Measurement error models with zero inflation and multiple sources of zeros, with applications to hard zeros.

We consider measurement error models for two variables observed repeatedly and subject to measurement error. One variable is continuous, while the other variable is a mixture of continuous and zero measurements. This second variable has two sources of zeros. The first source is episodic zeros, wherein some of the measurements for an individual may be zero and others positive. The second source is hard zeros, i.e., some individuals will always report zero. An example is the consumption of alcohol from alcoholic beverages: some individuals consume alcoholic beverages episodically, while others never consume alcoholic beverages. However, with a small number of repeat measurements from individuals, it is not possible to determine those who are episodic zeros and those who are hard zeros. We develop a new measurement error model for this problem, and use Bayesian methods to fit it. Simulations and data analyses are used to illustrate our methods. Extensions to parametric models and survival analysis are discussed briefly.

Issues in Implementing Regression Calibration Analyses.

Regression calibration is a popular approach for correcting biases in estimated regression parameters when exposure variables are measured with error. This approach involves building a calibration equation to estimate the value of the unknown true exposure given the error-prone measurement and other covariates. The estimated, or calibrated, exposure is then substituted for the unknown true exposure in the health outcome regression model. When used properly, regression calibration can greatly reduce the bias induced by exposure measurement error. Here, we first provide an overview of the statistical framework for regression calibration, specifically discussing how a special type of error, called Berkson error, arises in the estimated exposure. We then present practical issues to consider when applying regression calibration, including: 1) how to develop the calibration equation and which covariates to include; 2) valid ways to calculate standard errors of estimated regression coefficients; and 3) problems arising if one of the covariates in the calibration model is a mediator of the relationship between the exposure and outcome. Throughout, we provide illustrative examples using data from the Hispanic Community Health Study/Study of Latinos (United States, 2008-2011) and simulations. We conclude with recommendations for how to perform regression calibration.

Urinary Sucrose and Fructose From Spot Urine May Be Used as a Predictive Biomarker of Total Sugar Intake-Findings From a Controlled Feeding Study.

BACKGROUND: Recently, we confirmed 24-h urinary sucrose plus fructose (24 uSF) as a predictive biomarker of total sugar intake. However, the collection of 24-h urine samples has limited feasibility in population studies. OBJECTIVE: We investigated the utility of the urinary sucrose plus fructose (uSF) biomarker measured in spot urine as a measure of 24 uSF biomarker and total sugar intake. METHODS: Hundred participants, 18-70 y of age, from the Phoenix Metropolitan Area completed a 15-d feeding study. For 2 of the 8 collected 24-h urine samples, each spot urine sample was collected in a separate container. We considered 4 timed voids of the day [morning (AM) void: first void 08:30-12:30; afternoon (PM) void: first void 12:31-17:30; evening (EVE) void: first void 17:31-12:00; and next-day (ND) void: first void 04:00-12:00]. We investigated the performance of uSF from 1 void, and uSF combined from 2 and 3 voids as a measure of 24 uSF and sugar intake. RESULTS: The biomarker averaged from PM/EVE void strongly correlated with 24 uSF (partial r = 0.75). The 24 uSF predicted from the PM/EVE combination was significantly associated with observed sugar intake and was selected for building the calibrated biomarker equation (marginal R2 = 0.36). Spot urine-based calibrated biomarker, ie, biomarker-estimated sugar intake was moderately correlated with the 15-d mean-observed sugar intake (r = 0.50). CONCLUSIONS: uSF measured from a PM and EVE void may be used to generate biomarker-based sugar intake estimate when collecting 24-h urine samples is not feasible, pending external validation.

Measurement Error Affecting Web- and Paper-Based Dietary Assessment Instruments: Insights From the Multi-Cohort Eating and Activity Study for Understanding Reporting Error.

