Victor Kipnis

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.

Previous studies suggest that amino acid carbon stable isotope ratios (CIR_AAs) may serve as biomarkers of added sugar (AS) intake, but this has not been tested in a demographically diverse population. We conducted a 15-day feeding study of U.S. adults, recruited across sex, age, and BMI groups. Participants consumed personalized diets that resembled habitual intake, assessed using two consecutive 7-day food records. We measured serum (n = 99) CIR_AAs collected at the end of the feeding period and determined correlations with diet. We used forward selection to model AS intake using participant characteristics and 15 CIR_AAs. This model was internally validated using bootstrap optimism correction. Median (25th, 75th percentile) AS intake was 65.2 g/day (44.7, 81.4) and 9.5% (7.2%, 12.4%) of energy. The CIR of alanine had the highest, although modest, correlation with AS intake (r = 0.32, p = 0.001). Serum CIR_AAs were more highly correlated with animal food intakes, especially the ratio of animal to total protein. The AS model included sex, body weight and 6 CIR_AAs. This model had modest explanatory power (multiple R² = 0.38), and the optimism-corrected R² was lower (R² = 0.15). Further investigations in populations with wider ranges of AS intake are warranted.

Summary: 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.

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.

In a recent paper (Weller EA, Milton DK, Eisen EA, Spiegelman D. Regression calibration for logistic regression with multiple surrogates for one exposure. Journal of Statistical Planning and Inference 2007; 137: 449‐461), the authors discussed fitting logistic regression models when a scalar main explanatory variable is measured with error by several surrogates, that is, a situation with more surrogates than variables measured with error. They compared two methods of adjusting for measurement error using a regression calibration approximate model as if it were exact. One is the standard regression calibration approach consisting of substituting an estimated conditional expectation of the true covariate given observed data in the logistic regression. The other is a novel two‐stage approach when the logistic regression is fitted to multiple surrogates, and then a linear combination of estimated slopes is formed as the estimate of interest. Applying estimated asymptotic variances for both methods in a single data set with some sensitivity analysis, the authors asserted superiority of their two‐stage approach. We investigate this claim in some detail. A troubling aspect of the proposed two‐stage method is that, unlike standard regression calibration and a natural form of maximum likelihood, the resulting estimates are not invariant to reparameterization of nuisance parameters in the model. We show, however, that, under the regression calibration approximation, the two‐stage method is asymptotically equivalent to a maximum likelihood formulation, and is therefore in theory superior to standard regression calibration. However, our extensive finite‐sample simulations in the practically important parameter space where the regression calibration model provides a good approximation failed to uncover such superiority of the two‐stage method. We also discuss extensions to different data structures. Copyright © 2012 John Wiley & Sons, Ltd.

Dietary measurement error creates serious challenges to reliably discovering new diet-disease associations in nutritional cohort studies. Such error causes substantial underestimation of relative risks and reduction of statistical power for detecting associations. On the basis of data from the Observing Protein and Energy Nutrition Study, we recommend the following approaches to deal with these problems. Regarding data analysis of cohort studies using food-frequency questionnaires, we recommend 1) using energy adjustment for relative risk estimation; 2) reporting estimates adjusted for measurement error along with the usual relative risk estimates, whenever possible (this requires data from a relevant, preferably internal, validation study in which participants report intakes using both the main instrument and a more detailed reference instrument such as a 24-hour recall or multiple-day food record); 3) performing statistical adjustment of relative risks, based on such validation data, if they exist, using univariate (only for energy-adjusted intakes such as densities or residuals) or multivariate regression calibration. We note that whereas unadjusted relative risk estimates are biased toward the null value, statistical significance tests of unadjusted relative risk estimates are approximately valid. Regarding study design, we recommend increasing the sample size to remedy loss of power; however, it is important to understand that this will often be an incomplete solution because the attenuated signal may be too small to distinguish from unmeasured confounding in the model relating disease to reported intake. Future work should be devoted to alleviating the problem of signal attenuation, possibly through the use of improved self-report instruments or by combining dietary biomarkers with self-report instruments.

