Given the global increase in obesity( Reference Ng, Fleming and Robinson 1 ), considerable effort has gone into determining the predictors of energy intake. These predictors include fat-free mass( Reference Blundell, Caudwell and Gibbons 2 ), psychological self-control and food drive( Reference Vainik, Dagher and Dubé 3 , Reference Dagher 4 ), socio-economic status( Reference Buckeridge, Charland and Labban 5 , Reference Harris, Perreira and Lee 6 ) and various environmental features( Reference Cohen and Farley 7 , Reference Wansink 8 ). All these research fields depend on the crucial assumption that energy intake is correctly measured. For accuracy reasons, these studies often expend effort to objectively measure energy intake in the laboratory or find other methods of indirect energy expenditure assessment( Reference Buckeridge, Charland and Labban 5 ). Although collecting such subjective energy intake (sEI) with questionnaires is considerably easier and cheaper, such data tend to be misreported, and are therefore often considered unreliable.
Misreporting can be observed when calculating the energy balance percentage (EB%) – that is, how well does energy intake match with total energy expenditure (TEE)? When calculating the EB% for sEI (sEI/TEE×100), many findings show that sEI tends to be under-reported in adults( Reference Livingstone and Black 9 ) and also in children( Reference Livingstone, Robson and Wallace 10 ). This phenomenon has been clearly established using very large data sets( Reference Archer, Hand and Blair 11 , Reference Börnhorst, Huybrechts and Ahrens 12 ). Under-reporting is particularly prevalent in adolescents, with 14–52 % of sample under-reporting( Reference Livingstone, Robson and Wallace 10 , Reference Noel, Mattocks and Emmett 13 ). The EB% can be predicted from several external variables, ranging from simple BMI( Reference Livingstone, Robson and Wallace 10 ) and demographic factors( Reference Börnhorst, Huybrechts and Ahrens 12 ) to brain activation to food stimuli( Reference Stice, Palmrose and Burger 14 ). Studies in adults add additional factors such as dietary restraint and social desirability (( Reference Tooze, Subar and Thompson 15 ), reviewed by Macdiarmid & Blundell( Reference Macdiarmid and Blundell 16 )). However, very few studies have focused on providing practical advice on how to handle inaccurate sEI data( Reference Huang, Roberts and Howarth 17 – Reference Mendez, Popkin and Buckland 19 ), and only one previous study has focused on this question in children( Reference Börnhorst, Huybrechts and Hebestreit 20 ).
The study by Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ) explored various approaches to recover a missing association between obesity and sEI (dietary recall) data in children. They first divided subjects into three groups of diet reporting accuracy – under-reporters (UR), plausible reporters (PR) and over-reporters (OR) – on the basis of discrepancy between energy expenditure and energy intake. Next, they tested various recovery approaches such as restricting analysis only to PR groups, stratifying analysis by reporting group or controlling for co-predictors of misreporting. They concluded that the best approach for recovering an association between BMI and energy intake is to control for predictors of misreporting, rather than excluding misreporting groups( Reference Börnhorst, Huybrechts and Hebestreit 20 ).
What was not evident in the study by Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ) is that excluding misreporting groups can generate artificial positive bias in later analyses. For instance, Mendez et al.( Reference Mendez, Popkin and Buckland 19 ) compared various methods for restricting adult sEI data to PR and then related that restricted sEI data to BMI. They concluded that some methods generate a higher effect size between sEI and BMI than others, recommending the ones with higher effect size. Rhee et al.( Reference Rhee, Sampson and Cho 21 ) recently re-analysed that data and suggested that the effect size increase likely occurs because of selection bias. Selection bias is well known in the field of epidemiology but can be hard to detect( Reference Greenland and Pearl 22 – Reference Elwert and Winship 24 ). Selection bias happens when the dependent variable is conditioned on a variable that partly relates to the independent variable. Using the case of Mendez et al.( Reference Mendez, Popkin and Buckland 19 ) and Rhee et al.( Reference Rhee, Sampson and Cho 21 ) as an example, the dependent variable (sEI) is restricted to PR using a formula that depends on body mass, and then sEI is related to BMI, which also depends on body mass. Rhee et al.( Reference Rhee, Sampson and Cho 21 ) demonstrated that when there was no selection bias, focusing on PR was reasonable. An example would be associating sEI with variables that do not relate to body mass, such as prospective BMI change or various biomarkers( Reference Rhee, Sampson and Cho 21 ). In the follow-up discussion, Mendez( Reference Mendez 25 ) acknowledged that not all methods for correcting sEI work as expected, and both Mendez( Reference Mendez 25 ) and Rhee & Willet( Reference Rhee and Willett 26 ) underlined that a better understanding of misreporting correction methods is needed.
