Evaluation of a two‐part regression calibration to adjust for dietary exposure measurement error in the Cox proportional hazards model: A simulation study

Dietary questionnaires are prone to measurement error, which bias the perceived association between dietary intake and risk of disease. Short‐term measurements are required to adjust for the bias in the association. For foods that are not consumed daily, the short‐term measurements are often characterized by excess zeroes. Via a simulation study, the performance of a two‐part calibration model that was developed for a single‐replicate study design was assessed by mimicking leafy vegetable intake reports from the multicenter European Prospective Investigation into Cancer and Nutrition (EPIC) study. In part I of the fitted two‐part calibration model, a logistic distribution was assumed; in part II, a gamma distribution was assumed. The model was assessed with respect to the magnitude of the correlation between the consumption probability and the consumed amount (hereafter, cross‐part correlation), the number and form of covariates in the calibration model, the percentage of zero response values, and the magnitude of the measurement error in the dietary intake. From the simulation study results, transforming the dietary variable in the regression calibration to an appropriate scale was found to be the most important factor for the model performance. Reducing the number of covariates in the model could be beneficial, but was not critical in large‐sample studies. The performance was remarkably robust when fitting a one‐part rather than a two‐part model. The model performance was minimally affected by the cross‐part correlation.     

Approximate maximum likelihood estimation for logistic regression with covariate measurement error

In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)‐InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC‐InterAct Study under a sensitivity analysis framework.     

A zero‐augmented generalized gamma regression calibration to adjust for covariate measurement error: A case of an episodically consumed dietary intake

Measurement error in exposure variables is a serious impediment in epidemiological studies that relate exposures to health outcomes. In nutritional studies, interest could be in the association between long‐term dietary intake and disease occurrence. Long‐term intake is usually assessed with food frequency questionnaire (FFQ), which is prone to recall bias. Measurement error in FFQ‐reported intakes leads to bias in parameter estimate that quantifies the association. To adjust for bias in the association, a calibration study is required to obtain unbiased intake measurements using a short‐term instrument such as 24‐hour recall (24HR). The 24HR intakes are used as response in regression calibration to adjust for bias in the association. For foods not consumed daily, 24HR‐reported intakes are usually characterized by excess zeroes, right skewness, and heteroscedasticity posing serious challenge in regression calibration modeling. We proposed a zero‐augmented calibration model to adjust for measurement error in reported intake, while handling excess zeroes, skewness, and heteroscedasticity simultaneously without transforming 24HR intake values. We compared the proposed calibration method with the standard method and with methods that ignore measurement error by estimating long‐term intake with 24HR and FFQ‐reported intakes. The comparison was done in real and simulated datasets. With the 24HR, the mean increase in mercury level per ounce fish intake was about 0.4; with the FFQ intake, the increase was about 1.2. With both calibration methods, the mean increase was about 2.0. Similar trend was observed in the simulation study. In conclusion, the proposed calibration method performs at least as good as the standard method.     

Modeling Data with Excess Zeros and Measurement Error: Application to Evaluating Relationships between Episodically Consumed Foods and Health Outcomes

Summary Dietary assessment of episodically consumed foods gives rise to nonnegative data that have excess zeros and measurement error. Tooze et al. (2006, Journal of the American Dietetic Association 106 , 1575–1587) describe a general statistical approach (National Cancer Institute method) for modeling such food intakes reported on two or more 24‐hour recalls (24HRs) and demonstrate its use to estimate the distribution of the food's usual intake in the general population. In this article, we propose an extension of this method to predict individual usual intake of such foods and to evaluate the relationships of usual intakes with health outcomes. Following the regression calibration approach for measurement error correction, individual usual intake is generally predicted as the conditional mean intake given 24HR‐reported intake and other covariates in the health model. One feature of the proposed method is that additional covariates potentially related to usual intake may be used to increase the precision of estimates of usual intake and of diet‐health outcome associations. Applying the method to data from the Eating at America's Table Study, we quantify the increased precision obtained from including reported frequency of intake on a food frequency questionnaire (FFQ) as a covariate in the calibration model. We then demonstrate the method in evaluating the linear relationship between log blood mercury levels and fish intake in women by using data from the National Health and Nutrition Examination Survey, and show increased precision when including the FFQ information. Finally, we present simulation results evaluating the performance of the proposed method in this context.     

