Estimation of the correlation between nutrient intake measures under restricted sampling

Food frequency questionnaires (FFQs) are commonly used to assess dietary intake in epidemiologic research. To evaluate the FFQ reliability, the commonly used approach is to estimate the correlation coefficient between the data given in FFQ and those in food records (for example, 4-day food records [4DFR]) for nutrients of interest. However, in a dietary intervention study, a criterion for eligibility may be to select participants who have baseline FFQ-measured dietary intake of percent energy from fat above a prespecified quantity. Other instruments, such as the 4DFR, may be subsequently administrated only to eligible participants. Under these circumstances, analysis without adjusting for the restricted population will usually lead to biased estimation of correlation coefficients and other parameters of interest. In this paper, we apply likelihood-based and multiple imputation (MI) methods to accommodate such incomplete data obtained as a result of the study design. A simulation study is conducted to examine finite sample performance of various estimators. We note that both the MI estimate and the maximum likelihood (ML) estimate based on a bivariate-normal model are not sensitive to departures from this normality assumption. This led us to investigate robustness properties of the ML estimator analytically. We present some data analyses from a dietary assessment study from the Women's Health Initiative to illustrate the methods.     

Interval Estimation of Simple Difference in Dichotomous Data with Repeated Measurements

When comparing two treatments, we often use the simple difference between the probabilities of response to measure the efficacy of one treatment over the other. When the measurement of outcome is unreliable or the cost of obtaining additional subjects is high relative to that of additional measurements from the obtained subjects, we may often consider taking more than one measurement per subject to increase the precision of an interval estimator. This paper focuses discussion on interval estimation of simple difference when we take repeated measurements per subject. This paper develops four asymptotic interval estimators of simple difference for any finite number of measurements per subject. This paper further applies Monte Carlo simulation to evaluate the finite‐sample performance of these estimators in a variety of situations. Finally, this paper includes a discussion on sample size determination on the basis of both the average length and the probability of controlling the length of the resulting interval estimate proposed elsewhere.     

Using local correlation in kernel-based smoothers for dependent data

We consider the general problem of smoothing correlated data to estimate the nonparametric mean function when a random, but bounded, number of measurements is available for each independent subject. We propose a simple extension to the local polynomial regression smoother that retains the asymptotic properties of the working independence estimator, while typically reducing both the conditional bias and variance for practical sample sizes, as demonstrated by exact calculations for some particular models. We illustrate our method by smoothing longitudinal functional decline data for 100 patients with Huntington's disease. The class of local polynomial kernel-based estimating equations previously considered in the literature is shown to use the global correlation structure in an apparently detrimental way, which explains why some previous attempts to incorporate correlation were found to be asymptotically inferior to the working independence estimator.     

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.     

Efficacy of repeated measures in regression models with measurement error.

Ignoring measurement error may cause bias in the estimation of regression parameters. When the true covariates are unobservable, multiple imprecise measurements can be used in the analysis to correct for the associated bias. We suggest a simple estimating procedure that gives consistent estimates of regression parameters by using the repeated measurements with error. The relative Pitman efficiency of our estimator based on models with and without measurement error has been found to be a simple function of the number of replicates and the ratio of intra- to inter-variance of the true covariate. The procedure thus provides a guide for deciding the number of repeated measurements in the design stage. An example from a survey study is presented.     

A targeted maximum likelihood estimator for two-stage designs

We consider two-stage sampling designs, including so-called nested case control studies, where one takes a random sample from a target population and completes measurements on each subject in the first stage. The second stage involves drawing a subsample from the original sample, collecting additional data on the subsample. This data structure can be viewed as a missing data structure on the full-data structure collected in the second-stage of the study. Methods for analyzing two-stage designs include parametric maximum likelihood estimation and estimating equation methodology. We propose an inverse probability of censoring weighted targeted maximum likelihood estimator (IPCW-TMLE) in two-stage sampling designs and present simulation studies featuring this estimator.     

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.     