The present study seeked to integrate evidence from adults( Reference Rhee, Sampson and Cho 21 ) and children( Reference Börnhorst, Huybrechts and Hebestreit 20 ) to study the optimal method of handling sEI data in adolescents. The main goal was to replicate the exploratory results of Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ) and extend them in several ways. First, as the effects between BMI and calories consumed are small, the current study focused on a relatively new finding that the amount of calories consumed is determined by fat-free mass( Reference Blundell, Caudwell and Gibbons 27 – Reference Fearnbach, Thivel and Meyermann 29 ). This association has been tested previously, as it is known to have medium effect size (β=0·28–0·42), with objective measures of energy intake( Reference Blundell, Caudwell and Gibbons 27 , Reference Fearnbach, Thivel and Meyermann 29 ). The other extensions compared with Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ) include the additional measure of objective energy intake (oEI) that enables to independently verify the association between fat-free mass and energy intake, a different type of source for sEI data (3-d dietary interview) that tests for generalisibility of the findings, more accurate estimate of TEE by including 7-d accelerometry in the model and extending the set of predictors for misreporting to several psychological predictors. In summary, the current study aimed to test the feasibility, conceptually replicate and extend the statistical approach suggested by Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ). As studies on adults have suggested the emergence of selection bias( Reference Rhee, Sampson and Cho 21 ), we scrutinised the results from that perspective.
Methods
Study population
The present study analysed data from the fourth wave of a larger project ‘Risk factors for metabolic syndrome in boys during pubertal development: a longitudinal study with special attention to physical activity and fitness’( Reference Ivuškāns, Jürimäe and Lätt 30 – Reference Vaitkeviciute, Lätt and Mäestu 39 ). The study was originally started in 2009, where all boys from Grades 3 and 4 from twenty-seven elementary schools in the city and the surroundings of Tartu, Estonia, were invited to participate. All schools were in an urban environment. A total of 313 boys, approximately 84 %, agreed to participate. All participants had no disease that prevented them from taking part in different parts of the study and were allowed to take part in the obligatory physical education classes at school (they had no health-related problems, injuries, etc.)( Reference Lätt, Mäestu and Ortega 34 ). The measurement period of the currently analysed wave was from November 2012 until April 2013.
A total of 190 participants provided accelerometer data and dietary interview (sEI) and body anthropometry data (age:
$$\bar{x}$$
=13·99 (sd 0·69), zBMI:
$$\bar{x}$$
=0·37 (sd 1·29), BMI:
$$\bar{x}$$
=20·91 (sd 4·66)). Responses from psychological questionnaires were available from 128 participants and oEI data from thirty-nine participants. Participants in the subsamples did not differ from participants not within a certain subsample (questionnaire v. no questionnaire; oEI v. no oEI) in terms of age (t(146·4)=−0·19, P=0·851; t(54·4)=−1·28, P=0·205) or zBMI (t(106·8)=0·97, P=0·334; t(66·8)=0·21, P=0·832), suggesting that the subsamples were a random part of the bigger sample.
Participants recorded their 72-h sEI for 3 or more days before onsite testing. Participants were asked to abstain from breakfast before coming to the test site at approximately 08.00 hours. As participants had to be picked up from school, sometimes kilometres away from the testing site, they arrived in groups of four to eight. The overall study design is presented in Table 1.
Summary timeline of the study
* For measurements included in the current study, see the ‘Anthropometry’, ‘Questionnaires’ and ‘Dietary data’ sections for details. No higher timing precision was possible, as boys participated in onsite testing session in groups because of the way they were transported onsite.
All participants completed various questionnaires about their health habits. A subset of the sample also completed various questionnaires related to personality and eating behaviours. All participants had to eat breakfast at the spot; in a subset of participants, their intake was also weighted.
This study was conducted according to the guidelines laid down in the Declaration of Helsinki, and all procedures involving human subjects/patients were approved by the Medical Ethics Committee of the University of Tartu. All children and parents were thoroughly informed of the purposes and contents of the study, written informed consent was obtained from the parents before participation, and the children provided their verbal assent.
Anthropometry
The participants’ body height and mass were obtained on the 1st day of the measurements. Body height was measured in standing position to the nearest 0·1 cm using a Martin metal anthropometer. Body mass was measured with minimal clothing using a medical balance scale (A&D Instruments) to the nearest 0·05 kg. BMI (kg/m2) was calculated as body mass divided by the square of body height. BMI is shown for informative purposes; the analysis was conducted with zBMI that corrects for developmental effects, created using World Health Organization scripts( 40 ). The boys’ weight status was categorised according to zBMI cut-off values. The biological age of the participants was assessed according to a self-assessed illustrative questionnaire of the pubertal stage according to the Tanner classification method by evaluation of pubic hair( Reference Marshall and Tanner 41 ).
Body composition: fat mass and fat-free mass were measured using dual-energy X-ray absorptiometry (DXA; DPX-IQ densitometer, Lunar Corporation) equipped with proprietary software (version 3.6). Boys were scanned in the supine position wearing light clothing. The medium scan mode and the standard subject positioning was used for total body measurements, which were analysed using the extended analysis option. To reduce the impact of the operator variability factor, one qualified observer analysed all scans over the 2-year period. The CV for these body composition measurements were <2 %; this was established in our laboratory using duplicate measures in twenty boys of the same age. Fat mass and fat-free mass correlated at 0·24, P=0·001.
