effects on BMI of influences such as school lunches, 1 physical education, or summer vacation often rely on estimates of change in BMI (hereafter ΔBMI) over periods of to 1 months. The design and interpretation of such studies depends on information about how quickly children s BMI changes at different ages. For example, researchers planning an intervention in middle school need to know how large an effect on ΔBMI could reasonably be expected, and how large a sample would be needed to detect an effect of the expected size. As another example, researchers working with new longitudinal data might first want to evaluate the data s quality by checking whether - and 1-month values of ΔBMI lay within plausible bounds. Data can contain implausible ΔBMI values if, for example, study protocols were inconsistent, study personnel made errors in data entry, or the scale used to measure children s weight was miscalibrated on one of the measurement occasions. All of these questions require statistics summarizing the distribution of - or 1-month ΔBMI values for children of different ages. Unfortunately, the availability of such statistics is limited. While percentiles of -, 1-, and -month change in height and weight have long been available for ages to 1y, similar percentiles for ΔBMI are lacking. It may seem tempting to estimate percentiles of ΔBMI by differencing the CDC s BMIfor-age percentiles (Figure 1), but unfortunately this does not work since the CDC s BMI-forage percentiles are derived from cross-sectional data. One cannot calculate the percentiles of - and 1-month Change in BMI 1

5 longitudinal ΔBMI by differencing the percentiles of cross-sectional BMI-for age. For example, between ages 1. and 1. y the median of ΔBMI, calculated from longitudinal data, is about 0 percent higher than the value one gets by differencing median BMI values from cross sections at age age 1. and age 1.. One problem with differencing percentiles is that children can change BMI-for-age percentile as they grow older; such changes are known as [per]centile crossing or decanalization. Figure 1 gives two examples of percentile crossing by superimposing on the CDC curves the BMI records of a boy and girl from the Fels Longitudinal Study (FLS). The girl falls from the 0 th to the 0 th percentile between ages and, while the boy hugs the 0 th percentile until age 1, then falls to the th percentile before returning to the 0 th percentile. Because of percentile crossing, the th percentile of ΔBMI, say, is not typically achieved by a child who starts at the th percentile of BMI-for-age and stays there. Instead, the th BMI percentile of ΔBMI is more likely to be achieved by a child whose BMI-for-age percentile rises from a lower percentile to a higher one. Figure 1 near here Another problematic way to evaluate changes in BMI is to use Figure 1 to convert BMI to an age- and sex-specific percentile rank (P BMI ) or a normally distributed Z score (Z BMI ), and then calculate the change scores ΔP BMI and ΔZ BMI. These are popular approaches, 1 but they have serious shortcomings. Compared to ΔBMI, the alternatives ΔP BMI and ΔZ BMI are relatively poor proxies for changes in body fat, 1 and studies using ΔP BMI and ΔZ BMI are less statistically powerful than studies using ΔBMI. ΔP BMI and ΔZ BMI are particularly insensitive to the BMI gains of overweight and obese children. The problem with ΔP BMI is that the BMI change associated with a ΔP BMI = gain in percentile rank changes as one moves up the BMI-for-age distribution. For example, while it is not uncommon to rise from P BMI =0 to P BM =0, it is less common to rise from P BM = to - and 1-month Change in BMI