Few biomarker-based validation studies have examined error in online self-report dietary assessment instruments, and food records (FRs) have been considered less than food frequency questionnaires (FFQs) and 24-hour recalls (24HRs). We investigated measurement error in online and paper-based FFQs, online 24HRs, and paper-based FRs in 3 samples drawn primarily from 3 cohorts, comprising 1,393 women and 1,455 men aged 45-86 years. Data collection occurred from January 2011 to October 2013. Attenuation factors and correlation coefficients between reported and true usual intake for energy, protein, sodium, potassium, and respective densities were estimated using recovery biomarkers. Across studies, average attenuation factors for energy were 0.07, 0.07, and 0.19 for a single FFQ, 24HR, and FR, respectively. Correlation coefficients for energy were 0.24, 0.23, and 0.40, respectively. Excluding energy, the average attenuation factors across nutrients and studies were 0.22 for a single FFQ, 0.22 for a single 24HR, and 0.51 for a single FR. Corresponding correlation coefficients were 0.31, 0.34, and 0.53, respectively. For densities (nutrient expressed relative to energy), the average attenuation factors across studies were 0.37, 0.17, and 0.50, respectively. The findings support prior research suggesting different instruments have unique strengths that should be leveraged in epidemiologic research.

Fatigue, anxiety, and quality of life in breast cancer patients compared to non-cancer controls: a nationwide longitudinal analysis.

PURPOSE: Fatigue and anxiety are common and significant symptoms reported by cancer patients. Few studies have examined the trajectory of multidimensional fatigue and anxiety, the relationships between them and with quality of life. METHODS: Breast cancer patients (n = 580) from community oncology clinics and age-matched controls (n = 364) completed fatigue and anxiety questionnaires prior to chemotherapy (A1), at chemotherapy completion (A2), and six months post-chemotherapy (A3). Linear mixed models (LMM) compared trajectories of fatigue /anxiety over time in patients and controls and estimated their relationship with quality of life. Models adjusted for age, education, race, BMI, marital status, menopausal status, and sleep symptoms. RESULTS: Patients reported greater fatigue and anxiety compared to controls at all time points (p's < 0.001, 35% clinically meaningful anxiety at baseline). From A1 to A2 patients experienced a significant increase in fatigue (ß = 8.3 95%CI 6.6,10.0) which returned to A1 values at A3 but remained greater than controls' (p < 0.001). General, mental, and physical fatigue subscales increased from A1 to A2 remaining significantly higher than A1 at A3 (p < 0.001). Anxiety improved over time (A1 to A3 ß = - 4.3 95%CI -2.6,-3.3) but remained higher than controls at A3 (p < 0.001). Among patients, fatigue and anxiety significantly predicted one another and quality of life. Menopausal status, higher BMI, mastectomy, and sleep problems also significantly predicted change in fatigue. CONCLUSION: Breast cancer patients experience significant fatigue and anxiety up to six months post-chemotherapy that is associated with worse quality of life. Future interventions should simultaneously address anxiety and fatigue, focusing on mental and physical fatigue subdomains.

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 2-More complex methods of adjustment and advanced topics.

We continue our review of issues related to measurement error and misclassification in epidemiology. We further describe methods of adjusting for biased estimation caused by measurement error in continuous covariates, covering likelihood methods, Bayesian methods, moment reconstruction, moment-adjusted imputation, and multiple imputation. We then describe which methods can also be used with misclassification of categorical covariates. Methods of adjusting estimation of distributions of continuous variables for measurement error are then reviewed. Illustrative examples are provided throughout these sections. We provide lists of available software for implementing these methods and also provide the code for implementing our examples in the Supporting Information. Next, we present several advanced topics, including data subject to both classical and Berkson error, modeling continuous exposures with measurement error, and categorical exposures with misclassification in the same model, variable selection when some of the variables are measured with error, adjusting analyses or design for error in an outcome variable, and categorizing continuous variables measured with error. Finally, we provide some advice for the often met situations where variables are known to be measured with substantial error, but there is only an external reference standard or partial (or no) information about the type or magnitude of the error.

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1-Basic theory and simple methods of adjustment.