Objectively measured physical activity was assessed using an accelerometer (GT1M ActiGraph) that was worn for 7 d on the right hip. The accelerometer was programmed to record activity counts in 15-s epochs, and non-wearing time was defined as ≥20 consecutive minutes of zero counts and was not included in the analysis. Data from the accelerometer were included for further analysis if the subject had accumulated a minimum 8 h of activity data/d, for at least 1 weekend day and 2 weekdays. In the final sample, the median number of valid weekend days was 2, and the median number of valid weekdays was 5. Other details of the accelerometer procedure and data processing have been described elsewhere( Reference Rääsk, Konstabel and Mäestu 35 , Reference Rääsk, Lätt and Jürimäe 36 ). In the present study, we used counts per min as an indicator of total physical activity. In a previous study, a similar analytic accelerometer approach together with body mass was able to predict doubly labelled water-based TEE with R 2 of 0·82, se of estimate 0·49, prediction error 0·28( Reference Ojiambo, Konstabel and Veidebaum 42 ) (Table 3).
Regression coefficients of fat-free mass predicting objective energy intake or subjective energy intake, accounting for participant’s age
* Regression diagnostics found one potentially influential outlier in this model (Cook’s distance=0·29, standardised residual=2·09). Without that outlier, the effect of fat-free mass would be β=0·64, B=3·58, se=0·91, t=3·91.
† These variables have been log-transformed to normalise distributions.
Questionnaires
We included several questionnaires that we suspected could influence EB%( Reference Tooze, Subar and Thompson 15 ).
The Eating Disorders Assessment Scale (EDAS( Reference Akkermann, Herik and Aluoja 43 )) is a twenty-nine-item, self-report questionnaire with four subscales: restrained eating, binge eating, purging and preoccupation with body image and body weight. These subscales show good internal consistency and discriminant validity. The construct validity of the questionnaire has been confirmed by strong correlations with Eating Disorders Inventory−2 Estonian version( Reference Podar, Hannus and Allik 44 ). In the current analysis, we used the binge eating subscale and restraint subscale, as these are the two main eating behaviour dimensions( Reference Vainik, Dagher and Dubé 3 , Reference Price, Higgs and Lee 45 ), and the current instrument assesses these behaviours in a continuous manner. The binge eating subscale is very similar to other known measures of loss of control over food( Reference Price, Higgs and Lee 45 , Reference Vainik, Neseliler and Konstabel 46 ), and loss of control over food is hypothesised to partly reflect reward sensitivity to food( Reference Price, Higgs and Lee 45 , Reference Epel, Tomiyama and Mason 47 ).
Social desirability was estimated from responses to Estonian Brief Big Five Inventory( Reference Laidra, Allik and Harro 48 ). This is a brief measure of personality based on the example of ‘Common Language’ California Child Q-Set( Reference John, Caspi and Robins 49 ). The scale assesses basic personality dimensions (neuroticism, extraversion, openness, agreeableness and conscientiousness) with eight items each on a five-point Likert-type scale, and has been previously validated in an adolescent sample( Reference Laidra, Allik and Harro 48 ). In the current analysis, we used previously measured social desirability scores of the items (unpublished data) to calculate a general tendency for responding in a socially desirable manner, ranging from −1 to 1. The methodology is described elsewhere( Reference Konstabel, Aavik and Allik 50 ).
Dietary data
sEI data were self-recorded. Before study start, participants were asked to record everything they ate during 2 weekdays and 1 weekend with the help of their parents. Participants were asked to observe their food intake as closely as possible before the testing day. During the testing day, participants brought their written summary of the 3 d, based on which they were interviewed by a trained nutritionist. The nutritionist helped in recalling possible forgotten energy items and entered the energy items into an energy database that automatically calculated relevant energy( Reference Pitsi, Kambek and Jõelecht 51 ). From that we estimated their average energy intake (MJ) per day as an indicator of sEI.
oEI data were measured once in a subset of the sample during morning snacking on the day of testing. The main goal of the snacking was to provide participants with an opportunity to recover from morning fast before various other measurements were obtained. In the current analysis, the oEI data provided an opportunity to verify independently that energy intake is related to fat-free mass. Clearly, the oEI meal was not the same as the previous meals, based on which sEI data were reported. At the same time, previous evidence has shown that the association between fat-free mass and energy intake is robust – it is present both for individual meals( Reference Fearnbach, Thivel and Meyermann 29 ) and for energy intake aggregated across a full day( Reference Blundell, Caudwell and Gibbons 27 ). Therefore, this single meal data were used to verify the association between fat-free mass and energy intake in this sample. Because of the study design, offering wide range of foods was not feasible; the participants were provided the following easy-to-handle foods: a Mars bar (1·89 MJ, 451 kcal) or Snickers bar (2·13 MJ, 509 kcal), a pack of cookies (1·81 MJ, 432 kcal) and a 0·5-litre bottle of juice (0·17 MJ, 41 kcal). After the participants had stopped eating, they were asked to leave the remaining food on the table. The remaining food was weighted using a Soehnle Attraction kitchen scale (Leifheit AG), with 1 g precision, and weight was converted to energy on the basis of nutritional information on the packaging. Number of total MJ consumed was the indicator of oEI.
