Estimation in capture-recapture models when covariates are subject to measurement errors

We consider estimation problems in capture-recapture models when the covariates or the auxiliary variables are measured with errors. The naive approach, which ignores measurement errors, is found to be unacceptable in the estimation of both regression parameters and population size: it yields estimators with biases increasing with the magnitude of errors, and flawed confidence intervals. To account for measurement errors, we derive a regression parameter estimator using a regression calibration method. We develop modified estimators of the population size accordingly. A simulation study shows that the resulting estimators are more satisfactory than those from either the naive approach or the simulation extrapolation (SIMEX) method. Data from a bird species Prinia flaviventris in Hong Kong are analyzed with and without the assumption of measurement errors, to demonstrate the effects of errors on estimations.     

Approximate maximum likelihood estimation for logistic regression with covariate measurement error

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

On Method of Moments Estimation in Linear Mixed Effects Models with Measurement Error on Covariates and Response with Application to a Longitudinal Study of Gene-Environment Interaction

We study a linear mixed effects model for longitudinal data, where the response variable and covariates with fixed effects are subject to measurement error. We propose a method of moment estimation that does not require any assumption on the functional forms of the distributions of random effects and other random errors in the model. For a classical measurement error model we apply the instrumental variable approach to ensure identifiability of the parameters. Our methodology, without instrumental variables, can be applied to Berkson measurement errors. Using simulation studies, we investigate the finite sample performances of the estimators and show the impact of measurement error on the covariates and the response on the estimation procedure. The results show that our method performs quite satisfactory, especially for the fixed effects with measurement error (even under misspecification of measurement error model). This method is applied to a real data example of a large birth and child cohort study.     

A Bayesian adjustment for multiplicative measurement errors for a calibration problem with application to a stem cell study

We develop a Bayesian approach to a calibration problem with one interested covariate subject to multiplicative measurement errors. Our work is motivated by a stem cell study with the objective of establishing the recommended minimum doses for stem cell engraftment after a blood transplant. When determining a safe stem cell dose based on the prefreeze samples, the postcryopreservation recovery rate enters in the model as a multiplicative measurement error term, as shown in the model. We examine the impact of ignoring measurement errors in terms of asymptotic bias in the regression coefficient. According to the general structure of data available in practice, we propose a two-stage Bayesian method to perform model estimation via R2WinBUGS (Sturtz, Ligges, and Gelman, 2005, Journal of Statistical Software 12, 1-16). We illustrate this method by the aforementioned motivating example. The results of this study allow routine peripheral blood stem cell processing laboratories to establish recommended minimum stem cell doses for transplant and develop a systematic approach for further deciding whether the postthaw analysis is warranted.     

Binary Regression Analysis with Pooled Exposure Measurements: A Regression Calibration Approach

Summary It has become increasingly common in epidemiological studies to pool specimens across subjects to achieve accurate quantitation of biomarkers and certain environmental chemicals. In this article, we consider the problem of fitting a binary regression model when an important exposure is subject to pooling. We take a regression calibration approach and derive several methods, including plug‐in methods that use a pooled measurement and other covariate information to predict the exposure level of an individual subject, and normality‐based methods that make further adjustments by assuming normality of calibration errors. Within each class we propose two ways to perform the calibration (covariate augmentation and imputation). These methods are shown in simulation experiments to effectively reduce the bias associated with the naive method that simply substitutes a pooled measurement for all individual measurements in the pool. In particular, the normality‐based imputation method performs reasonably well in a variety of settings, even under skewed distributions of calibration errors. The methods are illustrated using data from the Collaborative Perinatal Project.     

A comparison of two non-invasive methods for measuring scapular orientation in functional positions

Identification of scapular dyskinesis and evaluation of interventions depend on the ability to properly measure scapulothoracic (ST) motion. The most widely used measurement approach is the acromion marker cluster (AMC), which can yield large errors in extreme humeral elevation and can be inaccurate in children and patient populations. Recently, an individualized regression approach has been proposed as an alternative to the AMC. This technique utilizes the relationship between ST orientation, humerothoracic orientation and acromion process position derived from calibration positions to predict dynamic ST orientations from humerothoracic and acromion process measures during motion. These individualized regressions demonstrated promising results for healthy adults; however, this method had not yet been compared to the more conventional AMC. This study compared ST orientation estimates by the AMC and regression approaches to static ST angles determined by surface markers placed on palpated landmarks in typically developing adolescents performing functional tasks. Both approaches produced errors within the range reported in the literature for skin-based scapular measurement techniques. The performance of the regression approach suffered when applied to positions outside of the range of motion in the set of calibration positions. The AMC significantly underestimated ST internal rotation across all positions and overestimated posterior tilt in some positions. Overall, root mean square errors for the regression approach were smaller than the AMC for every position across all axes of ST motion. Accordingly, we recommend the regression approach as a suitable technique for measuring ST kinematics in functional motion.     

