- Research article
- Open Access
- Open Peer Review
Dietary energy density and adiposity: Employing bias adjustments in a meta-analysis of prospective studies
© Wilks et al; licensee BioMed Central Ltd. 2011
- Received: 20 July 2010
- Accepted: 22 January 2011
- Published: 22 January 2011
Dietary studies differ in design and quality making it difficult to compare results. This study quantifies the prospective association between dietary energy density (DED) and adiposity in children using a meta-analysis method that adjusts for differences in design and quality through eliciting and incorporating expert opinion on the biases and their uncertainty.
Six prospective studies identified by a previous systematic literature search were included. Differences in study quality and design were considered respectively as internal and external biases and captured in bias checklists. Study results were converted to correlation coefficients; biases were considered either additive or proportional on this scale. The extent and uncertainty of the internal and external biases in each study were elicited in a formal process by five quantitatively-trained assessors and five subject-matter specialists. Biases for each study were combined across assessors using median pooling and results combined across studies by random-effects meta-analysis.
The unadjusted combined correlation between DED and adiposity change was 0.06 (95%CI 0.01, 0.11; p = 0.013), but with considerable heterogeneity (I2 = 52%). After bias-adjustment the pooled correlation was 0.17 (95%CI - 0.11, 0.45; p = 0.24), and the studies were apparently compatible (I2 = 0%).
This method allowed quantitative synthesis of the prospective association between DED and adiposity change in children, which is important for the development of evidence-informed policy. Bias adjustment increased the magnitude of the positive association but the widening confidence interval reflects the uncertainty of the assessed biases and implies that higher quality studies are required.
- Target Setting
- External Bias
- Prospective Association
- Confounding Bias
- Bias Adjustment
The prevalence of obesity in childhood is increasing around the world and is causally linked to large predicted increases in morbidity [1–4]. The fundamental physiological cause of weight gain is a positive energy imbalance, generally caused by excessive energy intake . However, the dietary components that contribute to excess energy intake are not clear, which hampers policy making to prevent obesity. Research suggests that dietary energy density (DED, food energy/food weight) is an important determinant of total energy intake and experimental studies have shown that a low DED leads to a lower ad libitum energy intake in both adults and children [5–7]. The evidence from observational studies, however, is sparse. A recent narrative systematic review found that most studies reported positive prospective associations between DED and adiposity in adults and children  though the studies varied considerably in their design and quality such that it was not possible to produce an overall pooled estimate of the association. For example studies include either adults or children and follow-up times range between 9 months and 7 years. In addition, there is diversity in the way DED is modelled in the statistical analysis (continuous vs. categorical), the calculation of DED (including food only, food and all drinks, or food and caloric drinks), and the measures used for obesity status (e.g. body weight or fat mass) .
To overcome this diversity problem and to be able to estimate an overall pooled estimate of the association, we have adapted and applied a recently developed experimental meta-analysis method that allows adjustment for differences in study design and quality through a formal process of eliciting and incorporating expert opinion . This method attempts to quantify the biases and their uncertainty, independently of the results, rather than to ignore them and produce a pooled association which is difficult to interpret. Although use of expert opinion may be considered controversial, meta-analysts routinely rely on even stronger judgements when excluding some studies altogether and regarding those included as unbiased. Moreover, policy makers faced with imperfect evidence use expert opinion informally in making judgements and decisions. The aim of this research was to formalise this process, making it transparent and accountable, and use this novel meta-analysis method to quantitatively synthesize the evidence on the prospective association between DED and change in fat mass index (FMI, fat mass/height2) in children.
Summary of study characteristics
Butte et al 
1030 4 - 19y old Hispanic children/adolescences, who are either overweight or have ≥ 1 overweight sibling, USA.
24 hr recall; DEDFC
BW gain (kg/y)
Sex, age, age2, Tanner stage and BMI, all assessed at BL.
Deierlein et al 
2006 16-47y old pregnant women (≥ 16y), USA.
FFQ; DEDFC: Quartile 1-4 = 0.71, 0.86, 0.98 and 1.21
Gestational BW gain
Pregravid BMI, gestational age and residual energy intake.
Iqbal et al 
2025 30-60y old male and female adults. The 1936 cohort and WHO MONICA1, Dk.