An Evaluation of Methods for the Estimation of Sensitivity and Specificity of Site-Specific Diagnostic Tests

The performance of diagnostic tests is often evaluated by estimating their sensitivity and specificity with respect to a traditionally accepted standard test regarded as a “gold standard” in making the diagnosis. Correlated samples of binary data arise in many fields of application. The fundamental unit for analysis is occasionally the site rather than the subject in site-specific studies. Statistical methods that take into account the within-subject corelation should be employed to estimate the sensitivity and the specificity of diagnostic tests since site-specific results within a subject can be highly correlated. I introduce several statistical methods for the estimation of the sensitivity and the specificity of sitespecific diagnostic tests. I apply these techniques to the data from a study involving an enzymatic diagnostic test to motivate and illustrate the estimation of the sensitivity and the specificity of periodontal diagnostic tests. I present results from a simulation study for the estimation of diagnostic sensitivity when the data are correlated within subjects. Through a simulation study, I compare the performance of the binomial estimator pCBE, the ratio estimator pCBE, the weighted estimator pCWE, the intracluster correlation estimator pCIC, and the generalized estimating equation (GEE) estimator PCGEE in terms of biases, observed variances, mean squared errors (MSE), relative efficiencies of their variances and 95 per cent coverage proportions. I recommend using PCBE when σ == 0. I recommend use of the weighted estimator PCWE when σ = 0.6. When σ == 0.2 or σ == 0.4, and the number of subjects is at least 30, PCGEE performs well.     

Inference from single occasion capture experiments using genetic markers

Accurate estimation of the size of animal populations is an important task in ecological science. Recent advances in the field of molecular genetics researches allow the use of genetic data to estimate the size of a population from a single capture occasion rather than repeated occasions as in the usual capture–recapture experiments. Estimating the population size using genetic data also has sometimes led to estimates that differ markedly from each other and also from classical capture–recapture estimates. Here, we develop a closed form estimator that uses genetic information to estimate the size of a population consisting of mothers and daughters, focusing on estimating the number of mothers, using data from a single sample. We demonstrate the estimator is consistent and propose a parametric bootstrap to estimate the standard errors. The estimator is evaluated in a simulation study and applied to real data. We also consider maximum likelihood in this setting and discover problems that preclude its general use.     

Reproducibility and relative validity of a food frequency questionnaire developed for female adolescents in Suihua, North China

Background

This study aims to evaluate the reproducibility and validity of a food frequency questionnaire (FFQ) developed for female adolescents in the Suihua area of North China. The FFQ was evaluated against the average of 24-hour dietary recalls (24-HRs).

Methodology/Principal Findings

A total of 168 female adolescents aged 12 to 18 completed nine three consecutive 24-HRs (one three consecutive 24 HRs per month) and two FFQs over nine months. The reproducibility of the FFQ was estimated using intraclass correlation coefficients (ICCs), and its relative validity was assessed by comparing it with the 24-HRs. The mean values of the 24-HRs were lower than those of the FFQs, except for protein (in FFQ1) and iron (in FFQ2). The ICCs for all nutrients and food groups in FFQ1 and FFQ2 were moderately correlated (0.4–0.8). However, all the ICCs decreased after adjusting for energy. The weighted κ statistic showed moderate agreement (0.40–0.6) for all nutrients and food groups, except for niacin and calcium, which showed poor agreement (0.35). The relative validity results indicate that the crude Spearman''s correlation coefficients of FFQ1 and the 24-HRs ranged from 0.41 (for Vitamin C) to 0.65 (for fruit). The coefficients of each nutrient and food group in FFQ2 and the 24-HRs were higher than those in FFQ1 and the 24-HRs, indicating good correlation. Although all energy-adjusted Spearman''s correlation coefficients were lower than the crude coefficients, de-attenuation to correct for intra-individual variability improved the correlation coefficients. The weighted κ coefficients of nutrients and food groups ranged from 0.32 for beans to 0.52 for riboflavin in FFQ1 and the 24-HRs, and 0.32 for Vitamin C to 0.54 for riboflavin in FFQ2 and the 24-HRs.

Conclusion

The FFQ developed for female adolescents in the Suihua area is a reliable and valid instrument for ranking individuals within this 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.     

