Linear measurement error models with restricted sampling

The relationship between nutrient consumption and chronic disease risk is the focus of a large number of epidemiological studies where food frequency questionnaires (FFQ) and food records are commonly used to assess dietary intake. However, these self-assessment tools are known to involve substantial random error for most nutrients, and probably important systematic error as well. Study subject selection in dietary intervention studies is sometimes conducted in two stages. At the first stage, FFQ-measured dietary intakes are observed and at the second stage another instrument, such as a 4-day food record, is administered only to participants who have fulfilled a prespecified criterion that is based on the baseline FFQ-measured dietary intake (e.g., only those reporting percent energy intake from fat above a prespecified quantity). Performing analysis without adjusting for this truncated sample design and for the measurement error in the nutrient consumption assessments will usually provide biased estimates for the population parameters. In this work we provide a general statistical analysis technique for such data with the classical additive measurement error that corrects for the two sources of bias. The proposed technique is based on multiple imputation for longitudinal data. Results of a simulation study along with a sensitivity analysis are presented, showing the performance of the proposed method under a simple linear regression model.     

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.     

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.     

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.     

Selection of Log-Linear Models with Orthonormal Basis for Contingency Tables

A model selection criterion for log-linear models with orthonormal basis for contingency tables is developed using the Gauss discrepancy between the logarithms of the frequencies. The contribution of each parameter to the criterion may be determined separately. A test for the hypothesis that the use of a certain parameter increases the expected discrepancy is given.     

Accounting for uncertainty in the tree topology has little effect on the decision-theoretic approach to model selection in phylogeny estimation

Currently available methods for model selection used in phylogenetic analysis are based on an initial fixed-tree topology. Once a model is picked based on this topology, a rigorous search of the tree space is run under that model to find the maximum-likelihood estimate of the tree (topology and branch lengths) and the maximum-likelihood estimates of the model parameters. In this paper, we propose two extensions to the decision-theoretic (DT) approach that relax the fixed-topology restriction. We also relax the fixed-topology restriction for the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) methods. We compare the performance of the different methods (the relaxed, restricted, and the likelihood-ratio test [LRT]) using simulated data. This comparison is done by evaluating the relative complexity of the models resulting from each method and by comparing the performance of the chosen models in estimating the true tree. We also compare the methods relative to one another by measuring the closeness of the estimated trees corresponding to the different chosen models under these methods. We show that varying the topology does not have a major impact on model choice. We also show that the outcome of the two proposed extensions is identical and is comparable to that of the BIC, Extended-BIC, and DT. Hence, using the simpler methods in choosing a model for analyzing the data is more computationally feasible, with results comparable to the more computationally intensive methods. Another outcome of this study is that earlier conclusions about the DT approach are reinforced. That is, LRT, Extended-AIC, and AIC result in more complicated models that do not contribute to the performance of the phylogenetic inference, yet cause a significant increase in the time required for data analysis.     

Focused information criterion on predictive models in personalized medicine

Instead of assessing the overall fit of candidate models like the traditional model selection criteria, the focused information criterion focuses attention directly on the parameter of the primary interest and aims to select the model with the minimum estimated mean squared error for the estimate of the focused parameter. In this article we apply the focused information criterion for personalized medicine. By using individual‐level information from clinical observations, demographics, and genetics, we obtain the personalized predictive models to make the prognosis and diagnosis individually. The consideration of the heterogeneity among the individuals helps reduce the prediction uncertainty and improve the prediction accuracy. Two real data examples from biomedical research are studied as illustrations.     

Variable selection for logistic regression using a prediction-focused information criterion

In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the focused information criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the mean squared error of the estimator of the quantity of interest in the selected model. In this article, we propose more general versions of the FIC, allowing other risk measures such as the one based on L(p) error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy.     