Change in BW
BMI, age, leisure time physical activity, smoking status, educational level all assessed at BL; cohort.
Johnson et al 
1432 7y old children; ALSPAC, UK.
Adiposity defined by FMI; Quintile 5 vs. 1 - 4
BL energy misreporting, total EI, EI from drinks, dietary fat and fiber intake, sex, BL overweight, TV watching, maternal BMI and education.
McCaffrey et al 
115 6-8y old children from Coleraine, Northern Ireland.
FMI; Tertile 3 vs. 1 and 2
Sex, BL diet misreporting and FU Tanner stage.
Savage et al 
192 24-47y old Non-Hispanic women (n: Tertiles 1-3 = 61, 63&59) living in Pennsylvania, USA.
24 hr recall; DEDFO: Tertiles 1-3 = 1.3, 1.7 and 2.1
Change in BW
The analysis of interest was unadjusted.
Application of the bias-adjustment method
The bias-adjustment method is described in detail by Turner et al. . The steps used to implement this method for the six studies included in this meta-analysis are outlined below. The study by Savage et al.  is used throughout the paper to exemplify the method.
Target question and target setting
The precise definition of the public health target question, which the meta-analysis aims to address, was agreed as "Is dietary energy density associated with change in fat mass index in children?"
General population of children aged 4-11yrs in the UK
DED assessed by 7 day weighed food diaries calculated by dividing total food energy (kJ) by total food weight (g) excluding beverages
Change in FMI (fat mass/height2, kg/m2), measured from baseline to follow-up
Outcome assessed 2 years after the baseline measurement.
The target setting focuses on children between 4 and 11 years excluding both baby to toddler stages and advanced stages of puberty to match the policy focus on the UK Healthy Weight, Healthy Lives strategy . DED calculated as the ratio of total food energy to total food weight was used as the target exposure because inclusion of beverages disproportionately influences DED and water intake is often reported inaccurately . FMI was used as the measure of adiposity in children due to its independence of growth rates . Two year follow-up was selected since we anticipated diminished associations with increasing follow-up time, whereas shorter follow-up times would not adequately allow for the slow accumulation of fat mass.
Non-Hispanic women living in central Pennsylvania, USA
DED assessed by three 24 h recalls, including two weekdays and one weekend day and calculated by dividing total food energy by total food weight
Change in body weight measured from baseline to follow-up
Outcome assessed six years after the baseline measurement.
Internal and external biases
Potential internal biases in each study were identified by comparing the study against its idealized version. For this meta-analysis, internal biases were categorized as biases related to the measurement of the outcome ("outcome bias") and the exposure ("exposure bias"), missing data and loss to follow-up ("attrition bias"), appropriate confounders ("confounding bias") and whether the inclusion and exclusion criteria were clear and adhered to ("selection bias"). Biases related to inappropriate statistical analysis or any other flaws were included in a separate category ("other bias suspected"). Important variables potentially related to both the outcome and exposure were considered by the subject matter specialists and statisticians and the following reference set of confounders was selected: energy-containing beverages, sex, total energy intake or energy misreporting, socio-economic status, ethnicity, some measure of baseline body size, physical activity and, depending on the age of the study population, Tanner stage and smoking status. Many DED studies adjust for fat and fiber intake; we did not consider these as confounders as both are expected to be direct determinants of DED. The adjustment for confounding in each study was judged against this reference set.
Potential external biases were identified by comparing each idealized study against the target setting. External biases were categorized as biases related to the follow-up time ("timing bias"), the presented outcome ("outcome bias") and exposure measures ("exposure bias") and the study population ("population bias").
Bias checklists were prepared for each study, highlighting information that might be relevant in the assessment of each of the possible internal and external biases. To ensure consistency, biases were identified by the same subject-matter specialist together with one statistician for each study.
Common scale for study results
The studies expressed the association between baseline DED and change in adiposity differently, with a mix of regression coefficients, summary statistics, odds ratios and p-values. To allow pooling of results it was necessary to transform the associations onto a common metric. From the available information a p-value could be calculated for the association in each study and, using the respective sample size, this was subsequently transformed into a correlation and standard error for each study. Biases were assessed on the correlation scale. To do the calculations we applied a Fisher-transformation to the correlations, the Fisher-transformed correlation being z = 0.5ln[(1+r)/(1-r)] and z having a standard error SE(z) = 1/√ (n-3), where r is the correlation and n is the sample size. The number of SEs z is away from zero is derived from the p-value, thus providing an estimate of z. We back-transformed z to the correlation r in order to present results. The Fisher-transformed and original scales were in fact almost identical in the range - 0.3 to +0.3.