6 P BM =, and it is impossible to rise from P BM = to P BM = because no percentile rank can exceed 0. Z BMI is also insensitive to the gains of high-bmi children, in part because turning the skewed variable BMI into the normal variable Z BMI requires a log or root transformation that pulls in the upper tail. To repeat an example from past research, 1 consider the different meanings that an change of Z BMI =1 can have for boys who grow from to inches between ages and 1y. To increase Z BMI from +1 to + requires a gain ΔBMI=.1 kg/m, or 1. kg (. lb), which is very unusual. But to decrease Z BMI from 0 to 1 requires a loss of only ΔBMI=1. kg/m, or 0. kg (0. lb), which is only a little out of the ordinary. In summary, reference statistics for ΔBMI are needed and cannot be reverse-engineered from reference values of BMI-for-age. Unfortunately, the available statistics on ΔBMI are quite limited. In this study, we start to fill the gap by giving percentiles of - and 1-month ΔBMI values for children aged y to 1y in a longitudinal study. We also show how those percentiles have changed between two cohorts: (1) a reference cohort 1 that grew up before the obesity epidemic began in the mid-10s and () a more recent cohort that was affected by the obesity epidemic. 1 Data and Methods To estimate ΔBMI at a variety of ages, we require accurate, closely spaced longitudinal BMI measurements that cover the whole of childhood and adolescence. Unfortunately, there are no nationally representative data that meet these criteria. Instead, we use data from the Fels Longitudinal Study (FLS), which since 1 has measured children s height and weight at -to- 1 month intervals throughout childhood. 1 A strength of the FLS is that height and weight are not self-reported, but measured by study personnel at regular intervals. The major limitation of - and 1-month Change in BMI

7 the FLS is that it is not nationally representative. Few FLS participants come from the bottom quintile of socioeconomic status, and percent of participants are non-hispanic whites (nonwhite participants were excluded from the analyses in this paper). 1 1 percent of current FLS participants live in three southwest Ohio counties near FLS headquarters; these counties are of course not nationally representative, but they are close to the national average for adult obesity prevalence. 1 As in the national population, in the FLS the distribution of BMI has shifted upward in recent years as participants were affected by the obesity epidemic. 1 In this study we analyze two FLS cohorts. One cohort was born 1-10 and measured from 1 to 1; this cohort corresponds roughly to the pre-obesity reference population whose measurements, taken between 1 and 10, were used by the CDC to construct standards of BMI-for-age. The other cohort is more contemporary; its members were born 11-1 and spent at least part of their childhood in the obesity epidemic that started in the 10s. 1 We excluded FLS children born after 1 because they did not yet have longitudinal data through age 1y. We also excluded measurements taken before age y, because they used recumbent length, which exceeds standing height and therefore yields too small a value for BMI. Table 1 gives the number of boys and girls in each cohort, as well as the number of measurements of BMI, 1-month BMI, and -month BMI. The number of measurements per child is smaller in the more recent cohort, especially for -month BMI. The reason for this is changes in the FLS examination schedule. In the earlier cohort, FLS participants were measured every months, on their birthday and half-birthday, until age 1. In the more recent cohort, however, -month measurements were only taken before age y and during puberty (ages - 1y for boys and -1y for girls); at other ages, measurements were only taken at intervals of 1 months. - and 1-month Change in BMI

8 We differenced each participant s BMI series at intervals of 1 months and months (where available) to obtain annual and semiannual values of ΔBMI. Because some measurement dates did not coincide with children s birthday or half birthday, there was some variation in the intervals between measurements. Increments based on measurements taken at an interval that deviated by more than 1% of the target interval were excluded. Thus, annual increments had time intervals of 0. to 1.1 y, with a mean increment of 0. y, and semiannual increments had intervals of 0. to 0. y, with a mean of 0.00 y. Numbers of children and increments are shown in Table 1. We filled in missing ΔBMI values using a multiple imputation procedure 0 that replaced each missing value of ΔBMI with 0 residually normal values randomly generated by a longitudinal imputation model fit to the observed data. (Compared to the distribution of BMI, the conditional distribution of ΔBMI given age is much closer to normal.) Model fitting and multiple imputation were performed separately by sex and cohort, using the MIXED and MI procedures in SAS version.. After imputation, we estimated the distribution of ΔBMI. The distribution of BMI is commonly estimated using the LMS method, 1 but the LMS is limited to positive variables, whereas ΔBMI can be negative. We therefore estimated the distribution of ΔBMI using the flexible Johnson S u (JSU) distribution, whose parameters correspond to the mean (positive or negative), standard deviation, skewness, and kurtosis. Each parameter could be held constant or permitted to vary as a smooth (penalized B-spline) function of age. The decision whether to let a parameter vary with age was made by evaluating model fit using the GAIC() criterion. The age-varying distribution of ΔBMI was estimated separately for each sex and cohort, using the GAMLSS package in R. - and 1-month Change in BMI