Trends and dietary determinants of overweight and obesity in a multiethnic population

Objectives : To describe trends in BMI among different ethnic groups in Hawaii and to explore the relation of nutrient and food intake with excess weight. Research Methods and Procedures : We pooled demographic, anthropometric, and nutritional data derived from a detailed diet history for 159, 683 participants of 18 population‐based epidemiological studies conducted in Hawaii over a 25‐year period. The age‐adjusted prevalence of excess weight (BMI ≥ 25 kg/m²) was estimated for 5‐year intervals. To explore dietary determinants of excess weight, we computed odds ratios using logistic regression. Results : During the study period, the prevalence of excess weight increased considerably among all ethnic groups. Native Hawaiians had the highest and Asian Americans had the lowest prevalence of excess weight at all times. Although the percentage of calories consumed from carbohydrates increased, the percentage of calories from fat decreased over time. On an individual level, fat and protein consumption predicted a higher BMI, and dietary fiber intake predicted a lower BMI. Similarly, a higher consumption of meat, poultry, and fish was related to excess weight, whereas fruit and vegetable intake were inversely associated with excess weight. After stratification by ethnicity, the associations were not materially altered among women, but carbohydrates seemed to have a stronger association with excess weight among Native Hawaiian and Japanese men than among white men. Discussion : In this large ethnically diverse population, plant‐based foods and dietary fiber emerged as a potential protective factor against excess weight regardless of ethnicity.     

Allowing for never and episodic consumers when correcting for error in food record measurements of dietary intake

Food records, including 24-hour recalls and diet diaries, are considered to provide generally superior measures of long-term dietary intake relative to questionnaire-based methods. Despite the expense of processing food records, they are increasingly used as the main dietary measurement in nutritional epidemiology, in particular in sub-studies nested within prospective cohorts. Food records are, however, subject to excess reports of zero intake. Measurement error is a serious problem in nutritional epidemiology because of the lack of gold standard measurements and results in biased estimated diet-disease associations. In this paper, a 3-part measurement error model, which we call the never and episodic consumers (NEC) model, is outlined for food records. It allows for both real zeros, due to never consumers, and excess zeros, due to episodic consumers (EC). Repeated measurements are required for some study participants to fit the model. Simulation studies are used to compare the results from using the proposed model to correct for measurement error with the results from 3 alternative approaches: a crude approach using the mean of repeated food record measurements as the exposure, a linear regression calibration (RC) approach, and an EC model which does not allow real zeros. The crude approach results in badly attenuated odds ratio estimates, except in the unlikely situation in which a large number of repeat measurements is available for all participants. Where repeat measurements are available for all participants, the 3 correction methods perform equally well. However, when only a subset of the study population has repeat measurements, the NEC model appears to provide the best method for correcting for measurement error, with the 2 alternative correction methods, in particular the linear RC approach, resulting in greater bias and loss of coverage. The NEC model is extended to include adjustment for measurements from food frequency questionnaires, enabling better estimation of the proportion of never consumers when the number of repeat measurements is small. The methods are applied to 7-day diary measurements of alcohol intake in the EPIC-Norfolk study.     

Tracking of a Dietary Pattern and Its Components over 10-Years in the Severely Obese

Understanding how dietary intake changes over time is important for studies of diet and disease and may inform interventions to improve dietary intakes. We investigated how a dietary pattern (DP) tracked over 10-years in the Swedish Obese Subjects (SOS) study control group. Dietary intake was assessed at multiple time-points in 2037 severely obese individuals (BMI 41±4 kg/m²). Reduced rank regression was used to derive a dietary pattern using dietary energy density (kJ/g), saturated fat (%) and fibre density (mg/kJ) as response variables and score respondents at each follow-up. Tracking coefficients for the DP, its key foods and macronutrient response variables and corrected for time-dependent and time-independent covariates were calculated using generalised estimating equations to take into account all available data. The DP tracking coefficient was moderate for women (0.40; 95% CI: 0.38–0.42) and men (0.38; 95% CI: 0.35–0.41). Of the eleven foods key to this DP, fruit and vegetable intakes had the strongest tracking coefficient for both sexes. Fast food and candy had the lowest tracking coefficients for women and men respectively. Scores for an energy dense, high saturated fat, low fibre density DP appear moderately stable over a 10-year period in this severely obese population. Furthermore, some food groups appear more amenable to change while others, often the most healthful, appear more stable and may require intervention before adulthood.     

