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1.  Impact of Uncertainties in Exposure Assessment on Estimates of Thyroid Cancer Risk among Ukrainian Children and Adolescents Exposed from the Chernobyl Accident 
PLoS ONE  2014;9(1):e85723.
The 1986 accident at the Chernobyl nuclear power plant remains the most serious nuclear accident in history, and excess thyroid cancers, particularly among those exposed to releases of iodine-131 remain the best-documented sequelae. Failure to take dose-measurement error into account can lead to bias in assessments of dose-response slope. Although risks in the Ukrainian-US thyroid screening study have been previously evaluated, errors in dose assessments have not been addressed hitherto. Dose-response patterns were examined in a thyroid screening prevalence cohort of 13,127 persons aged <18 at the time of the accident who were resident in the most radioactively contaminated regions of Ukraine. We extended earlier analyses in this cohort by adjusting for dose error in the recently developed TD-10 dosimetry. Three methods of statistical correction, via two types of regression calibration, and Monte Carlo maximum-likelihood, were applied to the doses that can be derived from the ratio of thyroid activity to thyroid mass. The two components that make up this ratio have different types of error, Berkson error for thyroid mass and classical error for thyroid activity. The first regression-calibration method yielded estimates of excess odds ratio of 5.78 Gy−1 (95% CI 1.92, 27.04), about 7% higher than estimates unadjusted for dose error. The second regression-calibration method gave an excess odds ratio of 4.78 Gy−1 (95% CI 1.64, 19.69), about 11% lower than unadjusted analysis. The Monte Carlo maximum-likelihood method produced an excess odds ratio of 4.93 Gy−1 (95% CI 1.67, 19.90), about 8% lower than unadjusted analysis. There are borderline-significant (p = 0.101–0.112) indications of downward curvature in the dose response, allowing for which nearly doubled the low-dose linear coefficient. In conclusion, dose-error adjustment has comparatively modest effects on regression parameters, a consequence of the relatively small errors, of a mixture of Berkson and classical form, associated with thyroid dose assessment.
doi:10.1371/journal.pone.0085723
PMCID: PMC3906013  PMID: 24489667
2.  THE IMPACT OF DOSIMETRY UNCERTAINTIES ON DOSE-RESPONSE ANALYSES 
Health physics  2009;97(5):487-492.
Radiation dose estimates used in epidemiological studies are subject to many sources of uncertainty, and the error structure may be a complicated mixture of different types of error. Increasingly, efforts are being made to evaluate dosimetry uncertainties and to take account of them in statistical analyses. The impact of these uncertainties on dose response analyses depends on the magnitude and type of error. Errors that are independent from subject to subject (random errors) reduce statistical power for detecting a dose-response relationship, increase uncertainties in estimated risk coefficients, and may lead to underestimation of risk coefficients. The specific effects of random errors depend on whether the errors are “classical” or “Berkson.” Classical error can be thought of as error that arises from an imprecise measuring device, whereas Berkson error occurs when a single dose is used to represent a group of subjects (with varying true doses). Uncertainties in quantities that are common to some or all subjects are “shared” uncertainties. Such uncertainties increase the possibility of bias, and accounting for this possibility increases the length of confidence intervals. In studies that provide a direct evaluation of risk at low doses and dose rates, dosimetry errors are more likely to mask a true effect than to create a spurious one. In addition, classical errors and shared dosimetry uncertainties increase the potential for bias in estimated risks coefficients, but this potential may already be large due to the extreme vulnerability to confounding in studies involving very small relative risk.
doi:10.1097/HP.0b013e3181adc3b1
PMCID: PMC4051435  PMID: 19820458
analysis; statistical; dosimetry; epidemiology; National Council on Radiation Protection and Measurements
3.  Expected Estimating Equation using Calibration Data for Generalized Linear Models with a Mixture of Berkson and Classical Errors in Covariates 
Statistics in medicine  2013;33(4):675-692.