Weighted normality-based estimator in correcting correlation coefficient estimation between incomplete nutrient measurements

Consider the problem of estimating the correlation between two nutrient measurements, such as the percent energy from fat obtained from a food frequency questionnaire (FFQ) and that from repeated food records or 24-hour recalls. Under a classical additive model for repeated food records, it is known that there is an attenuation effect on the correlation estimation if the sample average of repeated food records for each subject is used to estimate the underlying long-term average. This paper considers the case in which the selection probability of a subject for participation in the calibration study, in which repeated food records are measured, depends on the corresponding FFQ value, and the repeated longitudinal measurement errors have an autoregressive structure. This paper investigates a normality-based estimator and compares it with a simple method of moments. Both methods are consistent if the first two moments of nutrient measurements exist. Furthermore, joint estimating equations are applied to estimate the correlation coefficient and related nuisance parameters simultaneously. This approach provides a simple sandwich formula for the covariance estimation of the estimator. Finite sample performance is examined via a simulation study, and the proposed weighted normality-based estimator performs well under various distributional assumptions. The methods are applied to real data from a dietary assessment study.     

Intake of dietary fats and colorectal cancer risk: Prospective findings from the UK Dietary Cohort Consortium

Introduction: Epidemiologic evidence for an association between colorectal cancer (CRC) risk and total dietary fat, saturated fat (SF), monounsaturated fat (MUFA) and polyunsaturated fat (PUFA) is inconsistent. Previous studies have used food frequency questionnaires (FFQ) to assess diet, but data from food diaries may be less prone to severe measurement error than data from FFQ. Methods: We conducted a case–control study nested within seven prospective UK cohort studies, comprising 579 cases of incident CRC and 1996 matched controls. Standardized dietary data from 4- to 7-day food diaries and from FFQ were used to estimate odds ratios for CRC risk associated with intake of fat and subtypes of fat using conditional logistic regression. We also calculated multivariate measurement error corrected odds ratios for CRC using repeated food diary measurements. Results: We observed no associations between intakes of total dietary fat or types of fat and CRC risk, irrespective of whether dietary data were obtained using food diaries or FFQ. Conclusion: Our results do not support the hypothesis that intakes of total dietary fat, SF, MUFA or PUFA are linked to risk of CRC.     

Reproducibility and Relative Validity of a Food Frequency Questionnaire Developed for Adults in Taizhou,China

Objective

To evaluate the reproducibility and validity of a food frequency questionnaire (FFQ) developed to investigate the relationship between dietary factors and diseases in the adult Chinese population in East China.

Methods

A total of 78 males and 129 females aged 30–75 years completed four inconsecutive 24-hour dietary recalls (24-HRs, served as a reference method) and two FFQs (FFQ1 and FFQ2) over a nine-month interval. The reproducibility of the FFQ was estimated with correlation coefficients, cross-classification, and weighted kappa statistic. The validity was assessed by comparing the data obtained from FFQ and 24-HRs.

Results

The median nutrient intakes assessed with FFQs were higher than the average of four 24-HRs. For the food groups, Spearman, Pearson, and intraclass correlation coefficients between FFQ1 and FFQ2 ranged from 0.23 to 0.61, 0.27 to 0.64, and 0.26 to 0.65, respectively. For total energy and nutrient intakes, the corresponding coefficients ranged from 0.25 to 0.61, 0.28 to 0.64, and 0.28 to 0.62, respectively. The correlations between FFQ1 and FFQ2 for most nutrients decreased after adjustment with total energy intake. More than 70% of the subjects were classified into the same and adjacent categories by both FFQs. For food groups, the crude, energy-adjusted, and de-attenuated Spearman correlation coefficients between FFQ2 and the 24-HRs ranged from 0.17 to 0.59, 0.10 to 0.57, and 0.11 to 0.64, respectively. For total energy and nutrient intakes, the corresponding coefficients ranged from 0.20 to 0.58, 0.08 to 0.54, and 0.09 to 0.56, respectively. More than 67% of the subjects were classified into the same and adjacent categories by both instruments. Both weighted kappa statistic and Bland-Altman Plots showed reasonably acceptable agreement between the FFQ2 and 24-HRs.

