Does Body Mass Index Adequately Capture the Relation of Body Composition and Body Size to Health Outcomes?

American Journal of Epidemiology Copyright 1998 by The Johns Hopkins University School of Hygiene and Public Health All rights reserved Vol. 147, No. 2 Printed in U.S.A A BRIEF ORIGINAL CONTRIBUTION Does Body Mass Index Adequately Capture the Relation of Body Composition and Body Size to Health Outcomes? Karin B. Michels, 12 Sander Greenland, 3 and Bernard A. Rosner 1-4 Body mass index () has become the most commonly used index of body composition in epidemiologic research. It has displaced weight, height, and other measures of body composition. In this paper, the authors show that use of alone does not always capture adequately the joint relation of body composition and body size to health outcomes, and that such use often represents implausible restrictions on the relation. Use of body mass index and height or weight and height will often be needed to describe this relation and to control confounding by these variables. Am J Epidemiol 1998; 147:167-72 anthropometry; body mass index; ponderal index The most commonly used measure of anthropometric variables in epidemiologic studies is the body mass index ( or Quetelet index), defined as weight/ height 2 (kg/m 2 ). One rationale for the use of this index is that it is supposed to be closely correlated with tissue density, which in turn is supposed to be closely correlated with percent fat in body tissues (adiposity) (1). Another rationale is that tends to be approximately uncorrelated with height; in contrast, height is highly correlated with weight, as well as with most other proposed obesity indices (1, 2). (Independence from height may facilitate comparisons across individuals.) It is often important to control for possible effects of anthropometric variables in assessing exposuredisease relations (1). For example, in studying risk factors for high blood pressure, obesity (excessive body fat) is one of the most powerful predictors of blood pressure. Because is often thought to be an adequate measure of adiposity, and weight and height are usually the only anthropometric measurements Received for publication July 14, 1997, and accepted for publication August 27, 1997. Abbreviation:, body mass index. 1 Channing Laboratory, Harvard Medical School, and Department of Medicine, Brigham and Women's Hospital, Boston, MA. 2 Department of Epidemiology, Harvard School of Public Health, Boston, MA. 3 Department of Epidemiology, UCLA School of Public Health, Los Angeles, CA. 4 Department of Biostatistics, Harvard School of Public Health, Boston, MA. Reprint requests to Dr. Karin Michels, Channing Laboratory, 181 Longwood Avenue, Boston, MA 02. available, is routinely used as a covariate in studies of blood pressure. Indices of body fat or obesity for use in epidemiologic analyses have been explored in several studies (2-5). For example, Criqui et al. (2) considered several possible measures of adiposity for use in cardiovascular disease epidemiology, including weight/height, weight/height 2, ^weight/height, height/ ^weight, and relative weight (observed weight divided by a standard weight for that sex and age). The correlation between each of these measures and height was considered in their data, and it was found that only and relative weight were approximately uncorrelated with height. In addition, among all the indices considered, and relative weight were most strongly correlated with standard cardiovascular disease risk factors such as blood pressure and lipid levels. Based on their findings, Criqui et al. recommended as a measure of adiposity in cardiovascular disease epidemiology. Unfortunately, an implicit assumption made in many epidemiologic analyses is that alone is a sufficient measure of anthropometric effects in regression analyses. This is not necessarily true, however; whether alone adequately captures the effect of anthropometric variables on health outcomes depends on many factors. In particular, although may capture most of the information on body composition contained in weight and height, it does not capture information on body size. In this paper, we argue that alone is often an inadequate anthropometric variable, and a measure of body size (such as height) is 167