In the United States the preferred method of obtaining dietary intake data is the 24-hour dietary recall, yet the measure of most interest is usual or long-term average daily intake, which is impossible to measure. Thus, usual dietary intake is assessed with considerable measurement error. Also, diet represents numerous foods, nutrients and other components, each of which have distinctive attributes. Sometimes, it is useful to examine intake of these components separately, but increasingly nutritionists are interested in exploring them collectively to capture overall dietary patterns. Consumption of these components varies widely: some are consumed daily by almost everyone on every day, while others are episodically consumed so that 24-hour recall data are zero-inflated. In addition, they are often correlated with each other. Finally, it is often preferable to analyze the amount of a dietary component relative to the amount of energy (calories) in a diet because dietary recommendations often vary with energy level. The quest to understand overall dietary patterns of usual intake has to this point reached a standstill. There are no statistical methods or models available to model such complex multivariate data with its measurement error and zero inflation. This paper proposes the first such model, and it proposes the first workable solution to fit such a model. After describing the model, we use survey-weighted MCMC computations to fit the model, with uncertainty estimation coming from balanced repeated replication. The methodology is illustrated through an application to estimating the population distribution of the Healthy Eating Index-2005 (HEI-2005), a multi-component dietary quality index involving ratios of interrelated dietary components to energy, among children aged 2–8 in the United States. We pose a number of interesting questions about the HEI-2005 and provide answers that were not previously within the realm of possibility, and we indicate ways that our approach can be used to answer other questions of importance to nutritional science and public health.

Summary: We propose a semiparametric Bayesian method for handling measurement error in nutritional epidemiological data. Our goal is to estimate nonparametrically the form of association between a disease and exposure variable while the true values of the exposure are never observed. Motivated by nutritional epidemiological data, we consider the setting where a surrogate covariate is recorded in the primary data, and a calibration data set contains information on the surrogate variable and repeated measurements of an unbiased instrumental variable of the true exposure. We develop a flexible Bayesian method where not only is the relationship between the disease and exposure variable treated semiparametrically, but also the relationship between the surrogate and the true exposure is modeled semiparametrically. The two nonparametric functions are modeled simultaneously via B‐splines. In addition, we model the distribution of the exposure variable as a Dirichlet process mixture of normal distributions, thus making its modeling essentially nonparametric and placing this work into the context of functional measurement error modeling. We apply our method to the NIH‐AARP Diet and Health Study and examine its performance in a simulation study.

Identifying diet-disease relationships in nutritional cohort studies is plagued by the measurement error in self-reported intakes.The authors propose using biomarkers known to be correlated with dietary intake, so as to strengthen analyses of diet-disease hypotheses. The authors consider combining self-reported intakes and biomarker levels using principal components, Howe's method, or a joint statistical test of effects in a bivariate model. They compared the statistical power of these methods with that of conventional univariate analyses of self-reported intake or of biomarker level. They used computer simulation of different disease risk models, with input parameters based on data from the literature on the relationship between lutein intake and age-related macular degeneration.The results showed that if the dietary effect on disease was fully mediated through the biomarker level, then the univariate analysis of the biomarker was the most powerful approach. However, combination methods, particularly principal components and Howe's method, were not greatly inferior in this situation, and were as good as, or better than, univariate biomarker analysis if mediation was only partial or non-existent. In some circumstances sample size requirements were reduced to 20-50% of those required for conventional analyses of self-reported intake.The authors conclude that (i) including biomarker data in addition to the usual dietary data in a cohort could greatly strengthen the investigation of diet-disease relationships, and (ii) when the extent of mediation through the biomarker is unknown, use of principal components or Howe's method appears a good strategy.

SummaryDietary 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.