Data collected in many epidemiological or clinical research studies are often contaminated with measurement errors that may be of classical or Berkson error type. The measurement error may also be a combination of both classical and Berkson errors and failure to account for both errors could lead to unreliable inference in many situations. We consider regression analysis in generalized linear models when some covariates are prone to a mixture of Berkson and classical errors and calibration data are available only for some subjects in a subsample. We propose an expected estimating equation approach to accommodate both errors in generalized linear regression analyses. The proposed method can consistently estimate the classical and Berkson error variances based on the available data, without knowing the mixture percentage. Its finite-sample performance is investigated numerically. Our method is illustrated by an application to real data from an HIV vaccine study.
doi:10.1002/sim.5966
PMCID: PMC3947110  PMID: 24009099
Berkson error; calibration subsample; classical error; expected estimating equation; generalized linear model; instrumental variable
4.  Mathematical modeling of a survey-meter used to measure radioactivity in human thyroids: Monte Carlo calculations of the device response and uncertainties 
This paper presents results of Monte Carlo modeling of the SRP-68-01 survey meter used to measure exposure rates near the thyroid glands of persons exposed to radioactivity following the Chernobyl accident. This device was not designed to measure radioactivity in humans. To estimate the uncertainty associated with the measurement results, a mathematical model of the SRP-68-01 survey meter was developed and verified. A Monte Carlo method of numerical simulation of radiation transport has been used to calculate the calibration factor for the device and evaluate its uncertainty. The SRP-68-01 survey meter scale coefficient, an important characteristic of the device, was also estimated in this study. The calibration factors of the survey meter were calculated for 131I, 132I, 133I, and 135I content in the thyroid gland for six age groups of population: newborns; children aged 1 yr, 5 yr, 10 yr, 15 yr; and adults. A realistic scenario of direct thyroid measurements with an “extended” neck was used to calculate the calibration factors for newborns and one-year-olds. Uncertainties in the device calibration factors due to variability of the device scale coefficient, variability in thyroid mass and statistical uncertainty of Monte Carlo method were evaluated. Relative uncertainties in the calibration factor estimates were found to be from 0.06 for children aged 1 yr to 0.1 for 10-yr and 15-yr children. The positioning errors of the detector during measurements deviate mainly in one direction from the estimated calibration factors. Deviations of the device position from the proper geometry of measurements were found to lead to overestimation of the calibration factor by up to 24 percent for adults and up to 60 percent for 1-yr children. The results of this study improve the estimates of 131I thyroidal content and, consequently, thyroid dose estimates that are derived from direct thyroid measurements performed in Belarus shortly after the Chernobyl accident.
doi:10.1016/j.apradiso.2011.12.032
PMCID: PMC3430078  PMID: 22245289
Chernobyl; Thyroid; Measurement; Survey meter; Monte Carlo
5.  Measurement error caused by spatial misalignment in environmental epidemiology 
Biostatistics (Oxford, England)  2008;10(2):258-274.
In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.
doi:10.1093/biostatistics/kxn033
PMCID: PMC2733173  PMID: 18927119
Air pollution; Measurement error; Predictions; Spatial misalignment
6.  Impact of exposure measurement error in air pollution epidemiology: effect of error type in time-series studies 
Environmental Health  2011;10:61.
Background
Two distinctly different types of measurement error are Berkson and classical. Impacts of measurement error in epidemiologic studies of ambient air pollution are expected to depend on error type. We characterize measurement error due to instrument imprecision and spatial variability as multiplicative (i.e. additive on the log scale) and model it over a range of error types to assess impacts on risk ratio estimates both on a per measurement unit basis and on a per interquartile range (IQR) basis in a time-series study in Atlanta.
Methods
Daily measures of twelve ambient air pollutants were analyzed: NO2, NOx, O3, SO2, CO, PM10 mass, PM2.5 mass, and PM2.5 components sulfate, nitrate, ammonium, elemental carbon and organic carbon. Semivariogram analysis was applied to assess spatial variability. Error due to this spatial variability was added to a reference pollutant time-series on the log scale using Monte Carlo simulations. Each of these time-series was exponentiated and introduced to a Poisson generalized linear model of cardiovascular disease emergency department visits.