Measurement error and misclassification of variables frequently occur in epidemiology and involve variables important to public health. Their presence can impact strongly on results of statistical analyses involving such variables. However, investigators commonly fail to pay attention to biases resulting from such mismeasurement. We provide, in two parts, an overview of the types of error that occur, their impacts on analytic results, and statistical methods to mitigate the biases that they cause. In this first part, we review different types of measurement error and misclassification, emphasizing the classical, linear, and Berkson models, and on the concepts of nondifferential and differential error. We describe the impacts of these types of error in covariates and in outcome variables on various analyses, including estimation and testing in regression models and estimating distributions. We outline types of ancillary studies required to provide information about such errors and discuss the implications of covariate measurement error for study design. Methods for ascertaining sample size requirements are outlined, both for ancillary studies designed to provide information about measurement error and for main studies where the exposure of interest is measured with error. We describe two of the simpler methods, regression calibration and simulation extrapolation (SIMEX), that adjust for bias in regression coefficients caused by measurement error in continuous covariates, and illustrate their use through examples drawn from the Observing Protein and Energy (OPEN) dietary validation study. Finally, we review software available for implementing these methods. The second part of the article deals with more advanced topics.

Combining a Food Frequency Questionnaire With 24-Hour Recalls to Increase the Precision of Estimation of Usual Dietary Intakes-Evidence From the Validation Studies Pooling Project.

Improving estimates of individuals' dietary intakes is key to obtaining more reliable evidence for diet-health relationships from nutritional cohort studies. One approach to improvement is combining information from different self-report instruments. Previous work evaluated the gains obtained from combining information from a food frequency questionnaire (FFQ) and multiple 24-hour recalls (24HRs), based on assuming that 24HRs provide unbiased measures of individual intakes. Here we evaluate the same approach of combining instruments but base it on the better assumption that recovery biomarkers provide unbiased measures of individual intakes. Our analysis uses data from the 5 large validation studies included in the Validation Studies Pooling Project: the Observing Protein and Energy Nutrition Study (1999-2000), the Automated Multiple-Pass Method validation study (2002-2004), the Energetics Study (2006-2009), the Nutrition Biomarker Study (2004-2005), and the Nutrition and Physical Activity Assessment Study (2007-2009). The data included intakes of energy, protein, potassium, and sodium. Under a time-varying usual-intake model analysis, the combination of an FFQ with 4 24HRs improved correlations with true intake for predicted protein density, potassium density, and sodium density (range, 0.39-0.61) in comparison with use of a single FFQ (range, 0.34-0.50). Absolute increases in correlation ranged from 0.02 to 0.26, depending on nutrient and sex, with an average increase of 0.14. Based on unbiased recovery biomarker evaluation for these nutrients, we confirm that combining an FFQ with multiple 24HRs modestly improves the accuracy of estimates of individual intakes.

Associations of Biomarker-Calibrated Intake of Total Sugars With the Risk of Type 2 Diabetes and Cardiovascular Disease in the Women's Health Initiative Observational Study.

The inconsistent findings from epidemiologic studies relating total sugars (TS) consumption to cardiovascular disease (CVD) or type 2 diabetes (T2D) risk may be partly due to measurement error in self-reported intake. Using regression calibration equations developed based on the predictive biomarker for TS and recovery biomarker for energy, we examined the association of TS with T2D and CVD risk, before and after dietary calibration, in 82,254 postmenopausal women participating in the Women's Health Initiative Observational Study. After up to 16 years of follow-up (1993-2010), 6,621 T2D and 5,802 CVD incident cases were identified. The hazard ratio for T2D per 20% increase in calibrated TS was 0.94 (95% confidence interval (CI): 0.77, 1.15) in multivariable energy substitution, and 1.00 (95% CI: 0.85, 1.18) in energy partition models. Multivariable hazard ratios for total CVD were 0.97 (95% CI: 0.87, 1.09) from energy substitution, and 0.91 (95% CI: 0.80, 1.04) from energy partition models. Uncalibrated TS generated a statistically significant inverse association with T2D and total CVD risk in multivariable energy substitution and energy partition models. The lack of conclusive findings from our calibrated analyses may be due to the low explanatory power of the calibration equations for TS, which could have led to incomplete deattenuation of the risk estimates.

Evaluation of the 24-Hour Recall as a Reference Instrument for Calibrating Other Self-Report Instruments in Nutritional Cohort Studies: Evidence From the Validation Studies Pooling Project.