Statistical methods
TEE (MJ) was estimated from weight and accelerometer data. The estimators were obtained from a validation analysis where body mass and accelerometer data could explain 81–82 % of TEE expenditure in children, estimated with doubly labelled water( Reference Ojiambo, Konstabel and Veidebaum 42 ). Although the validation sample was younger than the current sample, we are unaware of other validation studies that would provide estimations more suitable for the current sample. The formula is provided by the second author; it was inadvertently not published in the original article( Reference Ojiambo, Konstabel and Veidebaum 42 ):
$$\rm TEE\,\equals\,0\! \cdot\! 722\, \plus \, weight \, \times \, 0\! \cdot\! 160 \,\plus \, 0\! \cdot\! 003\, \times \, counts/min. $$
We compared the formula-based TEE with TEE derived from equations developed by Brooks et al.( Reference Brooks, Butte and Rand 52 ) that were based on age, weight, height and physical activity level. Physical activity level was converted from estimates of moderate-to-vigorous physical activity( Reference Noel, Mattocks and Emmett 13 ) based on accelerometry data. The two TEE estimates correlated very highly (r 0·97).
To detect UR and OR, energy balance percentage (EB%) was derived from the formula sEI/TEE×100. A common method to detect misreporting is to classify participants as UR or OR if they deviate more than ±1 sd from 100 %. The particular sd values are derived from a formula that accounted for intra-individual variation in energy intake (CV adjusted for age), day-to-day variation (here 3 d) and energy requirement predictor errors( Reference Noel, Mattocks and Emmett 53 ). We used the approach of Noel et al.( Reference Noel, Mattocks and Emmett 13 ) who provided updated CV for boys <14 and ≥14. As a result, the cut-off values for younger and older age groups for under-reporting were 85·675 and 85·798 % and the values for over-reporting were 114·325 and 114·202 %, respectively.
We first tested whether fat-free mass would predict oEI, in attempt to replicate previous findings( Reference Blundell, Caudwell and Gibbons 27 , Reference Fearnbach, Thivel and Meyermann 29 ) using linear regression, correcting for age. Next, we used a similar regression model to test whether fat-free mass would predict sEI. Thereafter, we tried various correction methods such as excluding UR and OR, controlling for dietary group status in the regression analysis and adding predictors of EB% to the regression. Predictors of EB% were chosen among variables suggested by previous studies (see first paragraph for an overview). These predictors included BMI, psychological traits such as restraint, binge eating and responding to a personality questionnaire in a socially desirable manner.
In the last model, we used multiple imputation to overcome the issue that anthropological data were available for the full sample (n 190) but psychological predictors were available only for a subset of the sample (n 128). When these predictors are used together in a regular multiple regression model, the models would use list-wise data deletion, which would have considerably reduced the statistical power of anthropological measures. Multiple imputation( Reference Schafer 54 ), in turn, creates multiple versions of the data set. In each data set, missing values are drawn from a plausible distribution. Each of the imputed data sets was analysed separately, and then the results were aggregated. In this case, we created 100 imputed versions of the data set using Amelia package( Reference Honaker, King and Blackwell 55 ). These data sets were analysed and aggregated with the mice package( Reference Buuren and Groothuis-Oudshoorn 56 ), relying on small-sample method to calculate aggregate df( Reference Barnard and Rubin 57 ).
As can be seen in the results, we recovered an unexpectedly strong association between fat-free mass and sEI when focusing only on PR (e.g. β=0·77, model 2 in Table 4). This suggests the emergence of selection bias. To test for selection bias, we re-sampled sEI data – every participant randomly received another participant’s sEI value. Different reporting groups (UR, PR, OR) were re-identified using the same method as mentioned above. Thereafter, we re-ran previously tested regression analyses. As re-sampled data are equivalent of random noise, no variable should be able to predict re-sampled data. However, if some variables are able to predict the re-sampled data, the prediction can be considered to be an artifact arising from correction methods or selection bias.
Fat-free mass predicting subjective energy intake across different approaches that adjust for misreporting*
UR, under-report; OR, over-report; EDAS, Eating Disorders Assessment Scale.
*The reference group in the ‘adjusting for group’ model provided plausible reports. Data were re-sampled by assigning each participant an energy intake value of another participant. Model 4 is based on the multiple imputation procedure (see the ‘Statistical methods’ section for details).
†These variables have been log-transformed to normalise distribution.
To explore how selection bias can influence the results, we simulated the study data 10 000 times to demonstrate a robust replication of the artifact. We further explored the extent of selection bias by varying the association strength between variables in the simulation. The code used to simulate the data is provided in the online Supplementary Material.