Results
Measurement error resulted in reduced statistical significance for the risk ratio estimates for all amounts (corresponding to different pollutants) and types of error. When modelled as classical-type error, risk ratios were attenuated, particularly for primary air pollutants, with average attenuation in risk ratios on a per unit of measurement basis ranging from 18% to 92% and on an IQR basis ranging from 18% to 86%. When modelled as Berkson-type error, risk ratios per unit of measurement were biased away from the null hypothesis by 2% to 31%, whereas risk ratios per IQR were attenuated (i.e. biased toward the null) by 5% to 34%. For CO modelled error amount, a range of error types were simulated and effects on risk ratio bias and significance were observed.
Conclusions
For multiplicative error, both the amount and type of measurement error impact health effect estimates in air pollution epidemiology. By modelling instrument imprecision and spatial variability as different error types, we estimate direction and magnitude of the effects of error over a range of error types.
doi:10.1186/1476-069X-10-61
PMCID: PMC3146396  PMID: 21696612
7.  A Measurement Error Model for Physical Activity Level as Measured by a Questionnaire With Application to the 1999–2006 NHANES Questionnaire 
American Journal of Epidemiology  2013;177(11):1199-1208.
Systematic investigations into the structure of measurement error of physical activity questionnaires are lacking. We propose a measurement error model for a physical activity questionnaire that uses physical activity level (the ratio of total energy expenditure to basal energy expenditure) to relate questionnaire-based reports of physical activity level to true physical activity levels. The 1999–2006 National Health and Nutrition Examination Survey physical activity questionnaire was administered to 433 participants aged 40–69 years in the Observing Protein and Energy Nutrition (OPEN) Study (Maryland, 1999–2000). Valid estimates of participants’ total energy expenditure were also available from doubly labeled water, and basal energy expenditure was estimated from an equation; the ratio of those measures estimated true physical activity level (“truth”). We present a measurement error model that accommodates the mixture of errors that arise from assuming a classical measurement error model for doubly labeled water and a Berkson error model for the equation used to estimate basal energy expenditure. The method was then applied to the OPEN Study. Correlations between the questionnaire-based physical activity level and truth were modest (r = 0.32–0.41); attenuation factors (0.43–0.73) indicate that the use of questionnaire-based physical activity level would lead to attenuated estimates of effect size. Results suggest that sample sizes for estimating relationships between physical activity level and disease should be inflated, and that regression calibration can be used to provide measurement error–adjusted estimates of relationships between physical activity and disease.
doi:10.1093/aje/kws379
PMCID: PMC3664335  PMID: 23595007
Berkson model; bias; energy metabolism; measurement error model; models, statistical; motor activity; self-assessment
8.  Measurement error adjustment in essential fatty acid intake from a food frequency questionnaire: alternative approaches and methods 
Background
We aimed at assessing the degree of measurement error in essential fatty acid intakes from a food frequency questionnaire and the impact of correcting for such an error on precision and bias of odds ratios in logistic models. To assess these impacts, and for illustrative purposes, alternative approaches and methods were used with the binary outcome of cognitive decline in verbal fluency.
Methods
Using the Atherosclerosis Risk in Communities (ARIC) study, we conducted a sensitivity analysis. The error-prone exposure – visit 1 fatty acid intake (1987–89) – was available for 7,814 subjects 50 years or older at baseline with complete data on cognitive decline between visits 2 (1990–92) and 4 (1996–98). Our binary outcome of interest was clinically significant decline in verbal fluency. Point estimates and 95% confidence intervals were compared between naïve and measurement-error adjusted odds ratios of decline with every SD increase in fatty acid intake as % of energy. Two approaches were explored for adjustment: (A) External validation against biomarkers (plasma fatty acids in cholesteryl esters and phospholipids) and (B) Internal repeat measurements at visits 2 and 3. The main difference between the two is that Approach B makes a stronger assumption regarding lack of error correlations in the structural model. Additionally, we compared results from regression calibration (RCAL) to those from simulation extrapolation (SIMEX). Finally, using structural equations modeling, we estimated attenuation factors associated with each dietary exposure to assess degree of measurement error in a bivariate scenario for regression calibration of logistic regression model.