Conclusion

The FFQ developed for adults in the Taizhou area is reasonably reliable and valid for assessment of most food and nutrient intakes.     

Validity of a self-administered food frequency questionnaire in the assessment of heterocyclic amine intake using 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) levels in hair

Several case-control studies have reported possible associations between heterocyclic amine (HCA) intake and the risk of cancer. The validity of questionnaires used to assess HCA intake has hardly been examined, however; in particular, no biomarker able to serve as an independent measure of habitual HCA intake has been established. In this study, we examined the validity of HCA intake estimated from a food frequency questionnaire (FFQ) using 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) level in hair as a reference method. Study subjects were 20 volunteers (7 men and 13 women) aged 25-57 years residing in Tokyo or neighboring cities in Japan. The subjects completed the FFQ, and gave 3-5g of hair twice at an interval of 1-3 months for use in establishing validity. Results showed that intakes of PhIP, MeIQ, Trp-P-1, and total HCA by the FFQ were significantly correlated with PhIP levels in hair when adjustment was made for melanin content (r=0.47, r=0.50, r=0.55, and r=0.51, respectively). The present study indicates that HCA intake estimated from this FFQ provides a reasonable ranking of individuals to allow the analysis of associations between HCA intake and risk of cancer in large-scale epidemiological studies.     

Viewing DVM via general behaviors of zooplankton: a way bridging the success of individual and population

In this paper, we viewed the diel vertical migration (DVM) of copepod in the context of the animal's immediate behaviors of everyday concerns and constructed an instantaneous behavioral criterion effective for DVM and non-DVM behaviors. This criterion employed the function of 'venturous revenue' (VR), which is the product of the food intake and probability of the survival, to evaluate the gains and losses of the behaviors that the copepod could trade-off. The optimal behaviors are to find the optimal habitats to maximize VR. Two types of VRs are formulated and tested by the theoretical analysis and simulations. The sensed VR, monitoring the real-time changes of trade-offs and thereby determining the optimum habitat, is validated to be the effective objective function for the optimization of the behavior; whereas, the realized VR, quantifying the actual profit obtained by an optimal copepod in the sensed-VR-determined habitat, defines the life history of a specific age cohort. The achievement of a robust copepod overwintering stock through integrating the dynamics of the constituent age cohorts subjected to the instantaneous behavioral criterion for DVM clearly exemplified a possible way bridging the immediate pursuit of an individual and the end success of the population.     

Empirical‐likelihood‐based criteria for model selection on marginal analysis of longitudinal data with dropout missingness

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equation (WGEE) approach is widely adopted for marginal analysis. Model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate criteria for the selection of marginal mean and correlation structures, unsatisfactory selection performance in small‐sample setups, and so forth. In particular, there are few studies to develop joint information criteria for selection of both marginal mean and correlation structures. In this work, by embedding empirical likelihood into the WGEE framework, we propose two innovative information criteria named a joint empirical Akaike information criterion and a joint empirical Bayesian information criterion, which can simultaneously select the variables for marginal mean regression and also correlation structure. Through extensive simulation studies, these empirical‐likelihood‐based criteria exhibit robustness, flexibility, and outperformance compared to the other criteria including the weighted quasi‐likelihood under the independence model criterion, the missing longitudinal information criterion, and the joint longitudinal information criterion. In addition, we provide a theoretical justification of our proposed criteria, and present two real data examples in practice for further illustration.     

