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Am J Clin Nutr 89: 491-499, 2009. First published January 13, 2009; doi:10.3945/ajcn.2008.26629
 American Journal of Clinical Nutrition, doi:10.3945/ajcn.2008.26629
Vol. 89, No. 2, 491-499, February 2009
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© 2009 American Society for Clinical Nutrition

ORIGINAL RESEARCH COMMUNICATION

Aggregate predictions improve accuracy when calculating metabolic variables used to guide treatment

Jonathan CK Wells1,2,3, Jane E Williams1,2,3, Dalia Haroun1,2,3, Mary S Fewtrell1,2,3, Antonio Colantuoni1,2,3 and Mario Siervo1,2,3

1 From the Childhood Nutrition Research Centre, UCL Institute of Child Health, London, United Kingdom (JCKW, JEW, DH, and MSF); the Department of Neuroscience, "Federico II" University, Medical School, Naples, Italy (AC); and MRC Human Nutrition Research, Elsie Widdowson Laboratory, Cambridge, United Kingdom (MS).

2 Supported by the UK Medical Research Council (core funding for the body-composition measurements) and by the Medical School of "Federico II" University, Naples, Italy (core funding for the metabolism measurements).

3 Reprints not available. Address correspondence to JCK Wells, Childhood Nutrition Research Centre, UCL Institute of Child Health, 30 Guilford Street, London WC1N 1EH, United Kingdom. E-mail: j.wells{at}ich.ucl.ac.uk.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 SUBJECTS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Background: Many components of clinical management are tailored to metabolic variables, such as fat-free mass, fat mass, resting metabolic rate (RMR), and body surface area. However, these traits are difficult to measure in routine care and are typically predicted from simple anthropometric or bedside body-composition measurements. Many prediction equations have been published, but validation studies have shown that these equations tend to have limited accuracy in individuals and many have significant average bias.

Objective: We tested a mathematical approach that assumes that the aggregate of many independent predictions is more accurate than the best single prediction.

Design: Body composition was measured in 196 children aged 4–16 y by using the 4-component model. RMR was measured in 142 adult women. Data on weight, height, age, skinfold thickness, and body impedance were used in published equations to predict body composition (12 equations) or RMR (13 equations). The accuracy of individual compared with aggregate predictions, relative to the reference measurements, was compared by using the Bland and Altman method.

Results: For children's body composition and adult RMR, the aggregate predictions had lower mean biases and lower limits of agreement than did the individual predictions, and the aggregate predictions performed better than did any individual prediction.

Conclusions: Aggregate predictions perform better than single predictions at predicting fat-free mass, fat mass, total body water, and RMR. Our findings indicate that the accuracy of calculating variables such as energy requirements and drug and dialysis dosages can be improved significantly with the use of our mathematical approach.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
SUBJECTS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Many aspects of medical treatment and management are best tailored to indexes of metabolic phenotype, such as total body water (TBW), fat-free mass (FFM), resting metabolic rate (RMR), and surface area (1–4). For example, energy and fluid requirements are predicted from RMR, chemotherapy and some drug dosages from surface area, dialysis dosage from TBW, and other drug dosages from FFM. Ideally, these metabolic indexes would be measured directly in individual patients. In practice, because of the lack of resources, they tend to be predicted from anthropometric measurements or simple bedside body-composition techniques, such as skinfold thickness measurement or bioelectrical impedance analysis.

Even minor errors in predicted treatment dosages may have adverse implications for patient well-being. Errors in the estimation of RMR, used to calculate energy requirements, over several days may lead to significant weight loss or gain, which in turn may impair response to treatment or increase morbidity. Errors in the estimation of body-composition variables may lead to an inaccurate drug therapy or dialysis dose, again with deleterious effects. Numerous scientific articles have been published, attempting to reduce the error in such predictions, typically either by addressing more specific patient populations or by incorporating more raw variables on which to base the prediction. However, individual equations generated in one sample rarely transfer successfully to other samples, even within healthy individuals or within a given disease state, and individual errors remain large.

This situation may be addressed using an approach known popularly as the "wisdom of crowds" (5). By convention, accuracy in any prediction is assumed to derive from selecting the highest quality source of information and discarding poor quality sources. The flaw in this approach, when requiring a prediction for clinical use, is that variability in the quality of information sources is likely to be evident only with hindsight. Research into the scientific basis of prediction has repeatedly shown that substantially improved accuracy derives when 4 conditions are satisfied (5): first, many predictions based on diverse criteria are used; second, these predictions are independent of one another; third, the individual predictions are based on different underlying assumptions; and fourth, these independent predictions are then aggregated. Under these conditions, error will not be correlated across the predictions, but rather will be randomly distributed across them and hence tend to cancel out, increasing the accuracy of the aggregate prediction (5).

