¹National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, USA

²National Cancer Institute, NIH, Bethesda, MD, USA

Correspondence to: K M Flegal, National Center for Health Statistics, 6525 Belcrest Rd., Room 900, Hyattsville, MD 20782, USA.kmf2@cdc.gov

BACKGROUND: National survey data show increases in mean body mass index (BMI) and in the prevalence of overweight and obesity for adults and children in the United States, indicating a change in the distribution of BMI.

OBJECTIVE: To apply graphical methods to describe changes in the distribution of BMI.

DESIGN: BMI values from the third National Health and Nutrition Examination Survey (NHANES III: 1988-94) were compared with data from earlier cross-sectional nationally representative surveys for adults 20-74 y of age and for children and adolescents 6-17 y of age. Tukey mean-difference plots were used to investigate the changes in the distributions of BMI within sex-age groups.

RESULTS: Mean-difference plots allow qualitative visual comparisons of the distributions of BMI between surveys. For all sex-age groups, there was increasing skewness with a greater shift in the upper part of the distribution so that, within each group, the heaviest subgroup was heavier in NHANES III than in prior surveys. For the youngest children, the lower part of the distribution showed virtually no change. With increasing age the whole distribution tended to shift upward slightly, suggesting an increase in BMI across the entire population.

CONCLUSIONS: These changes in the distribution of BMI suggest the combination of both profound environmental determinants and a population with a high degree of susceptibility. The reasons for the increasing prevalence of obesity should be sought in part by seeking to understand the factors causing increases in the population as a whole.

International Journal of Obesity (2000) 24, 807-818

adults; body weight; body mass index; children; health surveys; overweight; obesity; time trends; United States

Introduction

The prevalence of overweight and obesity have increased markedly in the United States for both children and adults.^1,2,3 National survey data show that between 1976-80 and 1988-94 the age-adjusted prevalence of obesity (body mass index (BMI) 30.0) increased by 8 percentage points, from 14.5% to 22.5%, in the US adult population ages 20-74 y. Mean levels of BMI also increased, from 25.3 to 26.5. The prevalence of overweight also increased markedly for children and adolescents in the United States over the same period. Before these observations, previous surveys had shown only slight increases from the 1960s to 1980 for both children and adults.^1,2,3

Little is known about the reasons for these increases in obesity in the population, although similar trends have been seen elsewhere in the world as well. Within a given population, these increases are likely to be responses to changes in environmental and social factors, rather than to genetic changes in the population or to the effects of immigration and emigration. As Rose has pointed out, increases in the prevalence of an elevated level of a characteristic such as blood pressure or BMI tend to be associated with shifts in the distribution of that characteristic in the entire population.^4,5,6

Several general models for the increase in the population prevalence of obesity are possible. One subgroup of the population may be heavier than the comparable subgroup in the past, with little change in the rest of the population. Or all subgroups of the population might be heavier than the comparable subgroups were previously. Because both these changes, as well as many other types of changes, would lead to increases both in the prevalence of overweight and in mean BMI, these increases do not in themselves show exactly what the underlying changes in the population distribution of BMI might be. The Rose model would suggest that increases in the prevalence of obesity are likely to be related to changes in the distribution of BMI in the population as a whole.

The objective of this paper is to apply graphical methods to investigate the changes in the distribution of BMI in the United States, using data from cross-sectional nationally representative health examination surveys. Because these comparisons are based on successive cross-sectional surveys, each of which examined a different sample of individuals, these increases over time do not show changes on an individual level. However, the differences in the distribution of BMI between two surveys can be examined.

Because we found no standard approach in the literature for comparing distributions of BMI, we reviewed a number of graphical methods. We selected Tukey mean-difference (m-d plots)⁷ to compare the distribution of BMI in NHANES III to the distribution of BMI in prior surveys for the same sex-age categories. Since these plots may be unfamiliar, we first describe the construction and use of m-d plots and give some examples. We then apply this method to data for the US population. We previously published some examples of m-d plots for a few selected age-sex groups for adults from the first phase of NHANES III (1988-91) and for children and adolescents.^3,8