Calibrating dietary self-report instruments is recommended as a way to adjust for measurement error when estimating diet-disease associations. Because biomarkers available for calibration are limited, most investigators use self-reports (e.g., 24-hour recalls (24HRs)) as the reference instrument. We evaluated the performance of 24HRs as reference instruments for calibrating food frequency questionnaires (FFQs), using data from the Validation Studies Pooling Project, comprising 5 large validation studies using recovery biomarkers. Using 24HRs as reference instruments, we estimated attenuation factors, correlations with truth, and calibration equations for FFQ-reported intakes of energy and for protein, potassium, and sodium and their densities, and we compared them with values derived using biomarkers. Based on 24HRs, FFQ attenuation factors were substantially overestimated for energy and sodium intakes, less for protein and potassium, and minimally for nutrient densities. FFQ correlations with truth, based on 24HRs, were substantially overestimated for all dietary components. Calibration equations did not capture dependencies on body mass index. We also compared predicted bias in estimated relative risks adjusted using 24HRs as reference instruments with bias when making no adjustment. In disease models with energy and 1 or more nutrient intakes, predicted bias in estimated nutrient relative risks was reduced on average, but bias in the energy risk coefficient was unchanged.

Measurement error models with interactions.

An important use of measurement error models is to correct regression models for bias due to covariate measurement error. Most measurement error models assume that the observed error-prone covariate (WW ) is a linear function of the unobserved true covariate (X) plus other covariates (Z) in the regression model. In this paper, we consider models for W that include interactions between X and Z. We derive the conditional distribution of X given W and Z and use it to extend the method of regression calibration to this class of measurement error models. We apply the model to dietary data and test whether self-reported dietary intake includes an interaction between true intake and body mass index. We also perform simulations to compare the model to simpler approximate calibration models.

A bivariate measurement error model for semicontinuous and continuous variables: Application to nutritional epidemiology.

Semicontinuous data in the form of a mixture of a large portion of zero values and continuously distributed positive values frequently arise in many areas of biostatistics. This article is motivated by the analysis of relationships between disease outcomes and intakes of episodically consumed dietary components. An important aspect of studies in nutritional epidemiology is that true diet is unobservable and commonly evaluated by food frequency questionnaires with substantial measurement error. Following the regression calibration approach for measurement error correction, unknown individual intakes in the risk model are replaced by their conditional expectations given mismeasured intakes and other model covariates. Those regression calibration predictors are estimated using short-term unbiased reference measurements in a calibration substudy. Since dietary intakes are often "energy-adjusted," e.g., by using ratios of the intake of interest to total energy intake, the correct estimation of the regression calibration predictor for each energy-adjusted episodically consumed dietary component requires modeling short-term reference measurements of the component (a semicontinuous variable), and energy (a continuous variable) simultaneously in a bivariate model. In this article, we develop such a bivariate model, together with its application to regression calibration. We illustrate the new methodology using data from the NIH-AARP Diet and Health Study (Schatzkin et al., 2001, American Journal of Epidemiology 154, 1119-1125), and also evaluate its performance in a simulation study.

Moment reconstruction and moment-adjusted imputation when exposure is generated by a complex, nonlinear random effects modeling process.

For the classical, homoscedastic measurement error model, moment reconstruction (Freedman et al., 2004, 2008) and moment-adjusted imputation (Thomas et al., 2011) are appealing, computationally simple imputation-like methods for general model fitting. Like classical regression calibration, the idea is to replace the unobserved variable subject to measurement error with a proxy that can be used in a variety of analyses. Moment reconstruction and moment-adjusted imputation differ from regression calibration in that they attempt to match multiple features of the latent variable, and also to match some of the latent variable's relationships with the response and additional covariates. In this note, we consider a problem where true exposure is generated by a complex, nonlinear random effects modeling process, and develop analogues of moment reconstruction and moment-adjusted imputation for this case. This general model includes classical measurement errors, Berkson measurement errors, mixtures of Berkson and classical errors and problems that are not measurement error problems, but also cases where the data-generating process for true exposure is a complex, nonlinear random effects modeling process. The methods are illustrated using the National Institutes of Health-AARP Diet and Health Study where the latent variable is a dietary pattern score called the Healthy Eating Index-2005. We also show how our general model includes methods used in radiation epidemiology as a special case. Simulations are used to illustrate the methods.

The impact of stratification by implausible energy reporting status on estimates of diet-health relationships.

