Measuring nutrition intake plays a pivotal role in obesity and nutrition studies. However, objectively measuring nutrition intake is not easy. Under natural settings with less restriction, two approaches are often used: self-report and biomarkers. Biomarker approaches are considered more accurate compared with self-report; however, they are typically expensive and require special equipment for each nutrient. Self-report approaches are less expensive and do not require special laboratory equipment or techniques, and can be applied to the measurement of any nutrition components from macronutrients (i.e. carbohydrates, fat, and protein) to micronutrients (i.e. minerals and vitamins); however, self-reported data are known to be fraught with bias (Schoeller et al., 1990; Dhurandhar et al., 2015).

Consider the example of biomarker versus self-report energy intake. Energy intake (EI) is defined as a sum of the total metabolizable energy content of consumed foods and beverages (Astrup, 2005). EI can be measured using biomarkers, especially by energy balance approaches in which respiratory gas analysis or doubly labeled water (DLW) are used for the calculation of energy expenditure (EE) (Ferrannini, 1988). EI can be calculated using EE accounting for change in energy stores (i.e. body composition) during the period of measurement. The respiratory gas analysis typically requires the participants to wear a gas mask or stay in a metabolic chamber (Leonard, 2012), which restricts participants’ behavior; thus, the measured EI using the respiratory gas analysis may not reflect EI from habitual eating behavior. DLW requires the participants to visit the laboratory to drink labeled water enriched with stable hydrogen and oxygen isotopes and collect urine for measurement of isotope levels. It is considered to reflect habitual eating behavior and widely accepted as a standard and reliable approach in measuring EI in free-living individuals (Schoeller et al., 1986; Speakman, 1997; Schoeller and van Santen, 1982). However, given the high cost of isotopes and laboratories to analyze collected urine, DLW is not practical in large-scale epidemiological surveillance (Banna et al., 2017).

EI measured using self-report approaches (EI_SR) is computed by summing up the energy intake from foods and beverages reportedly consumed during the period of measurement, which can commonly range from a day to a year depending on approaches (e.g. 24 hr recall, food diary, and food frequency questionnaire; Leung et al., 2017; Sugiyama et al., 2014; Oftedal et al., 2017). Given that self-report approaches are low cost and scale-up relatively easily, EI_SR is still widely used in epidemiological studies. However, EI_SR is biased compared with the EI measured by biomarker such as DLW (EI_BIO) (Schoeller et al., 1990) and is discouraged from use to estimate actual EI (Dhurandhar et al., 2015). The mechanism behind the reporting bias in EI_SR has been argued elsewhere. For example, EI_SR is computed from the information of reported foods and beverages using tables of food and beverage nutrients, composed of weights, calories, and the amount of macro- and micronutrients. Compositions of foods and beverages are different among brands, stores, and seasons (Martelli et al., 2018), and thus nutrient databases cannot be exhaustive. Consequently, EI_SR using such databases may not be accurate (McHenry et al., 1945). Further factors, including social desirability (i.e. people do not want to be seen as a ‘big eater’ in general) (Heymsfield et al., 1995) and weight/social status (Heymsfield et al., 1995; Johansson et al., 1998; Macdiarmid and Blundell, 1998; Johansson et al., 2001; Klesges et al., 1995), are known to be associated with reporting bias. Thus, the difference between EI_BIO and EI_SR is due to systemic biases rather than a random error.

Despite concerns about the accuracy of self-report approaches, they have been predominantly used in large-scale nutrition epidemiology due to their high feasibility. Approaches to mitigate the bias in EI_SR have been argued, including commonly used approaches to exclude the data of EI_SR that are considered unreliable. For example, one approach is to exclude those reporting EI_SR out of the range considered by the researchers to be plausible, such as from 500 to 3500 kcal/day (Banna et al., 2017). However, this rule does not consider individual variability and is not appropriate for those whose intake is truly above 3500 kcal/day, such as elite athletes or those whose body size is large and requires more than 3500 kcal/day to maintain their weight (Santos et al., 2014; DeLany et al., 2013).

Other approaches are to use EE prediction equations to account for individual variability in EI (McCrory et al., 2002; Huang et al., 2005; Vinken et al., 1999; Livingstone and Robson, 2000; Xie et al., 2003; Briefel et al., 1995; Huang et al., 2004). If the EE predicted considering various factors (e.g. age, weight, sex) is far from EI_SR, those individuals are considered under/overreporting their actual EI. Indeed, such an approach has evidently reduced misclassification (Tooze et al., 2012). Among proposed approaches, the Goldberg cutoffs Goldberg et al., 1991 have been used in nutrition epidemiology to assess nutritional status in specific populations and investigate the association between nutritional status and health and socioeconomic outcomes (Livingstone and Robson, 2000; Xie et al., 2003; Briefel et al., 1995; Huang et al., 2004; Martin et al., 2018). Note that nutritional status in this context means dietary intakes in general; not only EI but also nutritional constituents (vitamin, fish oil, etc.) and dietary styles (Mediterranean, vegan, etc.; Grimes et al., 2013; Molina-Montes et al., 2017; New et al., 2000; Shaheen et al., 2001; O’Sullivan et al., 2011). Therefore, the rationale of using the Goldberg cutoffs (and other similar approaches) to exclude data from individuals considered to have unreliable EI_SR is based on an assumption, ‘if total EI is underestimated, it is probable that the intakes of other nutrients are also underestimated’ (Livingstone and Black, 2003). The corollary for overestimation may also be true.