168 Michels et al. often needed as well. We illustrate this issue with data concerning the relation of weight and height to blood pressure among adolescents. To predict variation in mean systolic blood pressure, one might consider the following normal linear regression model: AN EXAMPLE: BLOOD PRESSURE IN ADOLESCENT GIRLS Data from the Pediatric Task Force Data Base (6) comprise clinical and anthropometric measurements obtained in 11 large epidemiologic studies conducted in the United States during the 1970s and 1980s (for a description of the methods of blood pressure measurement, see reference 6). To simplify our illustration, we restrict our analyses to 3,543 white 13-year-old girls, the largest subgroup homogenous in sex, race, and age. Systolic blood pressures for this subgroup were available from eight of the studies in the database. Among children of a given age, sex, and race, the strongest predictors of blood pressure are weight and height. Therefore, no other covariates were considered in our analyses. Table 1 shows mean levels of systolic blood pressure within evenly spaced categories of weight and height. With some exceptions (chiefly due to unstable means), mean blood pressure levels increased with increasing weight and increasing height. The height-blood pressure relation was stronger for girls of lower weight. y, = /3,height, 2weight, where + /3 2 height, X weight, 4- e it y, = systolic blood pressure for person i, s ki = 1 if person i is in study k, - 0 otherwise, k = 1,..., 8, height, = height for subject i, minus mean height, in units of 10 cm, weight, = weight for subject i, minus mean weight, in units of 20 kg, and the e, are Gaussian with mean zero and unknown variance. To obtain results interpretable in terms of body composition, however, some analysts would replace all weight and height variables by : k=l e h TABLE 1. Mean body mass index () (in kg/m*) and systolic blood pressure (SBP) (in mmhg) by categories of weight and height among 3,543 white 13-year-old girls (number of girls in parentheses): data from the Pediatric Task Force Data Base (6) (kg) <150 150-159 (cm) 160-169 S170 <40 Mean 16 101 (155) 16 (157) 14 (18) (0) 40-49.9 Mean 20 (127) 19 (839) 17 (373) 16 (3) 50-59.9 Mean 25 (27) 22 (432) 20 (629) 19 (63) 60-69.9 Mean 29 (7) 26 (137) 24 (264) 21 (43) 70-79.9 Mean 33 123 (4) 30 (45) 28 (94) 25 (28) 80 Mean (0) 36 (17) 32 (62) 30 (19)

Body Mass Index as a Measure of Body Composition and Body Size 169 where, is in units of 5 kg/m and has mean subtracted. Table 2 provides results of regression analyses of the uncategorized data. alone and height alone (models 1 and 2) both show positive relations to blood pressure. When examined together, only weight appears important (model 3). The correlation of weight and height is 0.53, however. Replacement of height by inverse of height (model 4) or inverse of height squared (model 5) does not yield any improvement; note that I/height 2 is the form of height used in. TABLE 2. Linear regression of systolic blood pressure on weight, height, body mass index (), and their combinations among 3,543 white 13-year-old girls: data from the Pediatric Task Force Data Base (6) Model* and regressor(s)t Model 1 Model 2 Model 3 Model 4 1/height Model 5 1/height* x height Model 7 * Models Model 9 2 Model 10 Model 12 x height Model 13 2 Regression coefficient (P) 5.6 2.5 5.7-0.1 5.6 7.7 5.6 25.7 5.8-0.2-1.0 6.5-1.0-0.4 3.9 4.3-0.4 0.5 5.0 3.6 1.7 3.7 1.7-0.4 3.9-0.29 1.7 95% confidence interval 5.0 to 6.2 1.9 to 3.0 5.0 to 6.4-0.7 to 0.6 4.9 to 6.4-146 to 160 4.9 to 6.3-1,175 to 1,226 5.1 to 6.5-0.8 to 0.5-1.8 to-0.2 5.6 to 7.4-1.6to-O.3-1.0 to 0.3 3.5 to 4.4 3.7 to 4.8-0.7 to -O.1-0.7 to 1.7 3.3 to 6.6 3.2 to 4.1 1.2 to 2.3 3.2 to 4.1 1.1 to 2.2-1.1 to 0.2 3.4 to 4.5-0.62 to 0.04 1.1 to 2.2 P value 0.84 < 0.001 0.92 0.97 0.57 0.012 0.004 0.26 < 0.001 