黑龙江不同区域人工红松心边材及树皮削度可加性模型系统构建

基于黑龙江省孟家岗林场、东京城林业局和林口林业局不同林分条件下103株人工红松解析木的2977个圆盘数据,结合林业研究中常见的Kozak(1988)、Muhairwe(1999)、Lee(2003)、Kozak(2004)可变指数削度方程,构建带皮直径、心材直径、边材宽度、树皮厚度的削度方程,并对比选出最优基础模型;采用SAS软件PROC MODEL模块中似乎不相关回归(SUR),建立带皮直径、心材直径、边材宽度和树皮厚度削度方程的可加性模型系统,同时将区域作为哑变量引入模型中,通过调整确定系数(R_adj²)、均方根误差(RMSE)、赤池信息准则(AIC)、贝叶斯信息准则(BIC)等模型评价指标,对模型进行综合评价。结果表明: 带皮直径、心材直径、边材宽度和树皮厚度最优基础模型均为Kozak(2004);可加性模型系统在满足各分量与总量可加性的基础上,也得到较好的预测效果,预估精度均达到98%以上,引入哑变量后,可加性模型系统预测能力均有不同程度的提升,尤其心材直径和边材宽度预测能力提升更显著;不同区域带皮直径和树皮厚度削度差异较小,而心材直径、边材宽度的削度存在明显差异。本研究构建的包含哑变量可加性模型系统,不但模型预测精度较高,还满足带皮直径、心材直径、边材宽度和树皮厚度之间的可加性逻辑,为人工红松心边材及树皮材积的准确估测提供了基础。     

Statistical Aspects of the Use of Biomarkers in Nutritional Epidemiology Research

Few strong and consistent associations have arisen from observational studies of dietary consumption in relation to chronic disease risk. Measurement error in self-reported dietary assessment may be obscuring many such associations. Attempts to correct for measurement error have mostly used a second self-reported assessment in a subset of a study cohort to calibrate the self-reported assessment used throughout the cohort, under the dubious assumption of uncorrelated measurement errors between the two assessments. The use, instead, of objective biomarkers of nutrient consumption to produce calibrated consumption estimates provides a promising approach to enhance study reliability. As summarized here, we have recently applied this nutrient biomarker approach to examine energy, protein, and percent of energy from protein, in relation to disease incidence in Women’s Health Initiative cohorts, and find strong associations that are not evident without biomarker calibration. A major bottleneck for the broader use of a biomarker-calibration approach is the rather few nutrients for which a suitable biomarker has been developed. Some methodologic approaches to the development of additional pertinent biomarkers, including the possible use of a respiratory quotient from indirect calorimetry for macronutrient biomarker development, and the potential of human feeding studies for the evaluation of a range of urine- and blood-based potential biomarkers, will briefly be described.     

Comparison of energy evaluation systems and a mechanistic model for milk production by dairy cattle offered fresh grass-based diets

Grass-based diets are of increasing social-economic importance in dairy cattle farming, but their low supply of glucogenic nutrients may limit the production of milk. Current evaluation systems that assess the energy supply and requirements are based on metabolisable energy (ME) or net energy (NE). These systems do not consider the characteristics of the energy delivering nutrients. In contrast, mechanistic models take into account the site of digestion, the type of nutrient absorbed and the type of nutrient required for production of milk constituents, and may therefore give a better prediction of supply and requirement of nutrients. The objective of the present study is to compare the ability of three energy evaluation systems, viz. the Dutch NE system, the agricultural and food research council (AFRC) ME system, and the feed into milk (FIM) ME system, and of a mechanistic model based on Dijkstra et al. [Simulation of digestion in cattle fed sugar cane: prediction of nutrient supply for milk production with locally available supplements. J. Agric. Sci., Cambridge 127, 247–60] and Mills et al. [A mechanistic model of whole-tract digestion and methanogenesis in the lactating dairy cow: model development, evaluation and application. J. Anim. Sci. 79, 1584–97] to predict the feed value of grass-based diets for milk production. The dataset for evaluation consists of 41 treatments of grass-based diets (at least 0.75 g ryegrass/g diet on DM basis). For each model, the predicted energy or nutrient supply, based on observed intake, was compared with predicted requirement based on observed performance. Assessment of the error of energy or nutrient supply relative to requirement is made by calculation of mean square prediction error (MSPE) and by concordance correlation coefficient (CCC). All energy evaluation systems predicted energy requirement to be lower (6–11%) than energy supply. The root MSPE (expressed as a proportion of the supply) was lowest for the mechanistic model (0.061), followed by the Dutch NE system (0.082), FIM ME system (0.097) and AFRC ME system (0.118). For the energy evaluation systems, the error due to overall bias of prediction dominated the MSPE, whereas for the mechanistic model, proportionally 0.76 of MSPE was due to random variation. CCC analysis confirmed the higher accuracy and precision of the mechanistic model compared with energy evaluation systems. The error of prediction was positively related to grass protein content for the Dutch NE system, and was also positively related to grass DMI level for all models. In conclusion, current energy evaluation systems overestimate energy supply relative to energy requirement on grass-based diets for dairy cattle. The mechanistic model predicted glucogenic nutrients to limit performance of dairy cattle on grass-based diets, and proved to be more accurate and precise than the energy systems. The mechanistic model could be improved by allowing glucose maintenance and utilization requirements parameters to be variable.     