We hypothesized that this approach could be applied to the prediction of metabolic phenotype. First, many predictive equations have been published (as described below for body composition and RMR), providing diversity. Second, the studies have been conducted on different study populations, providing independence. Third, the prediction equations have been generated using different technologies and hence incorporate diverse assumptions. Fourth, the predictions can readily be aggregated. We tested this hypothesis using 2 metabolic outcomes: body composition [FFM, TBW, fat mass (FM), and percentage of fat] and RMR. For proof of concept, we tested the hypothesis in healthy children and adults; however, the principle of our approach is equally relevant to diverse patient populations.


   SUBJECTS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 SUBJECTS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Data were obtained from ongoing research studies for body composition in 196 children aged 4–16 y, and for RMR in 142 women aged 18–35 y, ranging in body mass index (BMI; in kg/m2) from 18 to 45. Ethical approval for the children's study was granted by the Ethical Committee of the Institute of Child Health and Great Ormond Street Hospital and for the women's study by the Scientific and Ethical Committee of the Department of Neuroscience of the Federico II University Medical School, Naples, Italy.

Equations for the prediction of body composition in normal, healthy children of European ethnicity were searched for in the literature. All equations identified were accepted, provided that the age range spanned ≥6 y and embraced the 10-y age point, the midage of our sample (Table 1). Equations generated from samples that included children with conditions such as growth hormone deficiency were not included, due to likely effects of such conditions on body composition. Equations for the prediction of RMR in adults were likewise searched for in the literature (Table 2).


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  		TABLE 1. Equations for the prediction of body composition in children1

 

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  		TABLE 2. Equations for the prediction of resting metabolic rate in adult women1

 
In the children, body composition was measured using the 4-component model. This model, described in detail previously (30, 31), is considered the gold standard for measurement of total-body FM and FFM. The model requires data on weight (kg), TBW (L) by isotope dilution, total body volume (L) by air-displacement plethysmography, and bone mineral content (kg) by dual-energy X-ray absorptiometry, as described previously (31). Precision of FFM and FM by the 4-component model in children is 0.3 kg (32). Weight, height, and skinfold thicknesses at the biceps, triceps, subscapular, and suprailiac sites were measured on the left side of the body using standard protocols, as described previously (31). BMI was calculated from weight and height. Height and BMI SD scores were calculated using 1990 UK reference data (33, 34).

In the RMR group of adult women, body composition was measured using tetra polar bioelectrical impedance (RJL 101; Akern, Florence, Italy). FFM was obtained from the measures of resistance and reactance, using the algorithm provided by the manufacturer. Body surface area was predicted from the formula of Dubois and Dubois (35). RMR was measured using indirect calorimetry (V MAX 29n; Sensor Medics, Yorba Linda, CA). The device was calibrated before every measurement. The measurements began at 0800, with the subjects asked to lie in a supine position for ≥20 min. The measurements were taken in a peaceful and relaxing environment kept at constant temperature ({approx}25.0°C) and level of humidity, due to air conditioning and dehumidification systems. Data for final analysis was collected only when the subjects had reached a steady state condition, indicated automatically by the calorimeter when oxygen and carbon dioxide volumes had been stable for ≥5 min. The metabolic test lasted ≥25 min and was extended to a maximum of 45 min. RMR was then calculated from oxygen consumption and carbon dioxide production, according to Weir's equation (36). A more detailed description of the protocol of the measurements is provided elsewhere (37).

Using the equations presented in Table 2 and Table 3, body composition was predicted in the 196 children and RMR in the 142 women. Values for TBW or body density, obtained from some equations, were converted to FFM using published data on the hydration or density of lean tissue (38). Using the same approach in reverse, predicted values for FFM were also converted to TBW. FM was calculated as the difference between FFM and weight, and percentage of fat was calculated as [(FM/weight) x 100].


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  		TABLE 3. Description of the sample of children1

 
For each child, body-composition values (TBW, FFM, FM, and percentage fat) were first predicted using each of the 12 individual equations. For each body-composition outcome, the aggregate prediction was then calculated, as the average of the 12 predicted values. The same procedure was then undertaken for the women, using the 13 RMR prediction equations.