Bias elicitation meetings
Incorporating the bias elicitations into the meta-analysis
The elicited internal biases from each assessor were used to calculate the mean and variance of the total additive and total proportional bias for each study, which were then used to adjust the estimated correlation coefficients and standard errors. The same process was used to adjust these results for the external biases. All calculations used formulae adapted from Turner et al . The results were pooled across assessors, using the median estimate and the median standard deviation; such median pooling corresponds to a "typical" assessor . Finally, the fully adjusted results were combined across studies using random-effects meta-analysis. Statistical heterogeneity was assessed using the I2 statistic , which gives the percentage of variation between the study estimates attributable to true between-study heterogeneity rather than random variation; 0% indicates no heterogeneity. Analyses were conducted using STATA 11.0 (StataCorp 2009. College Station, TX: StataCorp LP).
Study characteristics and extracted results
Table 1 summarizes the six eligible prospective studies on DED and change in adiposity. Three studies included either children [15, 16] or adolescents . The other three studies analyzed male and/or female adults up to 60 years [13, 14, 17], of which one investigated pregnant women . Studies were carried out either in the USA [12, 13, 17] or in Europe [14–16]. Ethnicity was generally representative of the population from the place of study. Initial participant numbers per study ranged from 115 to 2025, while the analyses included between 48 and 1762 participants. Outcome was assessed after approximately 9 months to 7 years follow-up.
DED was assessed by food diaries [14–16], 24 h recalls [12, 17] or a food frequency questionnaire . In three of the six studies DED of food was reported and used as the exposure in the analyses [15–17]. Two studies reported DED of food and energy-containing beverages [12, 13] and one study DED of food and all drinks . In four studies change in body weight from baseline to follow-up was reported as the outcome [12–14, 17], while two studies used the follow-up FMI [15, 16]. With the exception of the study by Savage et al.  that presented unadjusted results, the estimated prospective association between DED and adiposity was adjusted for confounding factors. Depending on the study these included sex, age or Tanner stage, a baseline measure of body composition, energy intake and macronutrients or fiber intake, socioeconomic status, smoking and physical activity or inactivity.
Correlation coefficients of studies calculated from p-values according to the principal results extracted
Study (source for extracted results)
Model & results
Butte et al (Table 2) a
GEE: β = 0.23; SE = 0.35; p = 0.5
Deierlein et al (Table 2) b
Quartile mean differences from Q1: Q2 0.49; CI - 0.4,1.37; Q3 1.13; CI 0.24,2.01; Q4 1.08; CI 0.20,1.97
Iqbal et al (Table 4) c
LM;β- 13.49; SE = 36.46; p = 0.711
Johnson et al (Table 3, Model 4)
GLM; OR = 1.36; CI 1.09,1.69
McCaffrey et al (Table 6, Model 2)
GLM; OR = 2.16; CI 1.099, 4.25; p = 0.026
Savage et al (Text) d
Tertile means: T1 2.5, SD = 6.8; T2 4.8, SD = 9.2; T3 6.4, SD = 6.5
Important internal additive biases identified in the studies
Butte et al 
□ No information about immediate drop-outs; □ Recruitment not random.
□ 51 drop-outs, 81 exclusions from the analysis; □ Unclear whether drop-outs and exclusions differ from completers
□ Inappropriate adjustment; □ No stated justification for using confounders; □ Tanner stage assessed by self-report.
Deierlein et al 
□ Selections of clinics unclear.
□ ~12% losses to FU; □ ~30% exclusions from the analysis, who differ from completers.
□ Inappropriate adjustment; □ Self-reported pregravid BW; □ Assessment time unclear.
Iqbal et al 
□ Few inclusion, exclusion criteria&details of the original study cohorts; □ BL measures missing for 13% of the participants, unclear if they differ from those included.
□ Participation rate of 79%; □ 3 exclusions from the analysis.