The food frequency questionnaire (FFQ) is known to be prone to measurement error. Researchers have suggested excluding implausible energy reporters (IERs) of FFQ total energy when examining the relationship between a health outcome and FFQ-reported intake to obtain less biased estimates of the effect of the error-prone measure of exposure; however, the statistical properties of stratifying by IER status have not been studied. Under certain assumptions, including nondifferential error, we show that when stratifying by IER status, the attenuation of the estimated relative risk in the stratified models will be either greater or less in both strata (implausible and plausible reporters) than for the nonstratified model, contrary to the common belief that the attenuation will be less among plausible reporters and greater among IERs. Whether there is more or less attenuation depends on the pairwise correlations between true exposure, observed exposure, and the stratification variable. Thus exclusion of IERs is inadvisable but stratification by IER status can sometimes help. We also address the case of differential error. Examples from the Observing Protein and Energy Nutrition Study and simulations illustrate these results.

Pooled results from 5 validation studies of dietary self-report instruments using recovery biomarkers for potassium and sodium intake.

We pooled data from 5 large validation studies (1999-2009) of dietary self-report instruments that used recovery biomarkers as referents, to assess food frequency questionnaires (FFQs) and 24-hour recalls (24HRs). Here we report on total potassium and sodium intakes, their densities, and their ratio. Results were similar by sex but were heterogeneous across studies. For potassium, potassium density, sodium, sodium density, and sodium:potassium ratio, average correlation coefficients for the correlation of reported intake with true intake on the FFQs were 0.37, 0.47, 0.16, 0.32, and 0.49, respectively. For the same nutrients measured with a single 24HR, they were 0.47, 0.46, 0.32, 0.31, and 0.46, respectively, rising to 0.56, 0.53, 0.41, 0.38, and 0.60 for the average of three 24HRs. Average underreporting was 5%-6% with an FFQ and 0%-4% with a single 24HR for potassium but was 28%-39% and 4%-13%, respectively, for sodium. Higher body mass index was related to underreporting of sodium. Calibration equations for true intake that included personal characteristics provided improved prediction, except for sodium density. In summary, self-reports capture potassium intake quite well but sodium intake less well. Using densities improves the measurement of potassium and sodium on an FFQ. Sodium:potassium ratio is measured much better than sodium itself on both FFQs and 24HRs.

Application of a New Statistical Model for Measurement Error to the Evaluation of Dietary Self-report Instruments.

Most statistical methods that adjust analyses for dietary measurement error treat an individual's usual intake as a fixed quantity. However, usual intake, if defined as average intake over a few months, varies over time. We describe a model that accounts for such variation and for the proximity of biomarker measurements to self-reports within the framework of a meta-analysis, and apply it to the analysis of data on energy, protein, potassium, and sodium from a set of five large validation studies of dietary self-report instruments using recovery biomarkers as reference instruments. We show that this time-varying usual intake model fits the data better than the fixed usual intake assumption. Using this model, we estimated attenuation factors and correlations with true longer-term usual intake for single and multiple 24-hour dietary recalls (24HRs) and food frequency questionnaires (FFQs) and compared them with those obtained under the "fixed" method. Compared with the fixed method, the estimates using the time-varying model showed slightly larger values of the attenuation factor and correlation coefficient for FFQs and smaller values for 24HRs. In some cases, the difference between the fixed method estimate and the new estimate for multiple 24HRs was substantial. With the new method, while four 24HRs had higher estimated correlations with truth than a single FFQ for absolute intakes of protein, potassium, and sodium, for densities the correlations were approximately equal. Accounting for the time element in dietary validation is potentially important, and points toward the need for longer-term validation studies.

A statistical model for measurement error that incorporates variation over time in the target measure, with application to nutritional epidemiology.

Most statistical methods that adjust analyses for measurement error assume that the target exposure T is a fixed quantity for each individual. However, in many applications, the value of T for an individual varies with time. We develop a model that accounts for such variation, describing the model within the framework of a meta-analysis of validation studies of dietary self-report instruments, where the reference instruments are biomarkers. We demonstrate that in this application, the estimates of the attenuation factor and correlation with true intake, key parameters quantifying the accuracy of the self-report instrument, are sometimes substantially modified under the time-varying exposure model compared with estimates obtained under a traditional fixed-exposure model. We conclude that accounting for the time element in measurement error problems is potentially important.