Methods

NHANES III

The third National Health and Nutrition Examination Survey (NHANES III) was conducted from 1988 to 1994 by the National Center for Health Statistics (NCHS) of the Centers for Disease Control and Prevention. A nationally representative sample of the US civilian non-institutionalized population was selected using a complex, stratified, multistage probability cluster sampling design. Informed consent was obtained from all respondents and the protocol was reviewed and approved by the NCHS NHANES Institutional Review Board. A home interview was followed by a physical examination in a mobile examination center. A description of the plan and operation of the survey has been published.⁹

NHANES III is the most recent in a series of cross-sectional health examination surveys carried out by NCHS. Although each survey provides representative national data, different individuals are examined each time. In all surveys, weight and height were measured using standardized techniques and equipment.¹ Body mass index (BMI) was calculated as weight (kg) divided by the square of height (m). For adults, obesity was defined as a BMI value 30.0. For children and adolescents, overweight was defined as a BMI value equal to or greater than the preliminary month-of-age-and sex-specific 95th percentile values from the revision of the NCHS growth charts.

For adults aged 20-74 y, we compared the distribution of BMI in NHANES III with the distribution of BMI in the preceding survey, NHANES II, which was conducted from 1976 to 1980 using a similar design and similar methods. A description of that survey has also been published.¹⁰ In NHANES III there was no upper age limit. However, because for NHANES II, the upper age limit was 74 y, comparisons for adults are limited to the age range 20-74 y. Women who were pregnant at the time of the examination are excluded from these analyses. Unweighted sample sizes by sex and age group for adults are presented in Table 1.

For children and adolescents aged 6-17 y, we compared the distribution of BMI in NHANES III with the distribution of BMI in two earlier surveys in the series. Cycles II and III of the National Health Examination Survey (NHES II, 1963-65; NHES III, 1966-70). Descriptions of these surveys have also been published.^11,12 NHES II was limited to children aged 6-11 y and NHES III was limited to children and adolescents aged 12-17 y. Because the prevalence of overweight in these two earlier surveys was similar to that in NHANES II and because these surveys had large sample sizes for children and adolescents, these surveys were selected as the basis for comparison with children and adolescents from NHANES III. Unweighted sample sizes for children and adolescents are presented in Table 2. Pregnant girls aged 17 (n=15) in NHANES III were excluded from these analyses: pregnancy status was not available for younger girls or for earlier surveys.

Mean-difference plots

To examine the changes in the distribution of BMI, we used Tukey mean-difference plots (m-d plots) to compare the distributions from the two surveys.⁷ A mean-difference plot is a graphical method for comparing distributions that is related to the quantile-quantile (q-q) plot of Wilk and Gnanadesikan.⁷ For both types of plots, shifts in distributions are investigated by comparing corresponding quantiles (for example, percentiles) from two distributions. To construct a q-q plot, the quantiles from one distribution are graphed against the corresponding quantiles from the other distribution. To construct an m-d plot, the differences between the corresponding quantiles are graphed on the y axis against the means of the same quantiles on the x axis. The points on the plot represent the differences between two distributions at a given quantile level plotted against the means of the same quantile level from the two distributions. For example, if the value of the 40th percentile for one distribution was 21.5 and for the other distribution was 20.0, the plot would include a point for that percentile that showed the difference between the two values (1.5) plotted against the mean of the two values (20.75). If the two distributions were the same, the quantiles would be equal and the differences would all be zero. The location of the plotted point on the y axis shows the direction and magnitude of the shift. The shift is assessed by judging differences from the horizontal line representing zero.

Another graphical method sometimes used to compare distributions is a plot that shows the cumulative percent of the population from each distribution at each BMI value.^13,14,15 The information in a plot of cumulative distributions is similar to that contained in an m-d plot. However, the plot of cumulative distributions can be difficult to interpret and a clearer visual assessment of the type of shifts between the two distributions can often be derived from the m-d plot. The m-d plot shows the differences more explicitly than the cumulative distribution plot and is easier to assess visually because of the horizontal orientation. It also shows the numeric value of the shift more clearly.

Three simplified examples showing several types of possible differences between two distributions are presented in Figures 1, 2 and 3, along with the m-d plots and cumulative distribution plots corresponding to those differences. In the first example, both distributions have the same shape but the second distribution is shifted rightward (upward) by a constant amount relative to the first distribution (Figure 1). The constant shift appears in the m-d plot as a constant difference between percentiles of the two distributions. The amount of the constant shift can be read directly from the m-d plot axis.