Bias-correcting approaches like the Goldberg cutoffs are frequently used in nutrition studies. By bias, we are referring to the difference between the estimates and their true values. Here, we focus on two typical estimands in nutrition epidemiology: the mean of nutrition intake, and the associations between nutrition intake and health outcomes in a population. While reducing bias in the mean nutrition intake is useful for determining the true value of population nutrition intake from self-reported data, it is also important to reduce bias in the associations between nutrition intake and health outcomes. However, whether the Goldberg cutoffs reduce bias has not been proved theoretically or empirically. In our previous study, we demonstrated that the Goldberg cutoffs do not necessarily eliminate the bias in estimating the associations between EI and various health outcomes (Ejima et al., 2019). Extending our previous study, we consider nutritional intake beyond EI to include biomarkers of sodium, potassium, and protein with the primary goal to examine if the Goldberg cutoffs eliminate or reduce the bias using a single dataset from the Interactive Diet and Activity Tracking in the American Association of Retired Persons (IDATA) study.

Evaluating the performance of the Goldberg cutoffs solely depending on a single empirical dataset is limited because the dataset is a single realization from an unobserved data-generation process. Further, if the dataset is too small, conclusions may be limited because of issues related to power to detect bias in associations or the power to detect reductions in bias. Therefore, in addition to the empirical data analyses above, we also generated data through simulation and analyzed those generated data that preserve the characteristics of the empirical data. The simulation further enables us to assess the impact of sample size on the performance of the Goldberg cutoffs.

Dietary self-reporting is a basic component of nutrition epidemiology, particularly for studies of nutrition-health relationships. However, reporting bias in nutrition intake is perhaps one of the greatest impediments to understanding the true effect of nutrition on disease. Failure to account for this bias in self-reports can affect the analysis and interpretation of studies designed to assess the influences of nutrition on health. Correlation or regression coefficients estimating associations between self-reported nutrition intakes and health outcomes can be subject to substantial error (Freedman et al., 2011; Gibson et al., 2017). To address such reporting bias issues, there has been increased interest in the use of statistical models in conjunction with biomarker data (Freedman et al., 2010; Brown et al., 2021).

In this study, reporting bias in self-reported nutrition intake was demonstrated using both empirical data analysis and a simulation study. We first examined whether the bias in mean nutrition intake and the bias in the associations between nutrition intake and health outcomes are reduced by applying the Goldberg cutoffs to an empirical dataset, IDATA. We confirmed the bias in mean self-reported nutrition intake was eliminated by applying Goldberg cutoffs to exclude extreme reporters (mostly under-reporters). This bias can be mostly explained by differences in reporting between the accepted and rejected cases rather than a difference in actual nutrition intake between the accepted and rejected cases. We further tested whether the associations between health outcomes and nutrition intake are biased when self-reported data are used, and whether the bias is reduced by applying the Goldberg cutoffs. The significant bias for the associations between EI and BW and the association between EI and WC were reduced but remained after applying Goldberg cutoffs. We did not observe significant bias in associations for other nutrition-outcome pairs, and therefore cannot make conclusions regarding the utility of applying the Goldberg cutoffs to reduce bias for these associations in the empirical data.

To overcome the limitations of the data (i.e. sample size and weak associations among many nutrition-outcome pairs), we generated and analyzed data preserving the characteristics of the IDATA for the assessment of the Goldberg cutoffs. We confirmed the existence of bias in estimated associations when the self-reported data were used, and these biases were reduced, but not eliminated, by applying the Goldberg cutoffs in general. We also confirmed large MSE and low coverage probability when self-reported data were used; MSE and low coverage probability were improved by using Goldberg cutoffs, but were not recovered to the levels of biomarker data. Overall, the empirical data analyses and the simulation study suggest that the Goldberg cutoffs improve the estimates in nutrition-health outcome associations; however, the biases were not completely removed.