Blinded versus unblinded estimation of a correlation coefficient to inform interim design adaptations

Regulatory authorities require that the sample size of a confirmatory trial is calculated prior to the start of the trial. However, the sample size quite often depends on parameters that might not be known in advance of the study. Misspecification of these parameters can lead to under‐ or overestimation of the sample size. Both situations are unfavourable as the first one decreases the power and the latter one leads to a waste of resources. Hence, designs have been suggested that allow a re‐assessment of the sample size in an ongoing trial. These methods usually focus on estimating the variance. However, for some methods the performance depends not only on the variance but also on the correlation between measurements. We develop and compare different methods for blinded estimation of the correlation coefficient that are less likely to introduce operational bias when the blinding is maintained. Their performance with respect to bias and standard error is compared to the unblinded estimator. We simulated two different settings: one assuming that all group means are the same and one assuming that different groups have different means. Simulation results show that the naïve (one‐sample) estimator is only slightly biased and has a standard error comparable to that of the unblinded estimator. However, if the group means differ, other estimators have better performance depending on the sample size per group and the number of groups.     

One-step targeted maximum likelihood estimation for time-to-event outcomes

Researchers in observational survival analysis are interested in not only estimating survival curve nonparametrically but also having statistical inference for the parameter. We consider right-censored failure time data where we observe n independent and identically distributed observations of a vector random variable consisting of baseline covariates, a binary treatment at baseline, a survival time subject to right censoring, and the censoring indicator. We assume the baseline covariates are allowed to affect the treatment and censoring so that an estimator that ignores covariate information would be inconsistent. The goal is to use these data to estimate the counterfactual average survival curve of the population if all subjects are assigned the same treatment at baseline. Existing observational survival analysis methods do not result in monotone survival curve estimators, which is undesirable and may lose efficiency by not constraining the shape of the estimator using the prior knowledge of the estimand. In this paper, we present a one-step Targeted Maximum Likelihood Estimator (TMLE) for estimating the counterfactual average survival curve. We show that this new TMLE can be executed via recursion in small local updates. We demonstrate the finite sample performance of this one-step TMLE in simulations and an application to a monoclonal gammopathy data.     

A pseudo-likelihood method for estimating misclassification probabilities in competing-risks settings when true-event data are partially observed

Outcome misclassification occurs frequently in binary-outcome studies and can result in biased estimation of quantities such as the incidence, prevalence, cause-specific hazards, cumulative incidence functions, and so forth. A number of remedies have been proposed to address the potential misclassification of the outcomes in such data. The majority of these remedies lie in the estimation of misclassification probabilities, which are in turn used to adjust analyses for outcome misclassification. A number of authors advocate using a gold-standard procedure on a sample internal to the study to learn about the extent of the misclassification. With this type of internal validation, the problem of quantifying the misclassification also becomes a missing data problem as, by design, the true outcomes are only ascertained on a subset of the entire study sample. Although, the process of estimating misclassification probabilities appears simple conceptually, the estimation methods proposed so far have several methodological and practical shortcomings. Most methods rely on missing outcome data to be missing completely at random (MCAR), a rather stringent assumption which is unlikely to hold in practice. Some of the existing methods also tend to be computationally-intensive. To address these issues, we propose a computationally-efficient, easy-to-implement, pseudo-likelihood estimator of the misclassification probabilities under a missing at random (MAR) assumption, in studies with an available internal-validation sample. We present the estimator through the lens of studies with competing-risks outcomes, though the estimator extends beyond this setting. We describe the consistency and asymptotic distributional properties of the resulting estimator, and derive a closed-form estimator of its variance. The finite-sample performance of this estimator is evaluated via simulations. Using data from a real-world study with competing-risks outcomes, we illustrate how the proposed method can be used to estimate misclassification probabilities. We also show how the estimated misclassification probabilities can be used in an external study to adjust for possible misclassification bias when modeling cumulative incidence functions.     

Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample

Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called a calibration sample. In addition to the surrogate variables that are available among the subjects in the calibration sample, we consider the situation when there is an instrumental variable available for all study subjects. An instrumental variable is correlated with the unobserved true exposure variable, and hence can be useful in the estimation of the regression coefficients. In this paper, we propose a nonparametric method for Cox regression using the observed data from the whole cohort. The nonparametric estimator is the best linear combination of a nonparametric correction estimator from the calibration sample and the difference of the naive estimators from the calibration sample and the whole cohort. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via intensive simulation studies. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.     