Agreement between either the aggregate prediction or each individual prediction and the reference data was tested using the Bland and Altman method (39). This approach calculates the mean bias (predicted minus reference value) and the limits of agreement (twice the SD of the bias). However, statistical comparisons of biases, as undertaken here and shown in Figures 1, 2, and 4, require data on mean and SD of the bias. All mean biases were converted to positive values (ie, multiplied by –1 if negative) to compare error between equations regardless of its direction. Significant difference between these mean biases of the individual versus aggregate predictions was assessed using a 2-sample t test. Linear regression analysis was used to evaluate whether, for both individual and aggregate prediction, the bias was associated with the magnitude of the trait (eg, whether the bias in predicted TBW varied across the range of TBW). For TBW, the reference value was regressed either on the aggregate prediction or on each individual prediction to calculate the SEs of the individual or aggregate estimates.


Figure 1
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  		FIGURE 1. Mean (±SD) bias in fat-free mass or fat mass in 196 children, calculated as the predicted value minus the reference (measured) value. The bias in fat-free mass has the opposite sign of that in fat mass. The graph compares 12 individual predictions with the aggregate average of the 12 individual predictions. The vertical lines represent the mean bias, and the mean bias +1 SD, for the aggregate prediction to aid comparison with the other data. All mean biases were expressed as positive values. Asterisks denote bias that is significantly greater than the aggregate bias. BIA, bioelectrical impedance analysis; SKF, skinfold thickness.

 

Figure 2
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  		FIGURE 2. Mean (±SD) bias in percentage of fat in 196 children, calculated as the predicted value minus the reference (measured) value. The graph compares 12 individual predictions with the aggregate average of the 12 individual predictions. The vertical lines represent the mean bias, and the mean bias +1 SD, for the aggregate prediction to aid comparison with the other data. All mean biases were expressed as positive values. Asterisks denote bias that is significantly greater than the aggregate bias. BIA, bioelectrical impedance analysis; SKF, skinfold thickness.

 

Figure 4
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  		FIGURE 4. Mean (±SD) bias in resting metabolic rate in 142 adult women, calculated as the predicted value minus the reference (measured) value. The graph compares 13 individual predictions with the aggregate prediction of the 13 individual predictions. The vertical lines represent the mean bias, and the mean bias +1 SD, for the aggregate prediction to aid comparison with the other data. All biases were converted to positive values. Asterisks denote bias that is significantly greater than the aggregate bias. BIA, bioelectrical impedance analysis; WHO, World Health Organization; WT, weight; HT, height.

 

   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 SUBJECTS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
A description of the sample is given in Table 3 for the children and in Table 4 for the adult women. The children had mean height and BMI SD scores slightly above the 1990 UK reference data, but not significantly so. The women had a mean BMI of 29.2 and therefore tended to be overweight, but their BMIs also ranged from 18.3 to 45.2.


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  		TABLE 4. Description of the sample of women1

 
For the prediction of FFM and FM in children, the aggregate prediction had the second lowest mean bias (0.2 kg; NS) and the lowest limits of agreement (±3.4 kg) (Table 5, Figure 1). The biases in FFM and FM were of identical magnitude, but with opposite signs. The individual predictions ranged in bias from 0.1 to 3.5 kg, with 8 of the 12 equations exceeding a 1-kg mean bias. The bias of the individual predictions was significantly greater than the aggregate bias in 10 of the 12 equations, the exceptions being those of Mellits and Cheek (7) and Pietrobelli et al (9) The limits of agreement for the individual predictions ranged from ±3.6 kg to ±7.1 kg. For percentage of fat, the aggregate prediction again had the second lowest mean bias (0.1%; NS) and the second lowest limits of agreement (±7.9%) (Figure 2). The individual predictions ranged in bias from 0.1% to 9.0%, with 8 of the 12 equations exceeding 2% for the mean bias. The bias of the individual predictions was significantly greater than the aggregate bias in 10 of the 12 equations, the exceptions being those of Mellits and Cheek (7) and Houtkooper et al (14).The limits of agreement for the individual predictions ranged from ±7.7% to ±33.6%. For each of FFM, FM, and percentage of fat, when combining the criteria of mean bias and limits of agreement, the aggregate prediction performed better than any single prediction.