A Multilevel Model to Estimate the Within- and the Between-Center Components of the Exposure/Disease Association in the EPIC Study

In a multicenter study, the overall relationship between exposure and the risk of cancer can be broken down into a within-center component, which reflects the individual level association, and a between-center relationship, which captures the association at the aggregate level. A piecewise exponential proportional hazards model with random effects was used to evaluate the association between dietary fiber intake and colorectal cancer (CRC) risk in the EPIC study. During an average follow-up of 11.0 years, 4,517 CRC events occurred among study participants recruited in 28 centers from ten European countries. Models were adjusted by relevant confounding factors. Heterogeneity among centers was modelled with random effects. Linear regression calibration was used to account for errors in dietary questionnaire (DQ) measurements. Risk ratio estimates for a 10 g/day increment in dietary fiber were equal to 0.90 (95%CI: 0.85, 0.96) and 0.85 (0.64, 1.14), at the individual and aggregate levels, respectively, while calibrated estimates were 0.85 (0.76, 0.94), and 0.87 (0.65, 1.15), respectively. In multicenter studies, over a straightforward ecological analysis, random effects models allow information at the individual and ecologic levels to be captured, while controlling for confounding at both levels of evidence.     

Dietary fat increases energy intake across the range of typical consumption in the United States

Objective: The fat content of a diet has been shown to affect total energy intake, but controlled feeding trials have only compared very high (40% of total calories) fat diets with very low (20% of total calories) fat diets. This study was designed to measure accurately the voluntary food and energy intake over a range of typical intake for dietary fat. Methods and Procedures: Twenty‐two non‐obese subjects were studied for 4 days on each of three diets, which included core foods designed to contain 26, 34, and 40% fat, respectively of total calories and ad lib buffet foods of similar fat content. All diets were matched for determinants of energy density except dietary fat. Subjects consumed two meals/day in an inpatient unit and were provided the third meal and snack foods while on each diet. All food provided and not eaten was measured by research staff. Results: Voluntary energy intake increased significantly as dietary fat content increased (P = 0.008). On the 26% dietary fat treatment, subjects consumed 23.8% dietary fat (core and ad lib foods combined) and 2,748 ± 741 kcal/day (mean ± s.d.); at 34% dietary fat, subjects consumed 32.7% fat and 2,983 ± 886 kcal/day; and at 40% dietary fat subjects consumed 38.1% fat and 3,018 ± 963 kcal/day. Discussion: These results show that energy intake increases as dietary fat content increases across the usual range of dietary fat consumed in the United States. Even small reductions in dietary fat could help in lowering total energy intake and reducing weight gain in the population.     

Is Dietary Fat Intake Related to Liking or Household Availability of High‐ and Low‐Fat Foods?

Objectives : Despite the increasing availability of low‐ and reduced‐fat foods, Americans continue to consume more fat than recommended, which may be a contributing factor to the obesity epidemic. This investigation examined relationships between liking and household availability of high‐ and low‐fat foods and their association with dietary fat intake. Research Methods and Procedures : A food frequency questionnaire assessed percent calories from fat consumed over the past year in 85 men and 80 women. Participants reported their degree of liking 22 “high‐fat foods” (>45% calories from fat) and 22 “low‐fat foods” (<18% calories from fat), and the number and percentage (number of high‐ or low‐fat foods/total number of foods × 100) of these high‐ and low‐fat foods in their homes. Results : Hierarchical regression analyses examined the ability of liking and household availability of low‐ and high‐fat foods to predict percent dietary fat intake. After controlling for age, sex, and BMI, liking ratings for high‐ and low‐fat foods and the interaction of liking for low‐fat foods by the percentage of low‐fat foods in the household were significant predictors of percent dietary fat consumed. Greater liking of high‐fat foods and lower liking of low‐fat foods, both alone and combined with a lower percentage of low‐fat foods in the home, were predictive of higher dietary fat intake. Discussion : Interventions designed to reduce dietary fat intake should target both decreasing liking for high‐fat foods and increasing liking for low‐fat foods, along with increasing the proportion of low‐fat foods in the household.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Correcting for measurement error in individual-level covariates in nonlinear mixed effects models

