Introduction

Many studies have examined the associations between basal metabolic rate (BMR) and body weight, height, age and a variety of variables derived from these primary measures (such as body mass index=weight/height²). The most comprehensive examination of the matter to date was carried out by Schofield (1985a), who assimilated a wide-ranging collection of data from other published sources, and derived prediction equations from the combined database. These equations have been much used as a simple and widely applicable way of predicting BMR from weight, and possibly height, when it is impractical to measure it directly. They have been adopted by the World Health Organisation (WHO) for general use in predicting BMR (FAO/WHO/ UNU, 1985). Their study was based on an analysis of data, original and summary, collected in 114 previous studies. Their results therefore have an authority greater than that of the many local limited studies that have taken place before and since. However, being compiled from an unstructured set of data collection obtained for a diverse set of purposes over a long time range leads to potential problems, and Schofield (1985a) readily acknowledges the abuse of sampling assumptions.

However, there has been some doubt about the applicability of these studies to obese individuals. This matter has been raised by, for example, Pullicino et al (1996), who found that the Schofield equations systematically underestimated BMR in a sample of Maltese women. The obese are an increasing proportion of the population. Among the subjects used to derive the Schofield equations, 14.6% of those over 16 had a body mass index (BMI) in excess of 25 and 4.5% were in excess of 30. For a recent UK sample (DOH, 1999) the corresponding proportions were 40.8 and 9.7%. Because of the adverse effects of obesity on health, the obese are increasingly the focus of scientific studies. A central part of such studies is the comparison of individual energy intake and expenditure. Estimates of BMR are a central feature of many such studies, because BMR is used for a variety of purposes, for example to compare body energy requirements under a variety of conditions (eg pregnancy, lactation, undernutrition). They are also used to derive daily energy requirements as a multiple of BMR, and used for a variety of clinical and epidemiological purposes. Estimates of BMR obtained this way can be used to detect misreporting.

The Schofield equations are linear in weight, a choice that was made for ease of computation, and which seems a reasonable model over much of the weight range of the individuals studied. The assumption of linearity has been retained by others who have reassessed the data, such as Hayter and Henry (1994). Their work also draws attention to another problem with the data. There are significant differences in the BMR/weight association between the different populations comprising the Schofield data. Significant differences were found between most pairs of groups defined geographically (north European and American, Indian, Chinese, Italian), with the Italian group showing the greatest difference. This is of particular concern, since they comprise 45% of the data.

Our intention here is to question this use of linearity, and to investigate more carefully the BMR/weight association in heavier individuals. Any results will be subject to the same weaknesses as the original Schofield study. To the extent that the obese are a small subset of the original data, these weaknesses will be greater: the results will be strongly influenced by just a few of the component studies. We will also examine differences between groups in this association.

Methods

We have re-examined the data collection compiled for the Schofield (1985a) study, and described by Schofield (1985b). Our interest is in adults, and so we have considered only men and women in the age range 18–60. The data comprise 3514 observations on men and 1376 on women, when some high altitude studies have been excluded. Some of these observations are not of individuals, but are means of many individuals. These observations were given appropriately greater statistical weight in our analysis. Their contribution to the results was the same as if all individuals were placed at the mean.

Schofield (1985a) presents, for each sex, separate linear regressions for ages 18–30 and 30–60, and a table, intended to be applicable to all ages under 60. For the 18–60 age group, we have fitted, separately for men and women, a fourth-order cubic smoothing spline (Hastie & Tibshirani, 1990) to the weight/BMR association. This is a type of generalized additive model, and can be seen as an alternative to fitting polynomial terms to a non-linear association whose true parametric form is unknown. A series of cubic polynomial curves is constructed, constrained to be continuous in value and slope where they join. The order of the spline determines how smooth it is. We chose a fourth-order spline as the data were numerous enough to fit this order, and a greater order would allow too many fluctuations which might reflect only artefacts of the different study components. Any observations with a standardized residual greater than 3.5 were rejected as outliers. The effect of the influential study 20 was examined by recomputing the spline fit when it had been excluded. This study was of 116 male Chin and Kachin hill dwellers in Burma (Chitre et al, 1959).