9 Results Tables A1-A in the Appendix give the mean, standard deviation, skew, and kurtosis of ΔBMI, as estimated by our statistical model, for each age, sex, and cohort. The skew and kurtosis are generally positive; however, there is much less skew in ΔBMI than in BMI, and less skew in -month ΔBMI than in 1-month BMI. Tables A-A in the Appendix give the estimated percentiles of ΔBMI, which are also summarized in Figures and. We discuss the 1-month percentiles first, and then the -month percentiles. 1-month increments The 1-month ΔBMI percentiles are quite dispersed. They are more dispersed for girls than for boys, and more dispersed in adolescence than in childhood. Between age y and age 1y in the earlier cohort, the interquartile range (IQR) grows from 0. to 1.0 kg/m among boys, and from 0. to 1. kg/m among girls. Large BMI gains are common, especially in adolescence, but also at younger ages. In both cohorts and both sexes, the 0 th percentile of ΔBMI exceeds 1.0 kg/m by age y. However, BMI losses are common as well; in both cohorts and sexes, the 1 th percentile is negative at every age. Figure near here It bears repeating that the ΔBMI percentiles in Figure are much more dispersed than we would guess if we mistook the BMI-for-age curves in Figure 1 for a record of individual growth. A misinterpretation of Figure 1 would leave the impression that BMI losses are almost unheard of after age y, and that BMI gains rarely exceed 1.0 BMI unit in 1 months. That impression would be incorrect, as Figure shows. - and 1-month Change in BMI

10 There are differences between the later cohort, which grew up during the obesity epidemic, and the earlier cohort, which did not. The most obvious difference is that the later cohort typically has larger BMI gains. On average, the 1-month ΔBMI percentiles of the later cohort are about 0.1 kg/m above those of the earlier cohort. Among boys, the difference between the earlier and later cohorts is largest before age y; among girls, the difference between cohorts is similar at all ages. As is the case for the BMI distribution, in the ΔBMI distribution the increase associated with the obesity epidemic has been greatest at the higher percentiles. Among both boys and girls, the 0 th percentile of 1-month ΔBMI is on average 0. kg/m higher in the later cohort than in the earlier cohort. But the th percentile for girls is approximately the same in both cohorts, and the th percentile for boys is actually 0.1 kg/m lower, on average, in the later cohort than in the earlier cohort. Thus, the percentiles in the later cohort are more dispersed. A final difference between the cohorts is that the later cohort displays an earlier adiposity rebound. The adiposity rebound is a transition from BMI losses to BMI gains which, if it occurs at too young an age, may lead to obesity. In the earlier cohort of the FLS, the median of ΔBMI transitions from negative to positive at age.0y for boys and.y for girls. In the later cohort, the same transition takes place about months earlier. After the adiposity rebound, median ΔBMI increases, peaking around ages 1-1y for boys and 1-1y for girls in both cohorts. Among boys, the age when median ΔBMI peaks coincides with the median age of peak height velocity. Among girls, the age when median ΔBMI peaks is about a year later than the median age of peak height velocity and coincides with the median age at menarche. After the peak of ΔBMI, the deceleration of ΔBMI is steeper for girls than it is for boys. - and 1-month Change in BMI

11 -month increments Compared to the upper percentiles of 1-month BMI, the upper percentiles of -month BMI are less extreme on an absolute basis, but more extreme on an annualized basis. For example, in the earlier cohort, the 0 th percentile for girls ΔBMI peaks at.0 kg/m over 1 months but only 1. kg/m over months. On an annualized basis, however, the 0 th percentile of -month ΔBMI is. kg/m, which is greater than the 0 th percentile of 1-month ΔBMI. Evidently, faster rates of growth occur over months than can be sustained over 1 months. One possible reason for this is accelerated BMI growth during summer vacation. Figure near here Aside from its magnitude, the distribution of -month ΔBMI is similar to that of 1- month ΔBMI. Specifically, the adiposity rebound and the peak of growth occur around the same ages in the -month charts as in the 1-month charts. And as is the case for 1-month ΔBMI, for -month ΔBMI the upper percentiles are higher in the later cohort, but the lower percentiles are not. For example, the 0 th percentile of -month ΔBMI is, on average, 0.1 kg/m higher in the later cohort than in the earlier cohort; however, the th percentiles are, on average, 0.0 kg/m lower in the later cohort than in the earlier cohort. 1 Discussion Research on child obesity often uses longitudinal data on BMI. Yet researchers often lack key information about what to expect regarding BMI gains and losses at different ages. Context is vital, and our study provides context by summarizing the distributions of semiannual and annual change in BMI for two cohorts of children in the FLS. - and 1-month Change in BMI