The nonlinear mixed effects model is used to represent data in pharmacokinetics, viral dynamics, and other areas where an objective is to elucidate associations among individual-specific model parameters and covariates; however, covariates may be measured with error. For additive measurement error, we show substitution of mismeasured covariates for true covariates may lead to biased estimators for fixed effects and random effects covariance parameters, while regression calibration may eliminate bias in fixed effects but fail to correct that in covariance parameters. We develop methods to take account of measurement error that correct this bias and may be implemented with standard software, and we demonstrate their utility via simulation and application to data from a study of HIV dynamics.     

A new method for dealing with measurement error in explanatory variables of regression models

We introduce a new method, moment reconstruction, of correcting for measurement error in covariates in regression models. The central idea is similar to regression calibration in that the values of the covariates that are measured with error are replaced by "adjusted" values. In regression calibration the adjusted value is the expectation of the true value conditional on the measured value. In moment reconstruction the adjusted value is the variance-preserving empirical Bayes estimate of the true value conditional on the outcome variable. The adjusted values thereby have the same first two moments and the same covariance with the outcome variable as the unobserved "true" covariate values. We show that moment reconstruction is equivalent to regression calibration in the case of linear regression, but leads to different results for logistic regression. For case-control studies with logistic regression and covariates that are normally distributed within cases and controls, we show that the resulting estimates of the regression coefficients are consistent. In simulations we demonstrate that for logistic regression, moment reconstruction carries less bias than regression calibration, and for case-control studies is superior in mean-square error to the standard regression calibration approach. Finally, we give an example of the use of moment reconstruction in linear discriminant analysis and a nonstandard problem where we wish to adjust a classification tree for measurement error in the explanatory variables.     

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Summary Ye, Lin, and Taylor (2008, Biometrics 64 , 1238–1246) proposed a joint model for longitudinal measurements and time‐to‐event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two‐stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time‐to‐event data. In the second stage, the posterior expectation of an individual's random effects from the mixed‐model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time‐to‐event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008) . In agreement with the methodology proposed by Ye et al. (2008) , an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.     

Phytoestrogen consumption and association with breast, prostate and colorectal cancer in EPIC Norfolk

Phytoestrogens are polyphenolic secondary plant metabolites that have structural and functional similarities to 17β-oestradiol and have been associated with a protective effect against hormone-related cancers. Most foods in the UK only contain small amounts of phytoestrogens (median content 21 μg/100 g) and the highest content is found in soya and soya-containing foods. The highest phytoestrogen content in commonly consumed foods is found in breads (average content 450 μg/100 g), the main source of isoflavones in the UK diet. The phytoestrogen consumption in cases and controls was considerably lower than in Asian countries. No significant associations between phytoestrogen intake and breast cancer risk in a nested case-control study in EPIC Norfolk were found. Conversely, colorectal cancer risk was inversely associated with enterolignan intake in women but not in men. Prostate cancer risk was positively associated with enterolignan intake, however this association became non-significant when adjusting for dairy intake, suggesting that enterolignans can act as a surrogate marker for dairy or calcium intake.     

Methods for Assessment of Dietary Lead Exposure of the Inner-City Population

Abstract

Assessment of dietary lead exposure of individuals begins with the determination of food and beverage intake by the individuals, and concludes with an evaluation of the lead content of the foods and beverages consumed. Of several techniques available for assessment of dietary intake, the 24-hour food recall is recommended as the method of choice for assessing current dietary lead intakes in inner-city populations. The three-day food record can be used among cooperative and motivated subjects, while the dietary history method is available for assessing long-term intakes in the past. The unavailability of lead content values of a large number of foods will to a large extent restrict the use of these methods in large-scale dietary lead exposure studies. Until the time that such data becomes available, the most accurate estimates of lead intake can be provided by chemical analysis of duplicate samples of foods consumed, as is currently done. However, this method is feasible only for small samples.     