Robust inference on the average treatment effect using the outcome highly adaptive lasso

Many estimators of the average effect of a treatment on an outcome require estimation of the propensity score, the outcome regression, or both. It is often beneficial to utilize flexible techniques, such as semiparametric regression or machine learning, to estimate these quantities. However, optimal estimation of these regressions does not necessarily lead to optimal estimation of the average treatment effect, particularly in settings with strong instrumental variables. A recent proposal addressed these issues via the outcome-adaptive lasso, a penalized regression technique for estimating the propensity score that seeks to minimize the impact of instrumental variables on treatment effect estimators. However, a notable limitation of this approach is that its application is restricted to parametric models. We propose a more flexible alternative that we call the outcome highly adaptive lasso. We discuss the large sample theory for this estimator and propose closed-form confidence intervals based on the proposed estimator. We show via simulation that our method offers benefits over several popular approaches.     

Robust estimation of multivariate covariance components

In many settings, such as interlaboratory testing, small area estimation in sample surveys, and heritability studies, investigators are interested in estimating covariance components for multivariate measurements. However, the presence of outliers can seriously distort estimates obtained using standard procedures such as maximum likelihood. We propose a procedure based on M-estimation for robustly estimating multivariate covariance components in the presence of outliers; the procedure applies to balanced and unbalanced data. We present an algorithm for computing the robust estimates and examine the performance of the estimator through a simulation study. The estimator is used to find covariance components and identify outliers in a study of variability of egg length and breadth measurements of American coots.     

On the analysis of high order moments of fluorescence fluctuations.

A simple, straightforward analysis to characterize the distribution of aggregate sizes in a reversible aggregation system at equilibrium is presented. The method, an extension of fluorescence correlation spectroscopy (FCS), is based on measurements of higher order moments of spontaneous fluctuations of fluorescence intensity emitted from a defined open region of the sample. These fluctuations indicate fluctuations of the numbers of the fluorescent molecules in the observation region. Shot noise resulting from the random character of fluorescence emission and from the photoelectric detection system is modeled as a Poisson distribution and is subtracted from the measured photon count fluctuation moments to yield the desired fluorescence fluctuation moments. This analysis can also be used to estimate the fraction of immobile fluorophores in FCS measurements.     

Modified Gaussian estimation for correlated binary data

In this paper, we develop a Gaussian estimation (GE) procedure to estimate the parameters of a regression model for correlated (longitudinal) binary response data using a working correlation matrix. A two‐step iterative procedure is proposed for estimating the regression parameters by the GE method and the correlation parameters by the method of moments. Consistency properties of the estimators are discussed. A simulation study was conducted to compare 11 estimators of the regression parameters, namely, four versions of the GE, five versions of the generalized estimating equations (GEEs), and two versions of the weighted GEE. Simulations show that (i) the Gaussian estimates have the smallest mean square error and best coverage probability if the working correlation structure is correctly specified and (ii) when the working correlation structure is correctly specified, the GE and the GEE with exchangeable correlation structure perform best as opposed to when the correlation structure is misspecified.     

Segregation analysis of continuous phenotypes by using higher sample moments.

The present article discusses the use of computational methods based on generalized estimating equations (GEE), as a potential alternative to full maximum-likelihood methods, for performing segregation analysis of continuous phenotypes by using randomly selected family data. The method that we propose can estimate effect and degree of dominance of a major gene in the presence of additional nongenetic or polygenetic familial associations, by relating sample moments to their expectations calculated under the genetic model. It is known that all parameters in basic major-gene models cannot be identified, for estimation purposes, solely in terms of the first two sample moments of data from randomly selected families. Thus, we propose the use of higher (third order) sample moments to resolve this identifiability problem, in a pseudo-profile likelihood estimation scheme. In principle, our methods may be applied to fitting genetic models by using complex pedigrees and for estimation in the presence of missing phenotype data for family members. In order to assess its statistical efficiency we compare several variants of the method with each other and with maximum-likelihood estimates provided by the SAGE computer package in a simulation study.