The second example also shows two distributions (Figure 2). At the lower end, the two distributions are very similar and correspond closely, but at the upper end, one distribution is more skewed to the right than the other. In the corresponding m-d plot, the differences corresponding to the lower percentiles are close to zero, showing no shift of the distribution at the lower percentiles, and increase progressively at higher percentiles, showing the increasing skewness.

The third example (Figure 3) combines the features of the first and second examples. The second distribution, relative to the first, is both shifted upward and more skew. The corresponding m-d plot shows both the shift at lower percentiles and an increasing difference at upper percentiles indicating increased skewness as well.

These three figures provide schematic representations of three possible changes in the distribution of BMI, all of which would result both in an increased mean BMI and in an increase in the prevalence of obesity. These are presented simply as examples to show how m-d plots represent some specific changes between two distributions. Many other types of changes could also occur.

As a real-life example, a frequency distribution plot for men aged 40-49 y is presented in Figure 4 with the corresponding m-d plot and cumulative distribution plot. The frequency distribution is sensitive to the choice of intervals for the plots. In this example, the interval is 1 BMI unit. A wider interval would produce a smoother plot but lose detail and obscure some features of the distributions. A finer interval would produce a more detailed but more jagged plot. In contrast, the quantiles used for m-d plots are not affected by the choice of intervals. Although with smaller intervals between quantiles the number of points on the plot will increase, the value of any given point such as the 90th percentile is not affected by the choice of interval. As can be seen from this example and the preceding examples, in both the frequency distribution and the cumulative distribution plot, it is difficult to evaluate changes at the extremes of the distribution. It is also difficult to assess how constant or how variable the shift might be across the distributions. The m-d plot permits evaluation of both these features.

Data analysis and statistical methods

For adults, age was defined as age in years at the time of the household interview, which generally preceded the examination by 2-3 weeks. The age groups used were 20-29 y 30-39 y, 40-49 y, 50-59 y, 60-69 y and 70-74 y. For children and adolescents ages 6-17 y age was defined as age at the time of the examination. Single year of age groupings were used for children and adolescents because over this age range BMI increases with age and the BMI values for children of different ages are not directly comparable. In the age range 6-17 y, findings should be interpreted cautiously because the unweighted sample sizes for the NHANES III data are small, particularly for adolescents.

Statistical analyses were carried out using SAS and SUDAAN.^16,17 For each survey, sampling weights have been calculated that take into account the unequal probabilities of selection resulting from the sample design and from planned oversampling of certain subgroups. Confidence intervals were calculated using variance estimates that took into account the complex sample design of the surveys.

Weighted percentiles were calculated using the sampling weights. We calculated the even percentile values for each distribution (2nd, 4th, 6th percentile, etc., up to the 98th percentile). For each percentile level, we then calculated the mean of the corresponding percentile values from the two distributions and the difference between the corresponding percentile values from the two distributions, calculated as NHANES III minus the other survey. Each point on the plot represents the mean (on the x axis) and the difference (on the y axis) for an even percentile from the 2nd to the 98th percentile. Data were omitted from the m-d plots for one adolescent male age 14 y who had both a very high BMI (49.4) and a high sampling weight, making this single point unduly influential. For children and adolescents, analyses were repeated limiting the sample to white children and adolescents in NHES and to non-Hispanic white children and adolescents in NHANES III. The results were similar to those found including all race-ethnic groups (data not shown).

Results

Increases in mean BMI and the prevalence of obesity

For adults the increases in mean and median BMI and in the prevalence of obesity (BMI30.0) between the two surveys are shown in Table 3. For children and adolescents, the differences in mean and median BMI are presented in Table 4 by single year of age, and the differences in the prevalence of overweight are presented in Table 5 for broader age groups. For every age-sex group, both mean and median BMI and the prevalence of overweight or obesity were greater in NHANES III than in the previous survey, suggesting that for both children and adults the distribution of BMI values in NHANES III differs from previous surveys. For the changes in mean BMI and the changes in the prevalence of overweight, 95% confidence intervals generally did not include zero. For children and adolescents, the median BMIs were always greater in NHANES III than in NHES II/III although the confidence intervals generally included zero.