0.014 0.40 0.22 0.09 * All models contained an intercept for each of the eight studies from which data were used. f in 20 kg units, height in 10 cm units, and in 5 kg/m* units; all variables centered about their means. shows, however, that the product of weight and height is important, while model 7 shows that, when no product term is included in the model, the square of weight becomes important. (With both weight 2 and weight X height in the model, it becomes impossible to tell which terms are essential, although a simultaneous test of weight 2 and weight X height yields p = 0.01.) Table 3 displays the relation of and height to blood pressure. Mean blood pressure appears to increase with for a given height; there is also a suggestion that it increases with height for a given. In model 8, weight and height are replaced by alone. Models 9-11 indicate that alone is not adequate. Even more dramatic is that weight can take over most of the effect when both are entered in the model (model 10). With weight absent, does not appear to adequately capture all of the height effect (model 11); the result is unsurprising given that the correlation of and height is only 0.19. On the other hand, once height is entered with, further terms do not appear important (e.g., see models 12 and 13). Note, however, that X height is equal to weight/height, so that model 12 is merely a model with height and two ponderal indices (weight/ height 2 and weight/height). Table 4 displays the mean predicted blood pressures for models 6, 8, and 11, along with observed blood pressures, for the categories in table 1. Note that model 8 ( alone) predicts that height has a negative association with blood pressure in every weight category. Thus, the model predictions severely conflict with the observed data, which exhibit either a positive or a nonmonotone relation of height to blood pressure in five of the six weight categories. In contrast, models 6 and 11 exhibit a shift from a positive to a negative association across the weight categories, and are thus much closer to the observed patterns. It is apparent from the above analyses that neither alone nor a simple linear combination of weight and height are sufficient to capture the systematic variation of blood pressure. In particular,, a measure of body composition, does not account for the nonlinearities in this variation, and some additional measure of body size (e.g., height) is needed in the model. In the above example, anthropometric variables are primary predictors of blood pressure. In order to illustrate the role of anthropometric variables as confounding variables, we expand our data set to include all ethnicities. Table 5 provides the results for two models: model A describes the relation between ethnicity and systolic blood pressure adjusted for alone; in model B, height is added to the model. The association

170 Michels et al. TABLE 3. Mean observed level of systolic blood pressure (SBP) (in mmhg) by categories of body mass index () and height among 3,543 white 13-year-old girls (number of girls in parentheses): data from the Pediatric Task Force Data Base (6) (kg/m2) <150 150-159 (cm) 160-169 170 <17 101 (102) (218) (132) (8) 17-18.9 102 (77) (451) (328) (36) 19-20.9 (74) (412) (378) (38) 21-22.9 (31) (252) (282) (23) 23 (36) (294) (340) (51) TABLE 4. Means of predicted systolic blood pressure (SBP) (in mmhg) using different regression models: data from the Pediatric Task Force Data Base (6) Wleight (kg) <150 150-159 (cm) 160-169 170 <40 Modem 102 102 (101) () () 40-49.9 () () () () 50-59.9 () () () () 60-69.9 112 112 () 112 () () () 70-79.9 (123) () () () 80 Modem 119 121 119 () 117 117 117 () () between ethnicity and blood pressure for Hispanic and Asian girls changes considerably when height is added to the model. Although a difference of 2 mmhg in mean systolic blood pressure may seem like a small effect, it can translate into important differences in extreme quantiles. Hence, there is potentially an important difference in the interpretation of the results between models A and B of table 5.