This study has several strengths. First, although energy intake has traditionally been studied more with respect to Goldberg cutoffs, herein we also investigated three other nutrition intakes: sodium, potassium, and protein. In our previous study, we used only energy intake as a predictor (Ejima et al., 2019). However, given that the Goldberg cutoffs are believed to reduce the bias in nutrition intake broadly, we expanded the approach to these other nutrition intakes, which can be measured by biomarkers (Livingstone and Black, 2003). Second, we conducted the simulation in addition to empirical data analyses. There are two advantages of the simulation design. (1) The data generation process was based on the IDATA dataset. Thus, we were able to simulate datasets reflective of those that would be seen in the real world. Both the sample size of the generated dataset and the variables that we considered are reflective of what is often observed in nutrition studies. (2) Simulation can consider different models for the data-generating process. Although our objective was not to disentangle the underlying data generation mechanisms, we were able to generate data that preserve the characteristics of the IDATA.

The limitations of this study are worth noting. In the analysis of IDATA, we used only bivariate associations for nutrition-health outcomes. It is possible that including various covariates or different models may influence the existence or lack of bias in nutrition-health associations. In the data-generation process for the simulations, assumptions were made on parameter settings. The reporting bias was set to be normally distributed. Modeling the bias using other distributions (such as a heavier tailed distribution that may be more consistent with a zero-bounded intake) may improve model fit, and thus generated more realistic data. We simulated the bias with constant variance, consistent with the apparent stability of variance across the intake quantiles in Figure 4—figure supplement 2 and Supplementary file 3; however, modeling the variance as a function of intake quantile may alter the data-generating process. We used the self-reported nutrition intake reported by ASA24, as it reflects recent dietary intake. The bias we observed in this study may be different for other self-report methods. Finally, the simulation approach, although based on the IDATA, was nonetheless generated from a limited sample size. We are not aware of thresholds for sufficient sample size for empirical-data-based simulation, and we have had success with smaller plasmode based sampling in the past (Ejima et al., 2020; Alfaras et al., 2021); however, it is possible a larger, more representative, or more robust empirical data set may influence both the empirical and simulated results. Further as the data was from a single population in which white and relatively older people are predominant, generalizability of the study finding should be carefully considered.

In conclusion, our study demonstrated that the use of Goldberg cutoffs can effectively reduce or eliminate bias in mean nutrition intake measurements in the IDATA dataset. However, our analysis also revealed that these cutoffs have limited efficacy in addressing bias in the associations between nutrition intake and health outcomes, as both empirical and simulated results showed. Investigators considering excluding extreme reporters in epidemiological studies should consider whether such approaches are likely to be helpful in answering their specific research questions, as our study has shown that such cutoffs are more useful in estimating mean nutrition intakes than in studies of associations between nutrition intake and health outcomes.

We conducted a set of empirical analyses to assess the reporting bias due to self-report and examine whether the Goldberg cutoffs reduce reporting bias using the data from The Interactive Diet and Activity Tracking in the American Association of Retired Persons (IDATA) study (National Cancer Institute, 2018a). The reporting bias in the mean of nutrition intakes and the associations (regression coefficients) between nutrition intakes and health outcomes were assessed. We also conducted a simulation study to investigate the performance of Goldberg cutoffs using the results from the empirical analyses as ground truth. Note that in data analyses, we assumed the estimates from biomarkers are the true values, since the true values (i.e. population parameters) are unobservable.

Among various nutrition intakes (NI), we considered sodium intake (SI), potassium intake (PoI), and protein intake (PrI) in addition to energy intake (EI). These NI were selected because they can be measured by urine samples as well as self-reports. We denote self-reported NI by NI_SR: EI_SR, SI_SR, PoI_SR, and PrI_SR. We denote biomarker-based NI by NI_BIO: EI_BIO, SI_BIO, PoI_BIO, and PrI_BIO. The NI_SR data remaining after applying the Goldberg cutoffs (hereafter, we call those ‘accepted cases’) are denoted by NI_G: EI_G, SI_G, PoI_G, and PrI_G. Health outcomes (HO) that may be associated with NI were selected from the data dictionaries; body weight (BW), waist circumference (WC), heart rate after fitness test (HR), resting systolic blood pressure (SBP), resting diastolic blood pressure (DBP), and VO₂ max (VO2). The estimated regression coefficients are denoted by the subscript of the explanatory variables and the health outcomes (e.g., ${\beta }_{{EI}_{SR,},BW}$ represents the association between self-reported EI and body weight).