Results and conclusion
Attenuation factors for Approach A were smaller than B, suggesting a larger amount of measurement error in the dietary exposure. Replicate measures (Approach B) unlike concentration biomarkers (Approach A) may lead to imprecise odds ratios due to larger standard errors. Using SIMEX rather than RCAL models tends to preserve precision of odds ratios. We found in many cases that bias in naïve odds ratios was towards the null. RCAL tended to correct for a larger amount of effect bias than SIMEX, particularly for Approach A.
doi:10.1186/1471-2288-7-41
PMCID: PMC2048969  PMID: 17868465
9.  Risk of Second Primary Thyroid Cancer after Radiotherapy for a Childhood Cancer in a Large Cohort Study: An Update from the Childhood Cancer Survivor Study 
Radiation research  2010;174(6):741-752.
Previous studies have indicated that thyroid cancer risk after a first childhood malignancy is curvilinear with radiation dose, increasing at low to moderate doses and decreasing at high doses. Understanding factors that modify the radiation dose response over the entire therapeutic dose range is challenging and requires large numbers of subjects. We quantified the long-term risk of thyroid cancer associated with radiation treatment among 12,547 5-year survivors of a childhood cancer (leukemia, Hodgkin lymphoma and non-Hodgkin lymphoma, central nervous system cancer, soft tissue sarcoma, kidney cancer, bone cancer, neuroblastoma) diagnosed between 1970 and 1986 in the Childhood Cancer Survivor Study using the most current cohort follow-up to 2005. There were 119 subsequent pathologically confirmed thyroid cancer cases, and individual radiation doses to the thyroid gland were estimated for the entire cohort. This cohort study builds on the previous case-control study in this population (69 thyroid cancer cases with follow-up to 2000) by allowing the evaluation of both relative and absolute risks. Poisson regression analyses were used to calculate standardized incidence ratios (SIR), excess relative risks (ERR) and excess absolute risks (EAR) of thyroid cancer associated with radiation dose. Other factors such as sex, type of first cancer, attained age, age at exposure to radiation, time since exposure to radiation, and chemotherapy (yes/no) were assessed for their effect on the linear and exponential quadratic terms describing the dose–response relationship. Similar to the previous analysis, thyroid cancer risk increased linearly with radiation dose up to approximately 20 Gy, where the relative risk peaked at 14.6-fold (95% CI, 6.8–31.5). At thyroid radiation doses >20 Gy, a downturn in the dose–response relationship was observed. The ERR model that best fit the data was linear-exponential quadratic. We found that age at exposure modified the ERR linear dose term (higher radiation risk with younger age) (P < 0.001) and that sex (higher radiation risk among females) (P = 0.008) and time since exposure (higher radiation risk with longer time) (P < 0.001) modified the EAR linear dose term. None of these factors modified the exponential quadratic (high dose) term. Sex, age at exposure and time since exposure were found to be significant modifiers of the radiation-related risk of thyroid cancer and as such are important factors to account for in clinical follow-up and thyroid cancer risk estimation among childhood cancer survivors.