All analyses were conducted in R environment 3.2.3( 58 ), occasionally relying on ‘plyr’, ‘plotrix’, ‘truncnorm’, ‘MASS’, ‘Amelia’ and ‘mice’ packages( Reference Honaker, King and Blackwell 55 , Reference Buuren and Groothuis-Oudshoorn 56 , Reference Wickham and Francois 59 – Reference Trautmann, Steuer and Mersmann 62 ), as well as online resources( Reference Wagenmakers and Gronau 63 ). Variables that displayed non-normality based on the Shapiro–Wilk test and observing histograms were transformed to log scale. To avoid values taking log of 0, +1 was added to all EDAS scores when represented in the log form.
Regression diagnostics were first conducted by scrutinising the residuals for normality, homoscedasticity and linearity. No visual violations were found. Thereafter, we analysed whether any model would have standardised residuals higher than values usually expected based on typically used criteria. For instance, <5 % of observations should have standardised residuals above 1·95. Similarly, <1 % of observations should have standardised residuals >2·58, and <0·1 % of observations should have standardised residuals >3·29( Reference Field 64 ). Occasionally, some models were borderline (e.g. 5·3 % of observations had standardised residuals above 1·96). These borderline models were inspected further with visual analysis( Reference Fox 65 ). Visual analysis was based on Cook’s distance plots that were inspected for potential outliers – that is, we looked for data points that would have significantly higher Cook’s distance than other variables. Only in one analysis, such an outlier was found (see the ‘Associations between fat-free mass and energy intake’ section). However, as removing that outlier did not change the general model, all data points were retained. In the multiple imputation analysis, five randomly drawn regression analyses from the 100 analyses conducted were inspected for outliers.
Results
Descriptive variables
Plotting of EB% data revealed that under-reporting was widespread – 74·2 % of the participants under-report their sEI (Fig. 1). Table 2 summarises various descriptive statistics for the whole sample, as well as for each subgroup. Expectedly, the reporting groups differed in sEI. Compared with the median intake of PR, the median intake of under-reporters was 67 % and the median intake of OR was 127 %. At the same time, the groups had no difference in oEI, suggesting that the group differences in sEI were due to the EI measurement method. Regarding physiological variables, the groups differed in terms of BMI, zBMI, fat mass, fat mass index, fat-free mass and fat-free mass index. From psychological measures, the only difference was observed in restraint. However, restraint correlated with zBMI (r 0·42, P<0·001) and fat mass (r 0·42, P<0·001). As many variables displayed non-normality, their log-transformation values have been used in all reported correlation and regression analyses.
Histogram of different energy balance percentages. PR, plausible report; OR, over-report; UR, under-report. ----, Cut-off values of the younger group (see the ‘Statistical methods’ section for details). Tick marks (|) represent actual values, jittered with a factor of 1. When TEE was estimated with the Brooks et al. method( Reference Brooks, Butte and Rand 52 ), the diet group prevalence percentages were as follows: UR=80·5 %, PR=14·7 % and OR=4·7 %.
Descriptive analyses of variables stratified by reporting group and differences between the reporting groups tested with ANOVA or the Kruskal–Wallis rank sum testFootnote *( Means and standard deviations)
TOT, total sample; UR, under-report; PR, plausible report; OR, over-report;
$$\bar{x}$$
, mean; Md, median; sEI, subjective energy intake; oEI, objective energy intake; EDAS, Eating Disorders Assessment Scale.
* The Kruskal–Wallis rank sum test was applied on counts of participants in body weight category or Tanner stage.
† Non-normal variables. The median and range are reported in parentheses. In addition, these variables were log-transformed during ANOVA testing to obtain a distribution closer to normality.
‡ Reduced sample: TOT (n 39), UR (n 27), PR (n 10), OR (n 2).
§ Reduced sample: TOT (n 128), UR (n 91), PR (n 30), OR (n 7).
Associations between fat-free mass and energy intake
The results demonstrated that participants indeed chose the amount of food based on their fat-free mass, as suggested by Blundell( Reference Blundell, Caudwell and Gibbons 27 ). The association was clear for oEI but was considerably weaker for sEI (Table 2, Fig. 2, online Supplementary Fig. S1). Given that sEI was mostly under-reported (Fig. 1), the current results highlighted the need for a method for correcting varying EB% (Table 3).
Fat-free mass associations with objective (left) and subjective (right) energy intake. Objective energy intake was measured on the same day, whereas subjective energy intake was assessed from dietary interview from an earlier period of 3 d. Data not corrected for the effects of age. For illustrative purposes, variables here are not log-transformed. For log-transformed plots, see the online Supplementary Fig. S1.
Methods that adjust for misreporting
In Table 4, the left column summarises the results for different methods. As expected from Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ), the plain model (model 1) had the poorest explanatory power and R 2, and the model adjusting for predictors of EB% (model 4) was considerably better than model 1 by restoring the beta value closer to what was expected from oEI data and from previous studies. Intriguingly, excluding under- and OR (model 2) or controlling for dietary groups (model 3) seemed to provide even better results. Both models had very high R 2, and model 2 had very high standardised β. Do these results imply that these methods are even better?