12 The FLS is not nationally representative, so our analyses should be replicated in other longitudinal datasets to find out which results are typical and which are peculiar to the FLS. At present, published summaries of ΔBMI from other longitudinal studies are limited to specific percentiles and ages. For example, one article gives the median of ΔBMI for children ages - 1y in the Growing Up Today Study (GUTS). The GUTS children, who are the offspring of women who participated in the Nurses Health Study, are somewhat socioeconomically advantaged, % non-hispanic white, and born in the 10s in other words, they are similar to our recent cohort from the FLS. The two studies give fairly similar values for median ΔBMI. Among boys, the median ΔBMI in the GUTS is, on average, 0.0 kg/m below the median ΔBMI in the recent FLS cohort. Among girls, median ΔBMI in the GUTS is, on average, 0.1 kg/m below median ΔBMI in the recent FLS cohort. Our statistics on BMI have several uses. First, they can be used to evaluate data quality. The CDC and WHO have defined standards for flagging biologically implausible BMI values that suggest mismeasurement or errors in data entry. Standards of biological plausibility are cross-sectional in that they compare observed BMI values with the cross-sectional distribution of BMI-for-age. Longitudinal standards of ΔBMI provide additional value since a child s BMI may be biologically plausible at one age, and still plausible to 1 months later yet the ΔBMI between those two measurements may be implausibly large. Implausible values of ΔBMI can result from one-time errors in individual measurements, or they can result from systematic errors due to changes in equipment, calibration, or protocols from one measurement occasion to the next. Another use of our ΔBMI percentiles is to interpret effect size. An intervention with an effect size similar to the IQR of ΔBMI might be viewed as very effective, since an effect of that size implies that children whose ΔBMI who would otherwise have been at the th ΔBMI - and 1-month Change in BMI

13 percentile were brought down to the th percentile by treatment. For example, the most recent Cochrane review of child obesity prevention found that, among interventions targeting adolescents (typically lasting less than 1 months), the largest effect achieved was -1. kg/m which is impressive because it exceeds the IQR of 1-month ΔBMI for 1-year-old girls (1. kg/m ) and boys (1. kg/m ) in our more recent cohort. By contrast, the average effect size for adolescent obesity interventions, converted to the ΔBMI scale, was much smaller, at -0. kg/m. A final use of our ΔBMI statistics is to calculate the number of trial participants needed to detect an effect of a given size. For example, suppose we were designing a trial for an adolescent obesity intervention which we hoped would have an effect of at least -0. kg/m in months. Looking at Table A we see that the standard deviation of -month ΔBMI is approximately 0. kg/m for adolescent boys and girls in the recent cohort. If we want a balanced trial with 0% power to detect an effect of -0. kg/m with a two-tailed 0.0 significance test, then a simple calculation 0 shows that we would need approximately 00 subjects, 0 in the treatment arm and 0 in the control arm. Similar calculations can be carried out to calculate the sample size required for different effect sizes and different trial designs. 1 Acknowledgments We thank the participants of the Fels Longitudinal Study, as well as the data collection and management staff at the Lifespan Health Research Center, without whom this research would be impossible. This study was supported in part by NIH (R01-HD01). - and 1-month Change in BMI