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  		TABLE 5. Bland and Altman statistics for bias and limits of agreement between individual or aggregate equations and reference 4-component data for fat-free mass and percentage of fat1

 
The results for the12 individual predictions and the aggregate prediction of the linear regressions of the bias on the mean for FFM, FM, and percentage fat are shown in Table 6. For FFM, the bias was significantly associated with the mean in 10 of the 12 equations, and in 9 of these 10 the slope was negative. The aggregate prediction also showed a significant negative association, but with relatively modest slope. For FM, the bias was significantly associated with the mean in 11 of the 12 equations, but with 5 of these 11 showing a negative association and the other 6 a positive association. The aggregate did not show any significant association between bias and mean. For percentage of fat, the bias was significantly associated with the mean in 9 of the 12 equations, with the slope being negative in 3 of these 9 and positive in the other 6. The aggregate prediction showed a significant negative association between bias and mean, but again with relatively modest slope.


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  		TABLE 6. Linear regression analysis of the association between the magnitude of the bias and the mean value by both techniques: body-composition outcomes1

 
For TBW, the aggregate prediction had the lowest mean bias (0.11 L) and the lowest limits of agreement (±2.89 L). The individual equations ranged in bias from 0.29 to 2.42 L, with limits of agreement ranging from 3.15 to 5.46 L. The magnitude and distribution of these biases were very similar to those for FFM. The bias of the individual predictions was significantly greater than the aggregate bias in 11 of the 12 equations, the exception being that of Mellits and Cheek (7). The SEE for regressing predictions on the reference value was lowest in the aggregate prediction (1.33 L) and ranged from 1.41 to 2.15 L in the individual predictions (Figure 3). Again, the aggregate prediction outperformed any individual prediction.


Figure 3
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  		FIGURE 3. SEEs for the prediction of total body water (TBW) in 196 children. The independent variable is a predicted value obtained from either a single equation or as the aggregate prediction from all 12 equations. The vertical line represents the SEE for the aggregate prediction to aid comparison with the other data. BIA, bioelectrical impedance analysis; SKF, skinfold thickness.

 
For the prediction of RMR in adult women, the aggregate prediction once again had the second lowest mean bias of 36 kcal/d and the lowest limits of agreement of ±138 kcal/d (Table 7, Figure 4). The individual predictions ranged in bias from 25 to 194 kcal/d, with 8 of the 13 equations exceeding 50 kcal/d for the mean bias. The bias of the individual predictions was significantly greater than the aggregate bias in 6 of the 13 equations, with one further equation [Mifflin et al (20) bioelectrical impedance analysis equation] almost achieving significance for this test (P = 0.06). The limits of agreement for the individual predictions ranged from ±260 kcal/d to ±318 kcal/d. Combining the criteria of mean bias and limits of agreement, the aggregate prediction again performed better than any single prediction. The results of the linear regressions of the bias on the mean for RMR are shown in Table 8. The bias was significantly negatively associated with the mean in 12 of 13 of the individual predictions and also in the aggregate prediction. The slope of this association in the aggregate prediction was similar to that of the individual predictions.


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  		TABLE 7. Bland and Altman statistics for bias and limits of agreement between individual or aggregate equations and reference data for resting metabolic rate1

 

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  		TABLE 8. Linear regression analysis for the association between the magnitude of the bias and the mean value by both techniques: resting metabolic rate1

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 SUBJECTS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
As we hypothesized, an aggregate prediction based on a series of independent predictions was more accurate than those individual predictions in estimating reference values for FFM, FM, percentage of fat, TBW, and RMR. For FFM, FM, and percentage of fat, 10 of the 12 individual predictions had significantly poorer accuracy (greater mean bias) than the aggregate; for TBW, 11 of the 12 predictions had significantly poorer accuracy, while, for RMR, 6 of the 13 predictions had significantly poorer accuracy. However, according to the combined criteria of low mean bias and low limits of agreement in individuals, the aggregate equation performed better than any individual prediction for both body composition and RMR. Our findings have important implications for the optimal approach for tailoring clinical management to metabolic phenotype, suggesting that better use of raw data obtained at the bedside could substantially reduce error in both individuals and populations, and hence improve clinical care.

The results were more impressive for body composition than for RMR. This is likely to be due to the greater diversity among the body-composition equations, which variously used raw data on weight and height, BMI, 2 or 4 skinfold thicknesses, or impedance to generate the prediction. In contrast, RMR was predicted either from weight and/or height (6 equations) or from impedance (7 equations). Furthermore, all the equations predicting RMR from impedance used the same calculated FFM variable, although in the original equation derivations, FFM had been measured by a diversity of techniques. Greater homogeneity among the predictive strategies detracts from the strength of our approach; however, this could be readily addressed by developing more diverse predictive equations.