To test for potential method artifacts, we used the re-sampling procedure – every participant received a random sEI value of another participant. We expected that all models (Table 4, right column) should have non-significant results, as fat-free mass was predicting essentially noise. Indeed, the simple model (model 1) and the model adjusting for predictors of EB% (model 4) had R 2 <0·01 (Fig. 3, dashed line; Table 4, right column). However, the models based on dietary groups created from re-sampled sEI (models 2–3) still showed a strong effect (Fig. 3, dashed line; Table 4, right column). This suggests that group-based methods are unsuitable for the current purposes; there was an association between sEI and fat-free mass, even though the groups were created based on re-sampled sEI data and both diet reporting groups and sEI itself should not be informative. The scatter plots of models 1 and 2 for actual and simulated data are shown in the online Supplementary Fig. S2. Together, these results suggest that grouping methods are unsuitable for recovering the association between sEI and fat-free mass.
Graphical comparison of the standardised regression coefficients (β) of actual data (
) and re-sampled data (----). Initial observation of β in the actual data suggests that the association between fat-free mass and subjective energy intake (sEI) can be best recovered with data exclusion or group adjustment strategies (models 2 and 3). However, these strategies also show an effect in re-sampled data, where no effect should be present. Models 1 and 4 correctly show no effect in re-sampled data. Therefore, adjusting for predictors (model 4) is the most viable approach when recovering an association between fat-free mass and sEI. Re-sampled data were obtained by assigning each participant an energy intake value of another participant. Errors bars denote standardised standard errors, obtained by standardising the variables and re-computing the regressions in Table 4. sEI was assessed from a dietary interview from an earlier period of 3 d.
Possible causes of method artifacts
A possible reason as to why the sEI and fat-free mass association appears in models 2 and 3 is selection bias; fat-free mass relates to the variables used to create the diet reporting accuracy groups. Namely, the diet reporting groups are generated based on EB% – that is, the sEI:TEE ratio. In the current sample, TEE was highly dependent on participants’ body mass (see formula in the ‘Statistical methods’ section, r 0·98), and body mass correlates highly with fat-free mass (r 0·72, P<0·001). Indeed, fat-free mass correlates with TEE (r 0·71, P<0·001). Therefore, restricting re-sampled sEI data to a PR group that has an EB% from 85 to 115 could create an association between re-sampled sEI and fat-free mass (models 2 and 3 in Fig. 3). In contrast, when all re-sampled sEI data were used in the analysis, the re-sampled sEI and fat-free mass were not related (models 1 and 4 in Fig. 3).
The artificial emergence of the association between sEI and fat-free mass is illustrated in Fig. 4. Although we were interested in the direct relationship between fat-free mass and sEI (upper pathway), restricting sEI to PR created an indirect association between fat-free mass and sEI through body mass/TEE (lower pathway). This indirect association occurred because fat-free mass correlates with body mass, and body mass-based TEE defined the PR group in sEI. Even when whole sample is used, but the dietary restriction groups are used as covariates, one can still observe a similar bias (model 3 in Table 4 and Fig. 3, Fig. 5).
A summary of the direct and indirect pathways of how fat-free mass is associated with subjective energy intake (sEI). The direct effect between fat-free mass and sEI is of main interest. However, when sEI data are restricted to plausible reporters (PR), then this creates a selection bias – a secondary association between fat-free mass and sEI because fat-free mass is part of body mass, which defines total energy expenditure (TEE). TEE, in turn, defines the PR group. When the analysis does not account for the indirect pathway, the effect estimate of the direct pathway gets amplified.
The effect of restricting variance based on a partly related variable on standardised regression using simulated data. The expected standardised association (β) between fat-free mass (FFM) and energy intake (EI) is zero, and full sample data show this (
with 
). ----, Same analysis in case the analysis focused only on plausible reporters (---- with 
, as in model 2) or in case a variable with dietary groups was added as a covariate (---- with 
, as in model 3). In the latter two cases, the artificial association varied as a function of the associated strength between total energy expenditure (TEE) and fat-free mass. Data simulated on 10 000 participants, 10 000 times. Variables have similar properties as actual data in terms of distribution. For precise parameters, see the online Supplementary Material. Error bars denote 95 % CI (standard errors multiplied by 1·96). See the online Supplementary Fig. S3 for non-standardised regressions and the online Supplementary Material for R script used to generate the data. EB%, energy balance percentage.
To demonstrate the causal role of this sample restriction pathway, we created a simulation where we varied the correlation between fat-free mass and TEE. Namely, we created normally distributed variables with similar properties as actual data on 10 000 people. This included TEE and fat-free mass that correlated between 0 and 0·90 and EI, which in simulation did not correlate with any variable. We skipped body mass in the simulation, as it had high correlation with TEE (r 0·98). Thereafter, we calculated EB% (EI/TEE) and the association between fat-free mass and EI using full data and by creating dietary reporting groups, which were used for restricting the sample to PR (like model 2) or using dietary reporting groups as covariates (like model 3). Under-reporting was defined as EB% <85 %, plausible reporting was defined as EB% ranging from 85 to 115, and over-reporting was defined as EB% >115. The whole procedure was repeated 10 000 times to test for robustness.