Linear relations in biomechanics: the statistics of scaling functions

The problem of fitting a linear relation to a bivariate data cluster obtained from morphometric measurement or from experiment is formulated rigorously, and a family of solutions (the general structural relation , g.s.r.) is derived. The regression, reduced major axis and major axis models are special cases of this model; it permits a more realistic treatment of the errors in the variates, in particular when the errors are correlated, which is particularly important in the many biological situations in which the variates contain uncontrolled real variation in addition to measurement errors. The analysis is particularly directed to the testing of hypotheses about scaling relations derived from biomechanical theory. By making different assumptions about the configuration of the errors, the g.s.r. can also be used to test for transposition allometry and for the significance of an estimated or hypothesized gradient. The model generalizes simply to multivariate problems. Application is demonstrated with examples drawn from the study of bird flight mechanics. Finally, it is demonstrated that since observed quantities correspond to peaks of adaptation or of selective fitness, scaling relations are determined primarily by scale variation of constraints on adaptation and behaviour, and are the result of a variety of interacting factors rather than a response to a single selective force described by one simple hypothesis.     

Laplace approximation in measurement error models

Likelihood analysis for regression models with measurement errors in explanatory variables typically involves integrals that do not have a closed-form solution. In this case, numerical methods such as Gaussian quadrature are generally employed. However, when the dimension of the integral is large, these methods become computationally demanding or even unfeasible. This paper proposes the use of the Laplace approximation to deal with measurement error problems when the likelihood function involves high-dimensional integrals. The cases considered are generalized linear models with multiple covariates measured with error and generalized linear mixed models with measurement error in the covariates. The asymptotic order of the approximation and the asymptotic properties of the Laplace-based estimator for these models are derived. The method is illustrated using simulations and real-data analysis.     

总体平均处理效应的拟极大似然估计

本文给出可交换条件下多维协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质．     

Collaborative trial of the direct epifluorescent filter technique (DEFT), a rapid method for counting bacteria in milk

The direct epifluorescent filter technique (DEFT) is a new rapid method which uses membrane filtration and epifluorescent microscopy for counting bacteria in milk. A collaborative trial of the DEFT was conducted between six laboratories. Each laboratory obtained a highly significant relationship between the DEFT count and plate count with a correlation coefficient generally > 0.9 but there were significant differences between these relationships. The repeatability of the DEFT, although ca 1·5 times worse than that of the plate count, was of a level acceptable in practice. Reproducibility of the DEFT was ca 3 times that of the plate count. This poor reproducibility was probably mainly due to counting errors. Possible reasons for this and ways of reducing counting errors are discussed.     

单个协变量带有测量误差的多维结构回归模型

给出可交换条件下单个协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质.     

A robust curve-fitting procedure for the analysis of plasmid DNA strand break data from gel electrophoresis

A robust method for fitting to the results of gel electrophoresis assays of damage to plasmid DNA caused by radiation is presented. This method makes use of nonlinear regression to fit analytically derived dose-response curves to observations of the supercoiled, open circular and linear plasmid forms simultaneously, allowing for more accurate results than fitting to individual forms. Comparisons with a commonly used analysis method show that while there is a relatively small benefit between the methods for data sets with small errors, the parameters generated by this method remain much more closely distributed around the true value in the face of increasing measurement uncertainties. This allows for parameters to be specified with greater confidence, reflected in a reduction of errors on fitted parameters. On test data sets, fitted uncertainties were reduced by 30%, similar to the improvement that would be offered by moving from triplicate to fivefold repeats (assuming standard errors). This method has been implemented in a popular spreadsheet package and made available online to improve its accessibility.     

Quantitative Risk Assessment in Epidemiological Studies Investigating Threshold Effects

In this paper a method for quantitative risk assessment in epidemiological studies investigating threshold effects is proposed. The simple logistic regression model is used to describe the association between a binary response variable and a continuous risk factor. By defining acceptable levels for the absolute risk and the risk gradient the corresponding benchmark values of the risk factor can be calculated by means of nonlinear functions of the logistic regression coefficients. Standard errors and confidence intervals of the benchmark values are derived by means of the multivariate delta method. The proposed approach is compared with the threshold model of Ulm (1991) for assessing threshold values in epidemiological studies.     

Shared uncertainty in measurement error problems, with application to Nevada Test Site fallout data

In radiation epidemiology, it is often necessary to use mathematical models in the absence of direct measurements of individual doses. When complex models are used as surrogates for direct measurements to estimate individual doses that occurred almost 50 years ago, dose estimates will be associated with considerable error, this error being a mixture of (a) classical measurement error due to individual data such as diet histories and (b) Berkson measurement error associated with various aspects of the dosimetry system. In the Nevada Test Site(NTS) Thyroid Disease Study, the Berkson measurement errors are correlated within strata. This article concerns the development of statistical methods for inference about risk of radiation dose on thyroid disease, methods that account for the complex error structure inherence in the problem. Bayesian methods using Markov chain Monte Carlo and Monte-Carlo expectation-maximization methods are described, with both sharing a key Metropolis-Hastings step. Regression calibration is also considered, but we show that regression calibration does not use the correlation structure of the Berkson errors. Our methods are applied to the NTS Study, where we find a strong dose-response relationship between dose and thyroiditis. We conclude that full consideration of mixtures of Berkson and classical uncertainties in reconstructed individual doses are important for quantifying the dose response and its credibility/confidence interval. Using regression calibration and expectation values for individual doses can lead to a substantial underestimation of the excess relative risk per gray and its 95% confidence intervals.     