Mean-difference plots

M-d plots comparing the distribution of BMI in NHANES III with the distribution of BMI in NHES II are shown in Figure 5 by single year of age for children aged 6-11 y. The y-axis shows the value of the difference between corresponding percentiles of the two distributions and can be interpreted as showing the direction and distance of any shift between the distributions. The shape of the line formed by the points suggests the nature of the shift. These are qualitative graphical methods designed to summarize and display differences between two distributions. Because of this and because of the small sample sizes for some age groups the general patterns are more important than the individual details.

For 6-y-old children, both male and female, the m-d plots show that the distributions of BMI from the two surveys are virtually identical over most of the range. Most of the differences are very close to zero. However, at the upper (higher) end of the distribution, the differences begin to increase progressively until at the highest percentiles, the percentiles for NHANES III are 4-6 BMI units greater than the corresponding NHES II percentiles. These large differences show a marked upward shift and increased skewness at the upper end of the distribution, while most of the distribution is unchanged.

Although there are differences in detail, the patterns for children aged 6-11 y are broadly similar. Most of the plots suggest that the distributions of BMI in the two surveys have changed little if at all at the lower end, where the mean differences are close to and sometimes less than zero. However, at the upper end of the distribution all plots, except for 11-year-old girls, show a large difference of at least 2 BMI units and often much more. This shows pronounced increases in skewness with large shifts at the upper end of the distribution. Thus the changes in the distribution of BMI for children between NHES II and NHANES III are characterized by little or no difference at the lower end of the distribution, increasing skewness and large changes at the upper end of the distribution.

M-d plots comparing the distribution of BMI in NHANES III with the distribution of BMI in NHES III are shown in Figure 6 by single year of age for adolescents aged 12-17 y. Here again, the pattern is similar with little change at the lowest part of the distribution but strikingly large changes of 2-6 BMI units at the upper percentiles for most groups, except for girls aged 15 and 16 y.

M-d plots comparing the distribution of BMI in NHANES III with the distribution of BMI in NHANES II are shown in Figure 7 for men and women aged 20-74 y by 10 year age groups. Although the details differ between sex¾age groups, there are some broad similarities. In almost every case, the percentiles from NHANES III are greater than the corresponding percentiles from NHANES II. This shows that there is some upward shift in the distribution of BMI for every sex-age group. All age-sex groups also show greater differences in the upper portion of the distribution. This shows that there is also increased skewness in the distribution of BMI for every sex-age group. The magnitude of the differences varies from group to group. However, in most groups, the largest differences are approximately 3-4 BMI units and are seen at the highest percentiles of the distribution.

For younger men (aged 20-49 y), the differences at the lower end of the distribution are small (<1 BMI unit) and fairly constant. However, at the upper end of the distribution, the differences are much larger and are progressively greater at higher percentile levels. This pattern shows that, at these ages, there is a slight upward shift of the entire distribution and in addition a large increase at the upper end of the distribution, so that the distribution is also becoming more skewed.

For men in the older age ranges (50-74 y), the pattern is similar, but the degree of the shift is greater at lower levels and less at higher percentiles than for the younger age groups. This pattern suggests that for older men, the upward shift is stronger and the increased skewness at the upper end of the distribution is less than for younger men.

For women, the pattern is different. For most age groups of women, the differences increase steadily across percentiles. This shows that the entire distribution is shifting upward and becoming progressively more skewed at higher levels. Compared with men in the same age range, the shifts in the distribution for women are greater at lower percentiles for the age range 20-49 y.

Discussion

Increases in mean and median BMI and in the prevalence of BMI30.0 all show that the distribution of BMI for adults in NHANES III differs in some way from the distribution of BMI in NHANES II. Similar findings for mean and median BMI and the prevalence of BMI95th percentile also show that the distribution of BMI for children and adolescents in NHANES III differs from the distribution of BMI for the corresponding age-sex groups in NHES II and III. However, these findings do not in themselves give a complete picture of how the distributions of BMI have changed over time.

The changes in the distributions can be represented graphically by mean-difference plots. These graphical methods by their nature include a very large number of individual data points, as compared with summary statistics such as the mean or standard deviation. The purpose of these methods is not to focus closely on any given individual data point, but rather to depict graphically the overall differences in the two distributions. These methods are not suited, for instance, clearly to identify with certainty a particular value of BMI above which the distribution shifts. However, they can show broad qualitative differences between the distributions.