The residuals from the fitted spline were then used to investigate whether, at fixed weight, BMR changes with age. This was done by fitting a smoothing spline (again fourth-order) for age to the BMR/weight residuals. This was done separately for men and women. We considered this to be more natural than the separate fitting of prediction equations for different age groups, as done by Schofield (1985a). This produced unnatural jumps in predicted BMR, for example at age 30.

Finally, the residuals from this regression were used, in the same way, to determine whether there was a marginal association between BMR and height, at fixed age and weight. This differs from the multiple regression fitted to height and weight by Schofield (1985a). Because of the small effect of height at a given weight, we considered the presentation of this effect as an adjustment to the main prediction to be more useful.

Results

BMR and weight

Figure 1 shows the fitted spline (r=0.57) for BMR and weight for men. Also shown for comparison, are the Schofield 18–30 and 30–60 equations, and a table for under-60s presented in the original paper. The most striking feature of this plot is that there is good agreement up to about 75 kg, but that above this weight, mean BMR does not increase any further, but remains at 7.4 MJ/24 h. Some 13.8% of the Schofield males over 16 weighed more than 75 kg. However, 75 kg is now about the weight of the average western man. The behaviour of BMR in men over 75 kg is clearly of much greater importance now than when the Schofield equations were originally derived (as those over 75 kg were such a small proportion of the original data, we have not achieved substantial improvement in overall goodness of fit).

Figure 1.

Basal metabolic rate vs weight for men. The lines Sch:18–30 and Sch:30–60 denote predictions based on the Schofield equations for these age ranges. The line for Sch:18–30 is lower below 50 kg and higher above 50 kg. The Table 4 line refers to that table in Schofield (1985a).The Spl-x20 curve is derived with group 20 excluded.

Full figure and legend (107K)

Figure 2 shows the corresponding plot for women (r=0.70). Here the agreement with the Schofield results is much closer. There is no levelling off of BMR with increasing weight, up to 85 kg, although the rate of increase seems to decrease after about 60–65 kg. We present our revised prediction for BMR based on weight in Table 1.

Figure 2.

Basal metabolic rate vs weight for women. The lines Sch:18–30 and Sch:30–60 denote predictions based on the Schofield equations for these age ranges. The line for Sch:18–30 is lower below 50 kg and higher above 50 kg. The Table 4 line refers to that table in Schofield (1985a).

Full figure and legend (100K)

Table 1 - Mean basal metabolic rate (MJ/24 h) as a function of weight (kg).

Full table (20K)

Figure 3 shows a plot of individual BMR and weight values for the six largest groups of males over 70 kg. These are summarised in Table 3. Taken overall, there is no indication of an increase in BMR with weight: the correlation coefficient is -0.08 (P<0.05). However, within each group, the correlations are positive. For groups 20, 29, 55, 67, 80 and 84, the correlations are 0.25, 0.20, 0.30, 0.48, 0.30 and 0.14, all but the last being significant at 5%. Thus there is good evidence that, within populations, BMR does continue to increase at heavier weights in men. The flat line in the plot reflects between group differences. If the group 20, which had the heaviest weights, is omitted, a different prediction is obtained, and this is also indicated on Figure 1. A corresponding table is presented in Table 2. However, it should be remembered that, of the remaining five large groups, four are Italian military or police, and so can hardly be considered a statistically representative sample of humanity in general. Caution is needed in the use of any predictions. Adding in the smaller groups did not affect the overall pattern seen in Figure 3.

Figure 3.

Plot of BMR against weight for men between 70 and 100 kg for the six largest groups in the Schofield database.

Full figure and legend (17K)

Table 3 - Characteristics of the 6 largest groups of men over 70 kg in the Schofield database.

Full table (14K)

Table 2 - Mean basal metabolic rate (MJ/24 h) for men (kg), with Schofield study 20 excluded.

Full table (13K)

Differences between groups in women were much less (Figure 4), although this is likely to reflect the smaller number of studies than anything about sex differences in inter-population variation. Five of the six largest groups of heavier women were in the USA. As for the men, it must be questioned whether they are statistically representative of humanity in general.