Generalized varying coefficient models for longitudinal data

We propose a generalization of the varying coefficient modelfor longitudinal data to cases where not only current but alsorecent past values of the predictor process affect current response.More precisely, the targeted regression coefficient functionsof the proposed model have sliding window supports around currenttime t. A variant of a recently proposed two-step estimationmethod for varying coefficient models is proposed for estimationin the context of these generalized varying coefficient models,and is found to lead to improvements, especially for the caseof additive measurement errors in both response and predictors.The proposed methodology for estimation and inference is alsoapplicable for the case of additive measurement error in thecommon versions of varying coefficient models that relate onlycurrent observations of predictor and response processes toeach other. Asymptotic distributions of the proposed estimatorsare derived, and the model is applied to the problem of predictingprotein concentrations in a longitudinal study. Simulation studiesdemonstrate the efficacy of the proposed estimation procedure.     

A Bayesian Approach to Joint Mixed‐Effects Models with a Skew‐Normal Distribution and Measurement Errors in Covariates

Summary In recent years, nonlinear mixed‐effects (NLME) models have been proposed for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain intersubject variations. However, one often assumes that both model random error and random effects are normally distributed, which may not always give reliable results if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. In this article, we address these issues simultaneously by jointly modeling the response and covariate processes using a Bayesian approach to NLME models with covariate measurement errors and a skew‐normal distribution. A real data example is offered to illustrate the methodologies by comparing various potential models with different distribution specifications. It is showed that the models with skew‐normality assumption may provide more reasonable results if the data exhibit skewness and the results may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment.     

Comparison of regression methods for spatially‐autocorrelated count data on regularly‐ and irregularly‐spaced locations

It has long been known that insufficient consideration of spatial autocorrelation leads to unreliable hypothesis‐tests and inaccurate parameter estimates. Yet, ecologists are confronted with a confusing array of methods to account for spatial autocorrelation. Although Beale et al. (2010) provided guidance for continuous data on regular grids, researchers still need advice for other types of data in more flexible spatial contexts. In this paper, we extend Beale et al. (2010)‘s work to count data on both regularly‐ and irregularly‐spaced plots, the latter being commonly encountered in ecological studies. Through a simulation‐based approach, we assessed the accuracy and the type I errors of two frequentist and two Bayesian ready‐to‐use methods in the family of generalized mixed models, with distance‐based or neighbourhood‐based correlated random effects. In addition, we tested whether the methods are robust to spatial non‐stationarity, and over‐ and under‐dispersion – both typical features of species distribution count data which violate standard regression assumptions. In the simplest of our simulated datasets, the two frequentist methods gave inflated type I errors, while the two Bayesian methods provided satisfying results. When facing real‐world complexities, the distance‐based Bayesian method (MCMC with Langevin–Hastings updates) performed best of all. We hope that, in the light of our results, ecological researchers will feel more comfortable including spatial autocorrelation in their analyses of count data.     

Non-linear heteroscedastic regression model for determination of methotrexate in human plasma by high-performance liquid chromatography

Generalized least squares regression with variance function estimation was used to derive the calibration function for measurement of methotrexate plasma concentration and its results were compared with weighted least squares regression by usual weight factors and also with that of ordinary least squares method. In the calibration curve range of 0.05 to 100 microM, both heteroscedasticity and non-linearity were present therefore ordinary least squares linear regression methods could result in large errors in the calculation of methotrexate concentration. Generalized least squares regression with variance function estimation worked better than both the weighted regression with the usual weight factors and ordinary least squares regression and gave better estimates for methotrexate concentration.     

Generalized Binomial Regression Model

The generalized negative binomial distribution has been found useful in fitting over-dispersed as well as under-dispersed count data. We define and study the generalized binomial regression model which is used to predict a count response variable affected by one or more explanatory variables. The methods of maximum likelihood and moments are given for estimating the model parameters. Approximate tests for the adequacy of the model are considered. The generalized binomial regression model has been applied to two observed data sets to which binomial regression model was applied earlier.     

Effects of pH probe lag on bioreactor mixing time estimation

Mixing time is one of the most important characteristics of bioreactors used to validate computational fluid dynamics (CFD) models in bioprocess. The pH tracer based method is commonly used to estimate mixing time by monitoring the pH change after perturbation to the system. However, pH probe lag is known to introduce errors in the test results. To determine the impact of probe lag on the measurement, pH probe response times were investigated. A second order mathematical model was established to describe the probe response profile and calculate the probe transfer function which was used to correct the empirical results. The corrected mixing time was used to validate the CFD models and also showed that the impact of pH probe response time on mixing time measurement is significant even in larger (pilot and manufacturing) scales. In addition, comparison with a conductance based tracer method is also discussed in this paper.