14 Reference List Schanzenbach DW. Do School Lunches Contribute to Childhood Obesity? J. Hum. Resour. 00;():-0.. Datar A, Sturm R. Physical education in elementary school and body mass index: Evidence from the Early Childhood Longitudinal Study. Am. J. Public Health 00;(): Von Hippel PT, Powell B, Downey DB, Rowland N. The effect of school on overweight in childhood: Gain in body mass index during the school year and during summer vacation. Am. J. Public Health 00;():-0.. Berkey CS, Reed RB, Valadian I. Longitudinal growth standards for preschool children. Ann. Hum. Biol. 1;(1):-. doi:.0/ Berkey CS, Dockery DW, Wang X, Wypij D, Ferris Jr. B. Longitudinal height velocity standards for U.S. adolescents. Stat. Med. 1;1(-):0-1. doi:.0/sim.01.. Tanner JM, Davies PSW. Clinical longitudinal standards for height and height velocity for North American children. J. Pediatr. 1;():1-. doi:1/s00-() Kuczmarski RJ, Ogden CL, Grummer-Strawn LM, et al. CDC growth charts: United States. Adv. Data 000;(1):, 1.. Berkey C, Colditz G. Adiposity in Adolescents: Change in Actual BMI Works Better Than Change in BMI z Score for Longitudinal Studies. Ann. Epidemiol. 00;1(1):-0. doi:.1/j.annepidem Cole TJ. Children grow and horses race: is the adiposity rebound a critical period for later obesity? BMC Pediatr. 00;:-. doi:./ Li J, Park WJ, Roche AF. Decanalization of weight and stature during childhood and adolescence. Am. J. Hum. Biol. 1;():1 -.. Hollar D, Messiah SE, Lopez-Mitnik G, Hollar TL, Almon M, Agatston AS. Effect of a Two-Year Obesity Prevention Intervention on Percentile Changes in Body Mass Index and Academic Performance in Low-Income Elementary School Children. Am. J. Public Health 0;0():-. 1. Robbins JM, Khan KS, Lisi LM, Robbins SW, Michel SH, Torcato BR. Overweight Among Young Children in the Philadelphia Health Care Centers: Incidence and Prevalence. Arch Pediatr Adolesc Med 00;11(1):1-0. doi:.01/archpedi and 1-month Change in BMI

15 Economos CD, Hyatt RR, Goldberg JP, et al. A Community Intervention Reduces BMI z- score in Children: Shape Up Somerville First Year Results[ast]. Obesity 00;1(): Kring SII, Heitmann BL. Fiber Intake, Not Dietary Energy Density, Is Associated with Subsequent Change in BMI z-score among Sub-Groups of Children. Obes. Facts 00;1():-. doi:./ Campbell K, Andrianopoulos N, Hesketh K, et al. Parental use of restrictive feeding practices and child BMI z-score. A -year prospective cohort study. Appetite 0;(1):-. doi:.1/j.appet Cole TJ, Faith MS, Pietrobelli A, Heo M. What is the best measure of adiposity change in growing children: BMI, BMI %, BMI z-score or BMI centile? Eur J Clin Nutr 00;(): Wang Y, Beydoun MA. The Obesity Epidemic in the United States Gender, Age, Socioeconomic, Racial/Ethnic, and Geographic Characteristics: A Systematic Review and Meta-Regression Analysis. Epidemiol. Rev. 00;(1):-. doi:./epirev/mxm Roche AF. Growth, Maturation, and Body Composition: The Fels Longitudinal Study Cambridge University Press; Von Hippel PT, Nahhas RW. Extending the history of child obesity in the United States: The Fels Longitudinal Study, birth years Obesity 01;1():1 1. doi:.0/oby Rubin DB. Multiple Imputation for Nonresponse in Surveys. New York: Wiley; Cole TJ. The LMS method for constructing normalized growth standards. Eur. J. Clin. Nutr. 10;(1):-0.. Johnson NL. Systems of Frequency Curves Generated by Methods of Translation. Biometrika 1;(1/):1. doi:.0/.. Rigby RA, Stasinopoulos DM. Automatic smoothing parameter selection in GAMLSS with an application to centile estimation. Stat. Methods Med. Res. 01:0010. doi:./ Flegal KM, Troiano RP. Changes in the distribution of body mass index of adults and children in the US population. Publ. Online 0 July 000 Doisjijo ;(). doi:./sj.ijo Berkey CS, Rockett HRH, Field AE, et al. Activity, Dietary Intake, and Weight Changes in a Longitudinal Study of Preadolescent and Adolescent Boys and Girls. Pediatrics 000;():e-e. - and 1-month Change in BMI 1