These plots show that for both adults and children, the distribution of BMI is becoming more skewed in all sex-age groups. The heaviest subgroup of the population is much heavier in NHANES III than was the heaviest subgroup in previous surveys. In addition, for adults, the entire distribution of BMI is shifted upward in NHANES III relative to NHANES II. However, these plots show that this is not a uniform shift across the whole distribution.

The degree of these changes in the distribution differs by age. For younger children and to some extent for adolescents, the lower portion of the distribution seems to be anchored with no substantive change over time. In these age groups, the principal effect is increased positive skewness at the upper part of the distribution. For younger men (aged 20-49 y) the principal change is also increased positive skewness at the upper part of the distribution, but there is in addition a slight upward shift that tends to be small and fairly consistent. The differences in the lower portion of the distribution are small (<1 BMI unit). For older men (aged 50-74 y). however, the upward shift is more pronounced and the shift at the upper end, indicating skewness, less pronounced. For women, there is a more gradual increase across the entire distribution, suggesting both an upward shift and increasing positive skewness.

Taken together, these observations suggest that for adults some factors causing increases in BMI are affecting the entire distribution of BMI, although the changes in the distribution of BMI are most marked at the upper end of the distributions. These plots show that for adults in all age-sex groups, almost the entire distribution of BMI appears to have shifted upward to some extent in NHANES III compared with the corresponding distributions in NHANES II. Thus these findings do not suggest that the increases in mean BMI and in the prevalence of BMI30.0 in NHANES III, relative to NHANES II, are due solely to the heaviest people in NHANES III being heavier than the heaviest people in NHANES II. For adults, there is no part of the distribution that is clearly unresponsive to the influences that are causing the population increase in BMI and the prevalence of obesity. For older men there is almost a complete shift of the distribution.

These findings suggest that the causes for the increase in obesity should be sought in part at the population level rather than focusing on individuals. From the perspective of individual behaviors, changes in physical activity, energy intake and smoking initiation or cessation may lead to changes in energy balance and thus to the increases in overweight and obesity. However, these changes in behaviors are likely to be related to social and environmental changes that may affect the whole population. According to Rose, to find the determinants of prevalence and incidence rates, we need to study characteristics of populations, not of individuals.⁴ The social and environmental causes of changes in BMI are unclear but might include increased availability of food, changes in food composition, changes in patterns of food intake, fewer opportunities for physical activity, increased use of labor-saving devices, changes in cigarette smoking, and perhaps also changes in cultural and social attitudes and values that might directly or indirectly affect body weight.^18,19,20

The changes observed in the US affect the population broadly enough that they appear unlikely to be due to the effects on the population of immigration and emigration. Nor are they likely to be due to trends in the race-ethnic composition of the US population. The increases in the prevalence of overweight are as large or larger for non-Hispanic white children and adults than for other subgroups.^1,2,3 When the analyses were repeated limiting the sample to white children and adults, the general findings were unchanged. These changes might represent either a differential response to changing environmental conditions, or a subset increasingly exposed to changing environmental conditions, or possibly some combination of differential exposure and differential response. These data do not permit these effects to be disentangled. However, these findings are not inconsistent with a gene-environment interaction effect. The factors that are causing the increase in obesity appear to operate broadly and have an effect on the distribution of BMI for almost the entire adult population, but to have a stronger effect on the upper portion of the distribution, suggesting there may be a subgroup of the population that is more susceptible to these influences. These data also broadly support Rose's suggestion that changes in the upper portion of the distribution reflect changes occurring in the whole distribution.⁵

This interpretation is less true for children, however. For children, particularly younger children, and to some extent also for adolescents and young men, the main effect appears to be on the upper part of the distribution of BMI. This suggests that, for these groups, the increase in prevalence is chiefly due to the heaviest individuals being heavier in NHANES III than were the heaviest individuals in earlier surveys. This is consistent with Price's findings for secular trends in overweight among young Danish inductees, in which BMI could be modeled as a mixture of distributions of a 'normal' and 'overweight' component.¹⁴ Secular trends in overweight among young Danish men could be explained by an increase in the proportion in the overweight component, with no change in the mean of either the normal or the overweight component, leading to the speculation that the increases in overweight might represent a differential response to environmental change, possibly mediated by genotype. Although methodological differences preclude exact comparisons, our findings for children, adolescents and young men, showing only small or no shifts in the lower part of the distribution but with a much larger shift in the upper portion of the distribution, are consistent with the notion of a differential response in these age groups. For older men, however, our data suggest a more uniform response affecting all portions of the distribution.