Even though the aggregate prediction had negligible mean bias for body composition and only a small mean bias for RMR, accuracy was still variable between individuals. There was a tendency for each individual prediction equation to generate values where the magnitude of the bias was associated with the magnitude of the trait, and because in most cases (FFM, percentage of fat, RMR) this was consistent across the different equations, the aggregate values likewise showed a systematic association between bias and mean. However, for body-composition outcomes, the association between bias and mean was weaker in the aggregate predictions than in most individual predictions, indicating partial resolution of this problem. Ideally, actual measurements remain preferred for calculating treatment requirements, where resources permit. Nevertheless, where such measurements are not feasible, our approach can substantially improve accuracy in routine clinical practice.

The key implication of our analysis is that an aggregate prediction has 2 significant benefits. First, the aggregate tends to have accuracy similar to (FFM, FM, RMR) or better than (TBW) the best individual prediction equation, as well as having superior bias distribution among individuals. Second, use of the aggregate also minimizes the likelihood that, in the absence of any information about which equation might be best in a given population, one with high bias is inadvertently selected. The aggregate prediction had 3.3 kg, 2.3 kg, and 158 kcal/d better mean accuracy than the worst-performing single prediction equation for FFM, TBW, and RMR, respectively. These advantages are complementary, because although a prediction from an individual equation could be accurate, it is not possible to know prospectively which individual equation might perform best. Thus, our approach increases the likelihood of maximizing accuracy while also reducing the likelihood of selecting the worst-performing equation.

TBW provides a useful example of the importance of estimating metabolic phenotype with accuracy, as emphasized recently (40, 41). Patients with chronic renal failure undergoing dialysis require reduction of their TBW together with the removal of catabolic products such as urea and creatinine. During each dialysis session, excess fluids should be removed, with "excess" defined on the basis of assessment of normal TBW. The adequacy of dialysis is further defined in relation to the clearance of small solutes, urea and creatinine, with the clearances of these solutes needing adjustment for variations in body size. Creatinine clearance is standardized to body surface area, whereas the fractional clearance of urea is adjusted to TBW (42). An excessive or inefficient removal of TBW derived from erroneous calculations may lead to the development of symptoms such as dizziness, cramps, and hypotension due to hypovolemia or to an increase in body fluids (hypervolemia) and catabolic products, respectively (43). In our analysis, the negligible mean bias of 0.1 L, and the low SEE of 1.3 L, in TBW given by the aggregate prediction represents a substantial improvement on the scenario offered by the individual predictive equations, which had mean biases ranging from 0.3 to 2.4 L and an average SE of 29% (range: 6–62%) greater than the aggregate SE.

There are several possible reasons why individual prediction equations generated in one population tend not to perform well in others. First, there may be methodologic differences between studies, either in the techniques used to measure body composition or RMR or in the accuracy of the instruments (eg, indirect calorimetry). Second, there may be subtle differences in physiology between groups, deriving, for example, from different age ranges, varying nutritional status, or minor genetic influences. Third, the populations sampled may differ, for example, by including patients or athletes; however, we aimed to minimize this source of error by including equations generated only from normal healthy individuals. Thus, methodologic and physiologic variability is likely to contribute to limited accuracy when applying individual equations to a new population. Our approach indicates that a substantial proportion of this "error" is randomly distributed across the samples and hence is removed through the statistical approach that we applied. Further work will be required to assess how well our approach works in specific patient groups.

In conclusion, for proof of concept, we have demonstrated the validity of this approach in healthy children and adults. To benefit clinical practice regarding specific disease states, the same approach should be applied with data sets collected in these conditions. This will require, for any individual disease state, a number of predictions to be generated, using different patient populations and measurement technologies. However, such studies are not difficult to undertake. Our approach favors maximal diversity in such equations, using, eg, weight and height, BMI, circumferences, skinfold thickness, and impedance. The approach can be applied with little technical difficulty: the preparation of spreadsheets or a website, containing the appropriate individual prediction equations, would allow bedside calculation of metabolic phenotype from a few simple anthropometric or bioelectrical impedance measurements. Although very simple in concept, our approach could significantly improve the tailoring of treatment to metabolic phenotype.


   ACKNOWLEDGMENTS
 
The authors' responsibilities were as follows—JCKW: conceived the hypothesis and study design and wrote the first draft of the manuscript; JEW and DH: collected and modeled the body-composition data; JCKW and MSF: supervised the collection and modeling of the body-composition data; and MS and AC: collected the RMR data. All authors contributed to the subsequent revisions. None of the authors had any conflict of interest regarding the manuscript.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 SUBJECTS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 

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Received for publication July 1, 2008. Accepted for publication October 24, 2008.





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