□ Inappropriate adjustment; □ No stated justification for using confounders; □ Assessment of only leisure time PA; □ Measurement of confounders unclear.
Johnson et al 
□ 52% of children with incomplete datasets (little difference to children with complete datasets).
□ Inappropriate adjustment; □ Self-statement of parental BW and height; □ Time point of assessment of TV watching habits unclear.
McCaffrey et al 
□ Little information on the recruitment strategy, inclusion and exclusion criteria.
□ 58% of children were lost to FU (little difference to completers); □ 2 children were excluded from the analysis.
□ Inappropriate adjustment; □ Tanner stage assessed by self-report.
Savage et al 
□ No data describing the study sample.
□ 88% retention rate; □ Of the 68 women, dietary data were missing for 3, 9&18 women at years 2, 4&6.
□ The extracted model is unadjusted.
External biases were expected because of differences between the source studies and the pre-defined target setting regarding the way the diet was assessed and DED was calculated, the varying outcome measures, differences in the population as well as the follow-up time (Table 1).
This meta-analysis with bias-adjustment allows a quantitative evaluation of the totality of the evidence on the prospective relationship between DED and the change in FMI in children. A previous narrative review reported that decreasing the energy density of the diet may offset weight gain in childhood. However, because of the lack of prospective DED studies, their heterogeneous nature and the difficulties in comparing results presented in different ways, the evidence has not been synthesized quantitatively. This limits the possibility of drawing an overall conclusion and making policy related decisions.
Our analysis provides an overall quantitative synthesis of the evidence-base for decision-makers. The unadjusted results from the six studies gave a combined correlation of baseline DED with change in adiposity of 0.064 (95%CI 0.01, 0.11; p = 0.013). After bias adjustment the association between DED of food and the change in FMI in children for the target setting was 0.17 (95%CI - 0.11, 0.45; p = 0.24). Relative to the unadjusted analysis, the magnitude of the correlation coefficient was increased, indicating the possibility that DED is an important determinant of excess weight gain. However, the confidence interval widened after bias-adjustment, which is due to incorporating the assessors' uncertainty regarding the size of the biases, and implies that higher quality studies are required. The statistical heterogeneity among studies was large in the unadjusted meta-analysis (I2 = 52%), which therefore limits interpretability. The bias-adjustment process eliminated the heterogeneity amongst studies (I2 = 0%). Thus, while the association is no longer statistically significant, the data can now be interpreted with a clearer understanding of the biases. In our view, the magnitude of the correlation provides increased support to policymakers for interventions to reduce DED to prevent obesity in children, and for advice to consumers of the importance of reducing dietary energy density.
The process of bias-adjustment, at the heart of this method, relies on expert opinion and might be considered to be somewhat subjective. We do not claim that the elicited bias distributions are 'correct'; we are dealing with epistemic uncertainty, and they express judgements about our beliefs. However, the opinions of several experts are combined so that individual opinions do not unduly influence the final result of the meta-analysis. The experts were chosen for their quantitative or subject-matter skills, and we prefer to incorporate their judgements rather than simply ignore the suspected biases in the studies available. In addition, consistency across studies and transparency is ensured by the very structured and systematic process of bias-adjustment. Although some opinions on biases varied between the assessors, the differences were in general quite small (Figure 2) and mainly related to the width of intervals reflecting different levels of uncertainty about the effect of the biases. Hence, the adjusted estimates for individual assessors were similar to the pooled adjusted estimate (Figure 3).
A similar bias-adjusted meta-analysis has already been conducted for a systematic review of prospective observational studies of physical activity and subsequent gain in fat mass in children . This method may also be more widely applicable for evidence synthesis across a range of other areas in the population health sciences where studies often cannot be pooled in conventional meta-analyses due to their heterogeneity and differences in design and quality.
This bias-adjustment meta-analysis allowed quantitative synthesis of the prospective association between DED and change in adiposity in children. The result indicates that DED may be an important dietary determinant of unhealthy weight gain in children. Our analysis emphasizes the need for higher quality studies with more precise measurements of dietary intake and body composition and presentation of adequate analyses.
We are very grateful to Dr Laura Johnson and Dr Nita Forouhi for contributing to the external bias elicitation. This project was funded by the UK Medical Research Council Population Health Sciences Research Network grant number 27. The funding body had no role in the decision to publish this article.
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