Many investigations of BMI phenotypes suggest that BMI can often be modeled as a mixture of several components, although findings about the number and characteristics of these components vary from study to study.^15,21,22 These shifts over time in the distributions of BMI, which appear to vary by sex and age, may affect such phenotypic comparisons of BMI and could make it more difficult to find stable models for these distributions.^23,24

Rose and Day examined cross-sectional data on blood pressure, BMI, alcohol intake and sodium intake from 52 populations in the Intersalt study and found that the distributions of most health related characteristics appeared to move up and down as a whole so that the population mean predicted the number of deviant individuals.⁵ In the case of BMI, however, the distributions of BMI in the populations with higher values were not only shifted upward but also tended to become more skewed.⁶ This increasing skewness is similar to that seen in the NHANES data for adults, where small increases in mean and median BMI values are accompanied by greater than expected increases in the prevalence of high values because of the increasing skewness.

Within a given population, differences in characteristics such as serum cholesterol probably reflect principally genetic variability with some effects of behavioral differences. However, the large differences seen between populations in characteristics such as serum cholesterol suggest profound effects of social and environmental determinants of such characteristics. The environment includes not just the physical environment, but also social and cultural forces affecting work, leisure, time allocation, food patterns and availability, psychological factors and many other determinants. These trends in BMI suggest the combination of both profound environmental determinants at work and a population with a high degree of susceptibility. Following the line of thought put forth by Rose,^4,5,6 this would imply that the reasons for the increasing prevalence of obesity should be sought not by comparing obese and non-obese individuals but rather by seeking to understand what factors are causing increases in the population as a whole. Interventions may need to focus on the population rather than solely on the heaviest individuals.

1 Kuczmarski RJ, Flegal KM, Campbell SM, Johnson CL. Increasing prevalence of overweight among US adults. The National Health and Nutrition Examination Surveys, 1960 to 1991. JAMA 1994; 272: 205-211. MEDLINE

2 Flegal KM, Carroll MD, Kuczmarski RJ, Johnson CL. Overweight and obesity in the United States: prevalence and trends, 1960-1994. Int J Obes Relat Metab Disord 1998; 22: 39-47. MEDLINE

3 Troiano RP, Flegal KM. Overweight children and adolescents: description, epidemiology, and demographics. Pediatrics 1998; 101: 497-504.

4 Rose G. Sick individuals and sick populations. Int J Epidemiol 1985; 14: 32-38. MEDLINE

5 Rose G, Day S. The population mean predicts the number of deviant individuals. BMJ 1990; 301: 1031-1034. MEDLINE

6 Rose G. Ancel Keys Lecture. Circulation 1991; 84: 1405-1409. MEDLINE

7 Cleveland WS. Visualizing Data. Hobart Press, Summit, NJ, 1993. ,

8 Flegal KM. Trends in body weight and overweight in the U.S. population. Nutr Rev 1996; 54: S97-S100. MEDLINE

9 National Center for Health Statistics. Plan and operation of the Third National Health and Nutrition Examination Survey, 1988-1994. Vital Health Stat 1 1994; 32: 1-405. MEDLINE

10 National Center for Health Statistics, McDowell A, Engel A, Massey JT, Maurer K. Plan and Operation of the Second National Health and Nutrition Examination Survey 1976-80. Vital Health Stat 1 1981; 15: 1-144.