As can be seen in Fig. 5, the association between fat-free mass and EI is absent with complete data (solid line, filled circles). At the same time, restricting data to PR (dashed line, empty circles), or using dietary group variables as control variables (dashed line, empty diamonds), created an artificial association between EI and fat-free mass. The association magnitude depended on the correlation between fat-free mass and TEE, and as that correlation decreased the artificial association between EI and fat-free mass decreased. Nevertheless, the artificial association was present even at the smallest non-zero correlation (r 0·15). This demonstrates that the dietary group variable approaches would be appropriate only when the fat-free mass and TEE correlation is zero. See the online Supplementary Fig. S3 for non-standardised regressions. Scripts used for simulations are available in the online Supplementary Material.
Discussion
We compared three approaches to control for misreporting of sEI in adolescent boys – exclusion of misreporting groups, controlling for misreporting group status and statistically correcting for misreporting using external predictors of EB%. Our analysis confirmed the exploratory conclusion of Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ) that if children’s energy intake based on sEI data is related to other variables the sEI should be statistically corrected for misreporting using separate predictors of EB%. Such statistical correction recovered an association between fat-free mass and sEI, an association that was expected from both previous studies and oEI data. We further demonstrated the dangers of other approaches that exclude misreporting groups or statistically control for dietary group status; in our analysis, these approaches created selection bias that artificially boosted the expected association between fat-free mass and sEI.
Although exclusion of UR and OR has been suggested previously as a useful technique( Reference Huang, Roberts and Howarth 17 , Reference Mendez, Popkin and Buckland 19 ), our data suggest that plausibility of dietary interviews does not make the data more correct. Instead, focusing on plausible data might produce artifacts – creating an artificially strong association between sEI and fat-free mass. A likely reason is selection bias – fat-free mass relates to the body mass of a participant, and body mass is used to estimate TEE, on which the dietary groups are based (see formula in the ‘Statistical methods’ section, Fig. 4). If then participant range is restricted to a narrow range of plausible sEI values based on the sEI:TEE ratio, an artificial association emerges between sEI and fat-free mass. Our simulations showed that a detectable contamination is present even when the fat-free mass would relate to TEE only at 0·15. Similar to Rhee et al.( Reference Rhee, Sampson and Cho 21 ), our simulation showed that using a narrow range of PR is only reasonable when the predictor of sEI has a correlation of zero with TEE. However, this zero correlation can be difficult to achieve, as TEE has multiple components (BMR, body mass and physical activity), and many physiological variables tend to be related. Therefore, the zero correlation between TEE and predictor of sEI has to be demonstrated before dietary groups-based correction methods are used. To be on the safe side, we suggest using external predictors of EB% to correct sEI instead of approaches based on dietary groups.
The current results also highlight the usefulness of data re-sampling. Selection bias or any other bias can be difficult to detect, because understanding indirect associations between physiological variables can be a complex task. Data re-sampling provides a quick and simple test to check, whether the used data correction mechanism has created artifacts – an association that is different from zero. If a correction procedure creates an association between two variables, which should have zero association as one of them is random noise, then this correction mechanism should not be used.
Simulation provides further opportunities to test the mechanism of the artifact. In this case, we suspected that a correlation between a predictor variable (fat-free mass) and a variable used for determining PR (TEE) could cause selection bias – that is, overestimation of effect size. Simulation provided an opportunity to test how the overestimation would change with different correlation magnitudes between fat-free mass and TEE. Such testing is difficult in real data, as various types of predictors have to be available (although see Rhee et al.( Reference Rhee, Sampson and Cho 21 ) for an example). On the basis of simulation, we now know that even a small correlation between fat-free mass and TEE would have caused a selection bias and overestimation of the sEI–fat free mass association’s effect size.
The current study once again documented high under-reporting in adolescents. While the current high estimate (76 %) might be lower when a different sEI estimation method is used( Reference Mendez, Popkin and Buckland 19 , Reference Rhee, Sampson and Cho 21 ), the adolescent under-reporting problem is still widely known from previous literature. The under-reporting mechanism is hard to capture – ‘the detection of under-reporting does not automatically reveal the process responsible’( Reference Macdiarmid and Blundell 16 ). A previously outlined reason could be that the task of tracking food for 3 d could be cognitively too demanding for adolescents( Reference McPherson, Hoelscher and Alexander 66 ). They might forget food items or not comply with the task. However, current data cannot provide evidence to the reasons for under-reporting. To properly understand the mechanisms of under-reporting, future research should simultaneously measure both sEI and oEI( Reference Stubbs, O’Reilly and Whybrow 67 ) for the same meals, and experimentally manipulate or randomise possible mechanisms, such as perception bias( Reference Chandon and Wansink 68 ) or cognitive ability.