Compatible Models of Carbon Content of Individual Trees on a Cunninghamia lanceolata Plantation in Fujian Province,China

We tried to establish compatible carbon content models of individual trees for a Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantation from Fujian province in southeast China. In general, compatibility requires that the sum of components equal the whole tree, meaning that the sum of percentages calculated from component equations should equal 100%. Thus, we used multiple approaches to simulate carbon content in boles, branches, foliage leaves, roots and the whole individual trees. The approaches included (i) single optimal fitting (SOF), (ii) nonlinear adjustment in proportion (NAP) and (iii) nonlinear seemingly unrelated regression (NSUR). These approaches were used in combination with variables relating diameter at breast height (D) and tree height (H), such as D, D²H, DH and D&H (where D&H means two separate variables in bivariate model). Power, exponential and polynomial functions were tested as well as a new general function model was proposed by this study. Weighted least squares regression models were employed to eliminate heteroscedasticity. Model performances were evaluated by using mean residuals, residual variance, mean square error and the determination coefficient. The results indicated that models with two dimensional variables (DH, D²H and D&H) were always superior to those with a single variable (D). The D&H variable combination was found to be the most useful predictor. Of all the approaches, SOF could establish a single optimal model separately, but there were deviations in estimating results due to existing incompatibilities, while NAP and NSUR could ensure predictions compatibility. Simultaneously, we found that the new general model had better accuracy than others. In conclusion, we recommend that the new general model be used to estimate carbon content for Chinese fir and considered for other vegetation types as well.     

Joint model selection of marginal mean regression and correlation structure for longitudinal data with missing outcome and covariates

This work develops a joint model selection criterion for simultaneously selecting the marginal mean regression and the correlation/covariance structure in longitudinal data analysis where both the outcome and the covariate variables may be subject to general intermittent patterns of missingness under the missing at random mechanism. The new proposal, termed “joint longitudinal information criterion” (JLIC), is based on the expected quadratic error for assessing model adequacy, and the second‐order weighted generalized estimating equation (WGEE) estimation for mean and covariance models. Simulation results reveal that JLIC outperforms existing methods performing model selection for the mean regression and the correlation structure in a two stage and hence separate manner. We apply the proposal to a longitudinal study to identify factors associated with life satisfaction in the elderly of Taiwan.     

Bayesian inference for prevalence in longitudinal two-phase studies

We consider Bayesian inference and model selection for prevalence estimation using a longitudinal two-phase design in which subjects initially receive a low-cost screening test followed by an expensive diagnostic test conducted on several occasions. The change in the subject's diagnostic probability over time is described using four mixed-effects probit models in which the subject-specific effects are captured by latent variables. The computations are performed using Markov chain Monte Carlo methods. These models are then compared using the deviance information criterion. The methodology is illustrated with an analysis of alcohol and drug use in adolescents using data from the Great Smoky Mountains Study.