Body Mass Index as a Measure of Body Composition and Body Size 171 TABLE 5. Linear regression of systolic blood pressure on ethnicity among 5,888 13-year-old girls: data from the Pediatric Task Force Data Base (6) Model* and regressorst Model A White African American Hispanic Asian Native American Other Model B White African American Hispanic Asian Native American Other Regression coefficient (P) H- -0.31-1.54-1.72-2.00-1.87 4.32 * -0.34-0.45 0.67-2.06-1.71 4.06 2.28 P value 0.34 0.005 0.04 0.12 0.01 0.28 0.43 0.43 0.11 0.02 * All models contained an intercept for each of the eight studies from which data were used. t Body mass index () in 5 kg/m* units and centered about its mean. t Referent. DISCUSSION We have illustrated that alone does not adequately describe the relation of body composition and body size to blood pressure. Unfortunately, the use of alone has become a common practice. As illustrated in our example, there is a flaw in the logic in this practice. Because alone must carry the strong effects of adiposity, the coefficient will be positive if obesity is a risk factor. But a positive coefficient in a model without height implies that within levels of weight, height is inversely associated with the outcome, and in a quadratic fashion. For example, our model 8 implies that, for a given weight w, blood pressure is linearly related to I/height 2 with regression coefficient 3.9 w. Such a strong inverse relation of height to blood pressure is contradicted in our data (see the models with weight and height in table 2, and the data in table 1). More generally, we cannot think of any situation in which it would be reasonable to force an inverse-quadratic relation of height to risk given weight. Yet that is precisely what one does when one uses alone. In our example, a regression model with weight and height provided a better fit to the data than with alone. Nonetheless, one has to be aware that height with weight in the model no longer has its usual biologic meaning of overall body size. Within a given stratum of weight, taller people will necessarily be leaner, and thus height will reflect body composition as well as body size. Because height has this dual interpretation when weight is in the model, it can be almost uninterpretable. For example, it may appear to be unrelated to risk of disease if the effects of body composition and size oppose one another, or it may appear to be inversely related to risk if body composition is a risk factor but body size is not. In a model with and height, on the other hand, height remains a measure of overall body size. Our comments apply whether anthropometric variables are study exposures or confounders. For example, if the exposure under study and the outcome are associated with both body composition and size, as is the case for ethnicity, no single anthropometric variable is likely to provide complete control of confounding. In any event, there is little cost in controlling for height in addition to. Our example concerned linear regression, but our arguments apply equally to the log-linear and logistic regressions most common in epidemiology. Because these models force exponential trends on untransformed variables, it is often recommended that one take the logarithm of quantitative variables before entering them in such models, in order to produce more realistic trends (7). If we do so with, we obtain ln() = ln(weight/height 2 ) = ln(weight) - 21n(height). As a consequence, a regression with ln() and ln(height) is mathematically equivalent to a regression with ln(weight) and ln(height). For example, if r is the disease rate and then ln(r) = a + /31n() + yln(height), ln(r) = a + /3[ln(weight)-21n(height)]+yln(height) a 1n(weight) + y*ln(height), where -y* = y 2/3. Thus, use of ln() alone (7 set to zero) corresponds to a special case of a model with ln(weight) and ln(height), in which the ln(height) coefficient is forced to be minus 2 times the ln(weight) coefficient. In summary, while may be a useful measure of tissue density, we think it is an insufficient anthropometric measure for epidemiologic analysis. Use of alone corresponds to an implicit and possibly implausible assumption about the relation of body size to the outcome. This relation can be more accurately described by the joint use of weight and height in a

172 Michels et al. flexible model that allows interaction or (more interpretably) by the joint use of and height. We recommend that investigators consider different methods for modeling anthropometric variables in epidemiologic analysis, rather than using or other ponderal indices alone. Such approaches can yield more accurate descriptions of the relation between anthropometric variables and the outcome of interest, and hence more accurate predictions and more complete control of confounding. ACKNOWLEDGMENTS This work was supported by National Heart, Lung and Blood Institute grant no. RO1-HL54319. The authors are grateful to Dr. Walter C. Willett for his helpful comments on the manuscript. REFERENCES 1. Willett WC. Nutritional epidemiology. 2nd ed. New York: Oxford University Press, 1998. 2. Criqui MH, Klauber MR, Barrett-Connor E, et al. Adjustment for obesity in studies of cardiovascular disease. Am J Epidemiol 1982;:685-91. 3. Kholsa T, Lowe CR. Indices of obesity derived from body weight and height. Br J Prev Soc Med 1967;21:122-8. 4. Watson PE, Watson ID, Batt RD. Obesity indices. Am J Clin Nutr 1979;32:736-7. 5. Goldbourt U, Medalie JH. -height indices. Choice of the most suitable index and its association with selected variables among 10,000 adult males of heterogeneous origin. Br J Prev Soc Med 1974;28:-26. 6. National High Blood Pressure Education Program Working Group on Hypertension Control in Children and Adolescents. Update on the 1987 Task Force Report on High Blood Pressure in Children and Adolescents: a working group report from the National High Blood Pressure Education Program. Pediatrics 1996;98:649-58. 7. Rothman KJ, Greenland S. Modern epidemiology. 2nd ed. Philadelphia: JB Lippincott Co, 1998.