Intriguingly, controlling for predictors of EB% recovered the fat-free mass and sEI association rather well. Although the association between fat-free mass and oEI was even stronger (β=0·51), oEI was measured only for a single meal. Single meal association with fat-free mass has been similarly strong previously (r 0·42, 0·29). sEI at the same time was assessed for 3 d and averaged for a single day. On the basis of previous studies, one could expect that the association between fat-free mass and full day EI ranges between β=0·28 and 0·33( Reference Blundell, Caudwell and Gibbons 27 ). In the current study, the corrected effect size was β=0·35, which is surprisingly close. At the same time, such success might be the peculiarity of the current sample and has to be replicated.
The current study has several limitations. Our study group included adolescent boys, and therefore the effect sizes seen pertain to this study group. At the same time, our empirical data and simulations show that the basic principle of selection bias should remain, and that statistical correction using external predictors of EB% is likely the best approach. We were unable to obtain data from questionnaires and oEI from all participants. However, groups with and without more detailed data did not differ in terms of basic sample statistics (Table 1), suggesting that this is not a major concern. oEI and sEI were based on different measurements – sEI was based on 3-d self-observed dietary records, whereas oEI was based on one breakfast comprised of convenience food, which is likely not the most optimal choice of food. Further, as we captured only one meal for oEI, we were unable to evaluate the EB% for oEI. Nevertheless, replicating previously known findings that current oEI can be predicted by fat-free mass allowed us to be certain that oEI was measured reasonably well. However, future studies should have (a) more naturalistic food and (b) oEI and sEI data should be based on the same food consumed; people should report what they ate at the same time their eating habits are objectively captured (e.g. Stubbs et al. ( Reference Stubbs, O’Reilly and Whybrow 67 )). Finally, TEE was somewhat imprecise, as it was estimated from an equation, as opposed to measuring actual resting metabolic rate. Measuring actual resting metabolic rate could have decreased the association between TEE and fat-free mass, decreasing the size of the artifactual association between sEI and fat-free mass, if only PR are considered. Similarly, the TEE equation was derived from a younger sample than the current study sample, possibly making the TEE less accurate. Nevertheless, our simulations showed that any association between fat-free mass and TEE would have caused artifacts, when sEI is related to fat-free mass in a subsample of PR; therefore, despite the inaccuracies in TEE measurement, the major conclusion of the paper remains.
The current study also has several strengths, which allowed us to conclude that misreporting of sEI data should be statistically corrected using external predictors of EB%. Compared with Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ), we extended the results in several ways. We related sEI to a different predictor – fat-free mass. The supposed EI and fat-free mass association was first independently verified using oEI data, before we set to recover the association from sEI. Such an approach enabled us to know what type of effect size to look for. For methodological strengths, fat-free mass was objectively measured with DXA, and TEE for EB% was calculated based on objective physical activity. We also extended the previous findings by first using a different measure of sEI, 3-d dietary interview, which ensured that statistical correction applies for multiple measures of sEI. Second, we included various psychological predictors of EB% not included by Börnhorst et al.( Reference Börnhorst, Huybrechts and Hebestreit 20 ). Despite these methodological differences, we reached a very similar conclusion, suggesting the robustness of using statistical correction.
Another strength was the use of several methods to scrutinise the appearance of selection bias. We first re-sampled our analysed data, which should have eliminated any association between sEI and fat-free mass. However, some associations remained, suggesting the existence of selection bias. We further demonstrated the causal role of selection bias by varying association strength between fat-free mass and TEE in a simulation study.
In summary, we suggest that future studies on sEI should plan ahead to include the known predictors of EB% in their data collection procedures. These could include BMI, restraint, social desirability or other relevant variables( Reference Börnhorst, Huybrechts and Ahrens 12 ). Our empirical data and simulation indicated that studying only PR groups can artificially increase the regression coefficient in certain conditions due to selection bias. Until more accurate and easily applicable EI measures are developed, statistically correcting sEI remains the best approach in large-scale studies.
Acknowledgements
The authors thank Triin Rääsk, Maarja Aarlaid and Liisi Panov for helping with data collection, Kairi Kreegipuu and Jüri Allik for their support and Caroline Uhler for pointing us to the selection bias literature. Finally, the authors thank Yashar Zeighami, Selin Neseliler and the three anonymous reviewers for their feedback.
This research was supported by the Estonian Ministry of Education and Science Institutional Grants IUT 20-58 and IUT2-13 and by the Doctoral School of Behavioral, Social and Health Sciences created under the auspices of European Social Fund.
Formulating the current research question(s): U. V., K. K.; designing the study: U. V., E. L., J. M., P. P., J. J.; carrying out the study: U. V., E. L., J. M., P. P., J. J.; analysing the data: U. V.; and writing the article: U. V. All the authors have read and commented on the manuscript.
The authors declare that there are no conflicts of interest.
Supplementary material
For supplementary material/s referred to in this article, please visit http://dx.doi.org/doi:10.1017/S0007114516003317