Data generation

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We generated data composed of four variables: NI_BIO (biomarker), NI_SR (self-reported), HO (health outcomes: BW, WC, HR, SBP, DBP, and VO2), and FFM (fat-free mass). NI_BIO and FFM were resampled from the IDATA. HO is computed using a linear model using NI_BIO as a predictive variable:

$HO=a_0+a_1{NI}_{BIO}+ϵ,ϵ~N\left(0,{\eta }^2\right),$

where $a_0,a_1,$ and ${\eta }^2$ are the model parameters estimated from the IDATA. NI_SR is generated by adding an error term (i.e., reporting error), $e$, to NI_BIO, adapting the approach proposed by Ward et al., 2019:

${NI}_{SR}={NI}_{BIO}+e,$

where $e$ is determined by the percentile of NI_BIO in the empirical distribution, $p\left({NI}_{BIO}\right)$. The reporting error $e$ is assumed to follow a normal distribution parametrized by percentile-specific mean, $\mu \left(p\right({NI}_{BIO}\left)\right)$, and a constant standard deviation, $\sigma$: $e~N(\mu ,{\sigma }^2)$. µ and $\sigma$ were estimated by fitting polynomial models to the IDATA: $\mu \left(p\left({NI}_{BIO}\right)\right)=\sum _{k=0}^K{m}_{k}p{\left(N{I}_{BIO}\right)}^k$ , where ${\displaystyle K}$ is the order of the polynomial. The order of the polynomial function was varied from 1 to 5 and we selected the value of ${\displaystyle K}$ that yields the smallest MSE. We used k-fold cross-validation with 10 folds to calculate the test MSE for each model. This resulted in $K=1, 3, 3, 5$ for EI, SI, PoI, and PrI, respectively (Figure 4—figure supplement 2 and Supplementary file 4). For example, assuming EI_BIO is 3000 kcal, which corresponds to 90.4 percentile, the mean of the reporting error, μ, was –749.6 and the standard deviation of the reporting error, $\sigma$, was 759.1. Therefore his/her $e$ is randomly sampled from the normal distribution: $N\left(-\mathrm{749.6,759.1}\right)$ . We further confirmed our assumption of homoskedastic $\sigma$ is reasonable by the Goldfeld Quandt test (Goldfeld and Quandt, 1965; Supplementary file 3). The Goldfeld Quandt test compares variance in high and low values of a variable; we discarded the middle 20% of the total observations (eliminated the center 61 observations among 303 in total) to define the high and low groups. The simulated data were truncated so that NI_SR >0. The variable NI_G was generated by applying the Goldberg cutoffs to EI_SR using FFM (thus, NI_G is a subset of NI_SR). The above process was repeated for each NI. We generated $n=100$ individuals, and the data generation was repeated 1000 times, leading to 1000 replicates. The data generating process is summarized in Figure 4.

Figure 4 with 2 supplements see all

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The data can be obtained from NCI after permission, and we are not allowed to redistribute the data. Researchers interested in accessing the original data should submit a project proposal. Specifically, "To gain access to available IDATA data and/or biospecimens, you must submit a project proposal. These are reviewed by NCI. If your project is approved, you will be required to complete a Data Transfer Agreement (and a Material Transfer Agreement, if applicable) before you will be granted access". (https://cdas.cancer.gov/idata/). All simulations and analyses were performed using the statistical computing software R (version 4.0.1). Code book and analytic code will be made publicly and freely available without restriction at http://doi.org/10.5281/zenodo.7783842.

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Author details

1. Nao Yamamoto

   School of Human Evolution and Social Change, Arizona State University, Tempe, United States

   Contribution

   Software, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft

   Contributed equally with

   Keisuke Ejima

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3131-2368

2. Keisuke Ejima

   1. Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington, Bloomington, United States
   2. Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore, Singapore

   Contribution

   Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration

   Contributed equally with

   Nao Yamamoto

   For correspondence

   keisuke.ejima@ntu.edu.sg

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1185-3987

3. Roger S Zoh

   Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington, Bloomington, United States

   Contribution

   Formal analysis, Supervision, Methodology, Writing – review and editing

   Competing interests

   Reviewing editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0002-8066-1153

4. Andrew W Brown

   1. Department of Biostatistics, University of Arkansas for Medical Sciences, Little Rock, United States
   2. Arkansas Children’s Research Institute, Little Rock, United States

   Contribution

   Resources, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing – review and editing

   Competing interests

   AWB declares: in the past three years (since 2019-09-19), Dr. Brown has received travel expenses from International Food Information Council; speaking fees from Eastern North American Region of the International Biometric Society, Purchaser Business Group on Health, Purdue University, and University of Arkansas for the Medical Sciences; monetary awards from American Society for Nutrition; consulting fees from LA NORC, Pennington Biomedical Research Center, and Soy Nutrition Institute Global; and grants through his institution from Alliance for Potato Research & Education, American Egg Board, National Cattlemen's Beef Association, NIH/NHLBI, NIH/NIDDK, and NIH/NIGMS. In addition, he has been involved in research for which his institution or colleagues have received grants or contracts from Center for Open Science, Gordon and Betty Moore Foundation, Hass Avocado Board, Indiana CTSI, NIH/NCATS, NIH/NCI, NIH/NHLBI, NIH/NIA, NIH/NIGMS, NIH/NLM, and Sloan Foundation. His wife is employed by Reckitt Benckiser

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