Sugar-sweetened beverage intake and cardiovascular risk factor profile in youth with type 1 diabetes: application of measurement error methodology in the SEARCH Nutrition Ancillary Study.

The SEARCH Nutrition Ancillary Study aims to investigate the role of dietary intake on the development of long-term complications of type 1 diabetes in youth, and capitalise on measurement error (ME) adjustment methodology. Using the National Cancer Institute (NCI) method for episodically consumed foods, we evaluated the relationship between sugar-sweetened beverage (SSB) intake and cardiovascular risk factor profile, with the application of ME adjustment methodology. The calibration sample included 166 youth with two FFQ and three 24 h dietary recall data within 1 month. The full sample included 2286 youth with type 1 diabetes. SSB intake was significantly associated with higher TAG, total and LDL-cholesterol concentrations, after adjusting for energy, age, diabetes duration, race/ethnicity, sex and education. The estimated effect size was larger (model coefficients increased approximately 3-fold) after the application of the NCI method than without adjustment for ME. Compared with individuals consuming one serving of SSB every 2 weeks, those who consumed one serving of SSB every 2 d had 3.7 mg/dl (0.04 mmol/l) higher TAG concentrations and 4.0 mg/dl (0.10 mmol/l) higher total cholesterol and LDL-cholesterol concentrations, after adjusting for ME and covariates. SSB intake was not associated with measures of adiposity and blood pressure. Our findings suggest that SSB intake is significantly related to increased lipid levels in youth with type 1 diabetes, and that estimates of the effect size of SSB on lipid levels are severely attenuated in the presence of ME. Future studies in youth with diabetes should consider a design that will allow for the adjustment for ME when studying the influence of diet on health status.

Body mass and weight change in adults in relation to mortality risk.

Using data from the National Institutes of Health-AARP Diet and Health Study, we evaluated the influence of adulthood weight history on mortality risk. The National Institutes of Health-AARP Diet and Health Study is an observational cohort study of US men and women who were aged 50-71 years at entry in 1995-1996. This analysis focused on 109,947 subjects who had never smoked and were younger than age 70 years. We estimated hazard ratios of total and cause-specific mortality for recalled body mass index (BMI; weight (kg)/height (m)(2)) at ages 18, 35, and 50 years; weight change across 3 adult age intervals; and the effect of first attaining an elevated BMI at 4 successive ages. During 12.5 years' follow-up through 2009, 12,017 deaths occurred. BMI at all ages was positively related to mortality. Weight gain was positively related to mortality, with stronger associations for gain between ages 18 and 35 years and ages 35 and 50 years than between ages 50 and 69 years. Mortality risks were higher in persons who attained or exceeded a BMI of 25.0 at a younger age than in persons who reached that threshold later in adulthood, and risks were lowest in persons who maintained a BMI below 25.0. Heavier initial BMI and weight gain in early to middle adulthood strongly predicted mortality risk in persons aged 50-69 years.

Pooled results from 5 validation studies of dietary self-report instruments using recovery biomarkers for energy and protein intake.

We pooled data from 5 large validation studies of dietary self-report instruments that used recovery biomarkers as references to clarify the measurement properties of food frequency questionnaires (FFQs) and 24-hour recalls. The studies were conducted in widely differing US adult populations from 1999 to 2009. We report on total energy, protein, and protein density intakes. Results were similar across sexes, but there was heterogeneity across studies. Using a FFQ, the average correlation coefficients for reported versus true intakes for energy, protein, and protein density were 0.21, 0.29, and 0.41, respectively. Using a single 24-hour recall, the coefficients were 0.26, 0.40, and 0.36, respectively, for the same nutrients and rose to 0.31, 0.49, and 0.46 when three 24-hour recalls were averaged. The average rate of under-reporting of energy intake was 28% with a FFQ and 15% with a single 24-hour recall, but the percentages were lower for protein. Personal characteristics related to under-reporting were body mass index, educational level, and age. Calibration equations for true intake that included personal characteristics provided improved prediction. This project establishes that FFQs have stronger correlations with truth for protein density than for absolute protein intake, that the use of multiple 24-hour recalls substantially increases the correlations when compared with a single 24-hour recall, and that body mass index strongly predicts under-reporting of energy and protein intakes.