11 National Center for Health Statistics. Plan and operation of a health examination survey of U.S. youths 12-17 years of age. Vital Health Stat 1 1969; 1: 1-80. MEDLINE

12 National Center for Health Statistics. Plan, operation, and response results of a program of children's examinations. Vital Health Stat 1 1967; 1: 1-56. MEDLINE

13 Hodge AM, Dowse GK, Toelupe P, Collins VR, Imo T, Zimmet PZ. Dramatic increase in the prevalence of obesity in western Samoa over the 13 year period 1978-1991. Int J Obes Relat Metab Disord 1994; 18: 419-428. MEDLINE

14 Price RA, Ness R, Sorensen TI. Changes in commingled body mass index distributions associated with secular trends in overweight among Danish young men. Am J Epidemiol 1991; 133: 501-510. MEDLINE

15 Price RA, Lunetta K, Ness R, Charles MA, Saad MF, Ravussin E, Bennett PH, Pettitt DJ, Knowler WC. Obesity in Pima Indians. Distribution characteristics and possible thresholds for genetic studies. Int J Obes Relat Metab Disord 1992; 16: 851-857. MEDLINE

16 SAS Institute Inc. SAS Procedures Guide, Version 6. 3rd edn. SAS Institute Inc. Cary, NC, 1990. ,

17 Shah BV, Barnwell BG, Bieler GS. SUDAAN User's Manual, Release 6.40. Research Triangle Institute: Research Triangle Park, NC, 1995. ,

18 James WPT. A public health approach to the problem of obesity. Int J Obes 1995; 19: (Suppl 3) S37-S45.

19 Prentice AM, Jebb SA. Obesity in Britain: gluttony or sloth? BMJ 1995; 311: 437-439. MEDLINE

20 Flegal KM, Troiano RP, Pamuk ER, Kuczmarski RJ, Campbell SM. The influence of smoking cessation on the prevalence of overweight in the United States. N Engl J Med 1995; 333: 1165-1170. MEDLINE

21 Mitchell LE, Nirmala A, Rice T, Reddy PC, Rao DC. Commingling analysis of adiposity in an Indian population. Int J Obes Relat Metab Disord 1994; 18: 1-8. MEDLINE

22 Moll PP, Burns TL, Lauer RM. The genetic and environmental sources of body mass index variability: the Muscatine Ponderosity Family Study. Am J Hum Genet 1991; 49: 1243-1255. MEDLINE

23 Price RA, Charles MA, Pettitt DJ, Knowler WC. Obesity in Pima Indians: genetic segregation analyses of body mass index complicated by temporal increases in obesity. Hum Biol 1994; 66: 251-274. MEDLINE

24 Price RA. Within birth cohort segregation analyses support recessive inheritance of body mass index in white and African-American families. Int J Obes Relat Metab Disord 1996; 20: 1044-1047. MEDLINE

Figure 1 Schematic representation of a constant rightward (upward) shift between two distributions. (a) Frequency distributions, (b) Corresponding m-d plot. (c) corresponding cumulative distribution plot.

Figure 2 Schematic representation of a change to increased skewness. (a) Frequency distributions. (b) Corresponding m-d plot, (c) Corresponding cumulative distribution plot.

Figure 3 Schematic representation of both a rightward shift and increased skewness. (a) Frequency distributions, (b) Corresponding m-d plot. (c) Corresponding cumulative distribution plot.

Figure 4 Example of frequency distributions from NHANES II and NHANES III for men aged 40-49 y. (a) Frequency distributions, (b) Corresponding m-d plot. (c) Corresponding cumulative distribution plot.

Figure 5 Mean-difference plots for the distribution of body mass index from NHES II and NHANES III, for children aged 6-11 y, by sex and age group. The 10th, 50th and 90th percentiles are marked by a + sign.

Figure 6 Mean-difference plots for the distribution of body mass index from NHES III and NHANES III, for adolescents aged 12-17 y, by sex and age group. The 10th, 50th and 90th percentiles are marked by a + sign.

Figure 7 Mean-difference plots for the distribution of body mass index from NHANES II and NHANES III, for adults aged 20-74 y, by sex and age group. The 10th, 50th and 90th percentiles are marked by a + sign.

Table 1 Sample sizes by sex, age and survey for adults aged 20-74 y

Table 2 Sample sizes by age, sex and survey for children and adolescents aged 6-17 y

Table 3 Increases in mean and median BMI and in the prevalence of obesity (BMI30.0) for adults aged 20-74 y. United States, 1976-80 to 1988-94

Table 4 Increases in mean and median BMI for children and adolescents aged 6-17 y. United States, 1963-70 to 1988-94

Table 5 Mean prevalence of overweight (BMI95th percentile) for children and adolescents aged 6-17 y. United States, 1963-70 to 1988-94