The Harris and Benedict models (equations (1.16) and (1.17)) [86] for REE are frequently used today in both research and clinical practice, but were published over 90 years ago. In addition to the concern that what applied to the population in the early 20th century may not apply to the population today, there is also the fact and therefore potential issue of methodology having changed to some extent since 1919. The aim of this section is to attempt to validate the models shown above, making use of modern methods and statistical computing facilities. Here, we apply the original and any further models only to the original 1919 data. This analysis is not intended to validate these models with respect to today’s population.
The publication by Harris and Benedict gives data on 136 males and 103 females.
These data have been input to SPSS v 15.0 and R v 2.6.0 for analysis. Due to the significance of sex as an interaction term, we will treat males and females sepa-rately.
As a subjective initial analysis of these data, we considered correlation matrices and scatterplot matrices of all variables, for both males and females. We found that potential all independent variables have some relationship with the dependent variable (REE) for both males and females, though relationships for females are generally quite weak. There may be some issue of multicollinearity, particularly between body surface area (BSA) and weight.
Upon analysing these data using multiple linear regression, we obtain the following prediction equations. Note that this is simply an attempt to reproduce the analysis by Harris and Benedict.
REE(male) = 67.307 + 13.750× W (kg) + 499.816 × H(m) − 6.748 × age(y) (5.1)
REE(f emale) = 659.7920 + 9.6873× W (kg) + 176.3872 × H(m) − 4.6278 × age(y) (5.2)
These parameter estimates are essentially the same as those obtained by Harris and Benedict. The small differences are likely due to modern computational accuracy.
These models have adjusted R2 values of 0.7478 and 0.5121 respectively, and s values of 103.153 and 108.923 respectively. Checking diagnostics, as shown in Fig-ure A.4 reveals that the assumption of normality of residuals may be questionable.
Considering the coefficients of the parameters obtained in this analysis, we see that the parameter Height is not significant for females (Table 5.1) and the intercept is not significant for either sex.
Male Female
Coefficient P-value Coefficient P-value Intercept 67.3070 0.763 659.7320 0.056 Weight 13.7500 < 0.001 9.6873 < 0.001 Height 199.8160 < 0.001 176.8372 0.422 Age -6.7480 < 0.001 -4.6278 < 0.001
Table 5.1: Parameters and associated P-values from linear regressions of REE on age, height and weight using the HB data
Re-fitting the models without the intercept gives the following predictive equations for REE, with standard errors of the estimates for males and females of 102.800 and 110.410 respectively:
REE(male) = 13.638× W (kg) + 541.590 × H(m) − 6.669 × age(y) (5.3)
REE(f emale) = 9.359× W (kg) + 596.204 × H(m) − 4.678 × age(y) (5.4)
Note that there appears to be little change in the coefficients for weight or age, while the lack of significance previously seen for height in females is now resolved.
Why, though, height should be so sensitive to the presence or absence of the in-tercept, is unknown. All parameters are now significant.
Since we know that body composition is an important factor in determining resting energy expenditure, it seems logical that there should be some proxy measure of body composition included in a prediction equation. However, while considering only the data from the Harris-Benedict publication [86], we have limited access to such measures. we have therefore performed Stepwise regression (in an attempt to combat multicollinearity) including the variables BSA and BMI (calculated from height and weight), both potential proxies for body composition. The result of this modelling (steps not shown) was the following models for REE:
REE(male) = 421.992− 446.243 × H(m) − 6.679 × age(y) + 1226.603 × BSA(m2) (5.5)
REE(f emale) =−6.524 × age(y) + 1025.764 × BSA(m2) (5.6)
This suggests that when body surface area is accounted for in a model, there is no need to include a representation of body mass index. This could be due to multicollinearity, with the correlations between BMI and BSA in the 1919 data being 0.623 (males) and 0.845 (females). Note that the variability explained by these models (0.7478 and 0.5121 respectively) is roughly equal to that explained by models (5.1) and (5.2).
5.2.1 Conclusions
We should note that the models for males appear to consistently explain around 23% more of the variation in REE than those for females. This is, perhaps, to be expected because a key element of REE is fat-free mass - which generally occurs in higher proportions in males than in females, and Harris and Benedict had no direct measure of body composition.
During this analysis, it became clear that the most stable independent variable was age - with parameters remaining relatively unchanged and always highly sig-nificant. This suggests that age should always be included somehow in any resting energy expenditure model for adults. However, it seems unlikely that this should be done by developing different models for different age groups (as has been done in many of the models listed in section 1.2.2.2.2), since the other parameters are unlikely to change so dramatically at a specific age (unless age to be considered to be a marker for body composition - in which case, the relationship between age and body composition must be far better understood than at present)!
The aim of this analysis was to be able to validate the models originally developed by Harris and Benedict in 1919, using more modern approaches than would have been available to the authors at the time of the original study. The aim appears to be fulfilled for the data given in the original publication, although it is unlikely that these models will apply to today’s population.