16 Centers for Disease Control and Prevention. A SAS Program for the CDC Growth Charts. 0. Available at: Accessed July 1, 0.. World Health Organization. Physical status: the use and interpretation of anthropometry. Report of a WHO Expert Committee. No.. Tech. Rep. Ser. 1;. Available at: Accessed April, 0.. Centers for Disease Control and Prevention. Cut-offs to define outliers in the 000 CDC Growth Charts. 0. Available at: Waters E, de Silva-Sanigorski A, Burford BJ, et al. Interventions for preventing obesity in children. In: Cochrane Database of Systematic Reviews. John Wiley & Sons, Ltd; 01. Available at: Accessed October 1, Lachin JM. Introduction to sample size determination and power analysis for clinical trials. Control. Clin. Trials 11;():-. doi:.1/01-(1) and 1-month Change in BMI 1

17 Tables Table 1. Sample sizes in two cohorts of FLS participants with at least one m increment or at least one 1m increment Variable Birth years Sex Children Measurements BMI 1-10 Female 1 0 Male Female 1 1 Male month ΔBMI 1-10 Female 1 Male Female Male month ΔBMI 1-10 Female 1 0 Male Female 1 Male 1 - and 1-month Change in BMI 1

18 Appendix

19 Table A1. Smoothed parameters of the distribution of annual BMI increments, children born Boys Girls Age (y) Standard Standard Mean Skewness Kurtosis Mean Skewness deviation deviation Kurtosis.0 to to to to to to to to to to to to to to to to to to to to to to to to to to to to to Note. The normal distribution would have a skew and kurtosis of 0.

20 Table A. Smoothed parameters of the distribution of annual BMI increments, children born Age (y) Mean Standard deviation Boys Skewness Kurtosis Mean Standard deviation Girls Skewness Kurtosis.0 to to to to to to to to to to to to to to to to to to to to to to to to to to to to to

21 Table A. Smoothed parameters of the distribution of semiannual BMI increments, children born Age (y) Mean Standard deviation Boys Skewness Kurtosis Mean Standard deviation Girls Skewness Kurtosis.0 to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to

22 Table A. Smoothed parameters of the distribution of semiannual BMI increments, children born Age (y) Mean Standard deviation Boys Skewness Kurtosis Mean Standard deviation Girls Skewness Kurtosis.0 to to to to to.. to.0.0 to.. to.0.0 to.. to.0.0 to to to to to to to to to to to to to to to to Note. Due to changes in the FLS study designed frequency of visits after age y, there was insufficient data to estimate semiannual increments at pre- and post-pubertal ages.

23 Table A. Smoothed percentiles of annual BMI increments, children born 1-10 (see Figure, top panel) Age (y) Boys Girls th 1 th th 0 th th th 0 th th 1 th th 0 th th th 0 th.0 to to to to to to to to to to to to to to to to to to to to to to to to to to to to to

24 Table A. Smoothed percentiles of annual BMI increments, children born 11-1 (see Figure, bottom panel) Age (y) Boys Girls th 1 th th 0 th th th 0 th th 1 th th 0 th th th 0 th.0 to to to to to to to to to to to to to to to to to to to to to to to to to to to to to

25 Table A. Smoothed percentiles of semiannual BMI increments, children born 1-10 (see Figure, top panel) Age (y) Boys Girls th 1 th th 0 th th th 0 th th 1 th th 0 th th th 0 th.0 to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to

26 Table A. Smoothed percentiles of semiannual BMI increments, children born 11-1 (see Figure, bottom panel). Age (y) Boys th 1 th th 0 th th th 0 th th 1 th th 0 th th th 0 th Girls.0 to to to to to.. to.0.0 to.. to.0.0 to.. to.0.0 to to to to to to to to to to to to to to to to