Modelling REE with another dataset

The dataset used in this analysis was provided by Professor Jonathan Wells of the Institute of Child Health in London, in the spring of 2008. Resting energy expenditure measured by calorimetry (kcal/d) and body composition (fat mass and fat-free mass as determined by DEXA) are included for 16 boys and 14 girls of ages 8.1 - 12.1 years (mean = 9.7, sd = 1.3) and 8.2 - 12.4 years (mean = 10.1, sd = 1.4), respectively.

5.5.4 Linear models

We began by investigating separate linear models of REE on FM and FFM for each sex, which gave the following:

REE(boys) = 55.378× F F M − 13.845 × F M (5.16) REE(girls) = 46.098× F F M + 6.028 × F M (5.17)

However, it should be noted that sample size, and therefore statistical power, is extremely low, rendering these models tentative at best. In order to both increase power and investigate whether or not sex is a statistically significant covariate when it comes to these pre- or early-pubescent children (no data are available on pubertal staging), we combine the data for both sexes to consider ANCOVA models, treating sex as a covariate and FM and FFM as independent variables. As there is no biological realism in investigating an interaction between FM and FFM, the three way interaction will not be considered. Therefore, the first ANCOVA

model considered will be:

REE ∼ sex + F M + F F M + sex ∗ F M + sex ∗ F F M (5.18)

This model returns a F-statistic of 15.05 on 5 and 21 degrees of freedom, with P-values for the interactions of 0.98180 (sex∗ F M) and 0.52376 (sex ∗ F F M).

Since the two-way interactions are non-significant, we remove the one with the least significance (sex∗ F M) and re-fit the ANCOVA model as:

REE ∼ sex + F M + F F M + sex ∗ F F M (5.19)

This model returns an F-statistic of 19.23 on 4 and 22 degrees of freedom, and a P-value for the interaction of 0.534, showing no statistical significance at any reasonable level. As a result, we are able to remove this term and fit a model with just the main effects:

REE = sex + F M + F F M (5.20)

This procedure returns a marginally nonsignificant P-value for sex (0.52). However, removing the term sex from the model lowers the adjusted R² from 0.744 to 0.712, suggesting that since sex isn’t difficult or expensive to determine, it should perhaps remain in the model. Diagnostics for this model, as shown in Figure A.5 on page 285, show that there may be problems with the assumptions of modelling -particularly normality of residuals.

5.5.5 Nonlinear models

We went on to investigate nonlinear modelling of the BMR data provided by Pro-fessor Wells. We came across some initial problems with running the iterative model. To overcome these difficulties, it was necessary to increase the number of iterations used in the procedure from 50 to 150.

The model we are aiming to fit with this procedure is:

REE = β₀F M^β1+ β₂F F M^β3 (5.21)

This results in the following equations for boys and girls:

BOYS:

REE(kcal/d) = (99.6× F M^0.34) + (141.5× F F M^0.66) (5.22)

GIRLS:

REE(kcal/d) = (1034× F M^0.005) + (0.176× F F M^2.774) (5.23)

Considering the exponents in these models, we notice that the girls’ exponents are not remotely similar to anything we have already seen or would in fact expect from this modelling.

We investigate the variance covariance matrices of these models, finding the fol-lowing eigenvalues:

BOYS: 6496528.00, 5856.39, 0.06, 0.00005 GIRLS: 34276.68, 0.93, 0.0003, 0.000003

From these eigenvalues, we can assess the stability of the parameter estimates. If the condition number (the ratio of the largest to the smallest eigenvalue) is small, we may be confident in the stability of the estimates. A large condition number implies that any small change in the data could drastically alter parameter esti-mates. For these models, it is clear that the condition numbers for both boys and girls are extremely large, showing numerically very unstable models. This may be down to the small sample size. We can therefore not continue with this modelling.

5.6 Chapter summary

This chapter opened by exploring the data published by Harris and Benedict in 1919, which they used to develop models for estimating resting energy expenditure (REE) from anthropometric measurements.

The findings of this section were that despite the lack of techniques and equip-ment that would have been available many years ago, the best models that can be derived today from the published data are in-fact the same models that were originally published. It must be kept in mind, however, that these models were developed almost a century ago and therefore on a different population, yet are still in use to this day. It must also be kept in mind that while these models were developed using adult subjects, they are currently used to estimate REE in younger subjects.

Following on from this, seven sets of models for estimating REE from anthropo-metric measurements were applied to the ALSPAC datasets, showing that no two models are in agreement on the individual level. It was not possible to progress to marking any model as correct, however, due to the lack of gold standard data collected by ALSPAC.

The final part of this chapter considered alternative possibilities for REE mod-elling, including modelling based on body composition.. However, until the issues raised in Chapter 4 have been addressed - that is, until we have accurate methods of estimating body composition - it will not be possible to develop reliable models using such variables as predictors.

Chapter 6

The ideal study and a

simulation of resting energy

expenditure

6.1 Chapter aims

Chapter 6 will begin by describing an ‘ideal study’ in body composition and resting energy expenditure research. Following on from this, longitudinal resting energy expenditure and body composition data will be simulated, in a manner which generates reasonably realistic data, for several thousand children between the ages of 7 and 10 years. The chapter will focus mainly on potential issues with real-life data, such as sample size and missing data.