Diet and the risk of head-and-neck cancer among never-smokers and smokers in a Chinese population

BackgroundFew studies have been conducted in China to investigate the association between diet and the risk of head-and-neck cancer (HNC). The aim of this study was to determine the relationship between diet and HNC risk in the Chinese population and to examine whether smoking status has any effect on the risk.MethodsOur multicenter case–control study included 921 HNC cases and 806 controls. We obtained information on the frequency of both animal- and plant-based food consumption. Unconditional logistic regression was used to estimate the odds ratios (ORs) and 95% confidence intervals (95%CIs).ResultsThe risk of HNC increased with more frequent consumption of processed meat and fermented foods but decreased with frequent consumption of fruits and vegetables. There was a significant increasing P for trend of 0.006 among smokers who consumed meat and an increased OR among smokers who consumed processed meat (OR 2.95, 95%CI 1.12–7.75). Protective odds ratios for vegetable consumption were observed among smokers only. We also observed protective odds ratios for higher egg consumption among never-smokers (P for trend = 0.0.003).ConclusionsReduced HNC risks were observed for high fruit and vegetable intake, a finding consistent with the results of previous studies. Processed meat intake was associated with an increased risk. The role of dietary factors in HNC in the East Asian population is similar to that in European populations.     

Segmented regression in the presence of covariate measurement error in main study/validation study designs

This article considers the problem of segmented regression in the presence of covariate measurement error in main study/validation study designs. First, we derive a closed and interpretable form for the full likelihood. After that, we use the likelihood results to compute the bias of the estimated changepoint in the case when the measurement error is ignored. We find the direction of the bias in the estimated changepoint to be determined by the design distribution of the observed covariates, and the bias can be in either direction. We apply the methodology to data from a nutritional study that investigates the relation between dietary folate and blood serum homocysteine levels and find that the analysis that ignores covariate measurement error would have indicated a much higher minimum daily dietary folate intake requirement than is obtained in the analysis that takes covariate measurement error into account.     

Bayesian nonparametric regression analysis of data with random effects covariates from longitudinal measurements

We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply Bayesian nonparametric methods including cubic smoothing splines or P-splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data-augmentation schemes. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the "naive" approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves.     

The role of non-natural foods in the nutritional strategies of monkeys in a human-modified mosaic landscape

Many tropical animals inhabit mosaic landscapes including human-modified habitat. In such landscapes, animals commonly adjust feeding behavior, and may incorporate non-natural foods. These behavioral shifts can influence consumers' nutritional states, with implications for population persistence. However, few studies have addressed the nutritional role of non-natural food. We examined nutritional ecology of wild blue monkeys to understand how dietary habits related to non-natural foods might support population persistence in a mosaic landscape. We documented prevalence and nutritional composition of non-natural foods in monkey diets to assess how habitat use influenced their consumption, and their contribution to nutritional strategies. While most energy and macronutrients came from natural foods, subjects focused non-natural feeding activity on five exotic plants, and averaged about a third of daily calories from non-natural foods. Most non-natural food calories came from non-structural carbohydrates and least from protein. Consumption of non-natural foods related to time in human-modified habitats, which two groups used non-randomly. Non-natural and natural foods were similar in nutrients, and the amount of non-natural food consumed drove variation in nutritional strategy. When more daily calories came from non-natural foods, females consumed a higher ratio of non-protein energy to protein (NPE:P). Females also prioritized protein while allowing NPE:P to vary, increasing NPE while capitalizing on non-natural foods. Overall, these tropical mammals achieved a similar nutrient balance regardless of their intake of non-natural foods. Forest and forest-adjacent areas with non-natural vegetation may provide adequate nutrient access for consumers, and thus contribute to wildlife conservation in mosaic tropical landscapes.