Figure 4.

Plot of BMR against weight for women between 60 and 100 kg for the six largest groups in the Schofield database (15, Minnesota, USA; 27, New Orleans, USA; 41, Washington, USA; 59, Ohio, USA; 79, Italy; 91, Charleston, USA).

Full figure and legend (13K)

BMR and age

Age has only a small effect on BMR, once weight has been accounted for. Our spline regression indicates that some adjustment should made to the predictions in Table 1. These are shown in Table 4. We note that the pattern differs between men and women. In women, BMR is highest between 25 and 35, whereas in men it peaks between 18 and 20. The decrease above 50 in women is much more rapid than in men.

Table 4 - BMR adjustment for age (y).

Full table (7K)

BMR and height

Once weight is accounted for, height has only a small effect on BMR. As height increases, BMR increases. This is likely to be due to greater fat free mass in taller than shorter people at a fixed weight. The appropriate adjustment is shown in Table 5. The pattern in men and women is similar.

Table 5 - BMR adjustment for height.

Full table (7K)

Discussion

Our intention is not to reject the results presented by Schofield (1985a). They are applicable to the greater part of the weight range. Our particular interest is in the overweight, which regrettably form an increasing proportion of most populations. We fitted a nonparametric non-linear curve (the smoothing spline). This is not a model for how BMR increases with weight. Many different convex curves could have done this and it would have been difficult to discriminate among them. The non-parametric curve is flexible and allows predictions to be made if desired—these are in Tables 1 and 2. Departure from linearity can also be tested, and for the Schofield data it was significant (P<0.001).

We have looked at data in the heavier part of the distribution of weights in the Schofield data. This has led to the first of our two conclusions: BMR increases more slowly at heavier weights, and to ignore this is to overpredict BMR in the obese.

We have also looked at the different groups that comprise the Schofield data, and there are substantial differences, in mean weight, mean BMR and the association between them, in these groups. This implies that caution is needed in using any of our results. Although the sampling may have been suitably representative within the groups, it cannot be claimed that the groups are in any sense a statistically representative sample of human populations in general. Hayter and Henry (1994) have already pointed out that a large proportion of the data were obtained on Italian military trainees, servicemen and police, and that these differ significantly from the rest of the data. We have also seen that Burmese hill-dwellers, who form an important part of the upper tail of the weight distribution, also show different associations between BMR and weight. Our conclusion is that: any general equation for predicting BMR may be biased when used for some groups or populations.

We suggest that greater understanding of the determinants of BMR is needed, in order to better guide its prediction from other characteristics when its measurement is impractical.

Why do obese people have a lower BMR to weight ratio?

The apparent differences in the BMR of the obese relative to the lean can be explained in terms of body size and composition. There is little evidence that obese subjects are characterized by an inherently low metabolic rate. Indeed, it has been repeatedly demonstrated that under standardized conditions the obese have higher absolute energy requirements than do the lean, due to the greater mass of metabolically active tissue (James 1992; Rucker, 1978; Jequier, 1984; Prentice et al, 1989). As weight is gained both fat and fat-free mass are gained. However, this does not occur at a linear rate as body size increases. As the body gets fatter, a greater ratio of fat to lean tissue is deposited (Forbes, 1982, 1987). Thus adipose tissue expands faster than lean tissue. The metabolic rate of adipose tissue is very low compared with that of lean tissue (Miller & Blythe, 1953). These observations mean that obese subjects are absolutely larger than they were before they became obese. They have an absolutely higher fat and fat-free mass. By far the main determinant of resting metabolic rate is fat-free mass (Miller & Blythe, 1953; Webb, 1981). Therefore, the resting metabolic rate in absolute terms increases in a curvilinear manner as body weight (and fatness) increase (McNeill et al, 1987). While the absolute resting metabolic rate is higher, the BMR per kg of body weight is lower than that of the pre-obese subject (due to the lower percentage of fat-free mass contributing to body weight). By the same argument the BMR per kg fat-free mass for most subjects is very similar.

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