doi:10.1667/RR2240.1
PMCID: PMC3080023  PMID: 21128798
10.  Characterization of Ambient Air Pollution Measurement Error in a Time-Series Health Study using a Geostatistical Simulation Approach 
In recent years, geostatistical modeling has been used to inform air pollution health studies. In this study, distributions of daily ambient concentrations were modeled over space and time for 12 air pollutants. Simulated pollutant fields were produced for a 6-year time period over the 20-county metropolitan Atlanta area using the Stanford Geostatistical Modeling Software (SGeMS). These simulations incorporate the temporal and spatial autocorrelation structure of ambient pollutants, as well as season and day-of-week temporal and spatial trends; these fields were considered to be the true ambient pollutant fields for the purposes of the simulations that followed. Simulated monitor data at the locations of actual monitors were then generated that contain error representative of instrument imprecision. From the simulated monitor data, four exposure metrics were calculated: central monitor and unweighted, population-weighted, and area-weighted averages. For each metric, the amount and type of error relative to the simulated pollutant fields are characterized and the impact of error on an epidemiologic time-series analysis is predicted. The amount of error, as indicated by a lack of spatial autocorrelation, is greater for primary pollutants than for secondary pollutants and is only moderately reduced by averaging across monitors; more error will result in less statistical power in the epidemiologic analysis. The type of error, as indicated by the correlations of error with the monitor data and with the true ambient concentration, varies with exposure metric, with error in the central monitor metric more of the classical type (i.e., independent of the monitor data) and error in the spatial average metrics more of the Berkson type (i.e., independent of the true ambient concentration). Error type will affect the bias in the health risk estimate, with bias toward the null and away from the null predicted depending on the exposure metric; population-weighting yielded the least bias.
doi:10.1016/j.atmosenv.2012.04.045
PMCID: PMC3628542  PMID: 23606805
geostatistics; exposure modeling; air pollution; spatial modeling; measurement error; spatial misalignment
11.  Approximate and Pseudo-Likelihood Analysis for Logistic Regression Using External Validation Data to Model Log Exposure 
A common goal in environmental epidemiologic studies is to undertake logistic regression modeling to associate a continuous measure of exposure with binary disease status, adjusting for covariates. A frequent complication is that exposure may only be measurable indirectly, through a collection of subject-specific variables assumed associated with it. Motivated by a specific study to investigate the association between lung function and exposure to metal working fluids, we focus on a multiplicative-lognormal structural measurement error scenario and approaches to address it when external validation data are available. Conceptually, we emphasize the case in which true untransformed exposure is of interest in modeling disease status, but measurement error is additive on the log scale and thus multiplicative on the raw scale. Methodologically, we favor a pseudo-likelihood (PL) approach that exhibits fewer computational problems than direct full maximum likelihood (ML) yet maintains consistency under the assumed models without necessitating small exposure effects and/or small measurement error assumptions. Such assumptions are required by computationally convenient alternative methods like regression calibration (RC) and ML based on probit approximations. We summarize simulations demonstrating considerable potential for bias in the latter two approaches, while supporting the use of PL across a variety of scenarios. We also provide accessible strategies for obtaining adjusted standard errors to accompany RC and PL estimates.
doi:10.1007/s13253-012-0115-9
PMCID: PMC3766852  PMID: 24027381
Consistency; Likelihood; Multiplicative measurement error; Probit; Validation
12.  Semiparametric Bayesian Analysis of Nutritional Epidemiology Data in the Presence of Measurement Error 
Biometrics  2009;66(2):444-454.
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.
doi:10.1111/j.1541-0420.2009.01309.x
PMCID: PMC2888615  PMID: 19673858
B-splines; Dirichlet process prior; Gibbs sampling; Measurement error; Metropolis-Hastings algorithm; Partly linear model
13.  Multiple Indicators, Multiple Causes Measurement Error Models 
Statistics in medicine  2014;33(25):4469-4481.
Multiple Indicators, Multiple Causes Models (MIMIC) are often employed by researchers studying the effects of an unobservable latent variable on a set of outcomes, when causes of the latent variable are observed. There are times however when the causes of the latent variable are not observed because measurements of the causal variable are contaminated by measurement error. The objectives of this paper are: (1) to develop a novel model by extending the classical linear MIMIC model to allow both Berkson and classical measurement errors, defining the MIMIC measurement error (MIMIC ME) model, (2) to develop likelihood based estimation methods for the MIMIC ME model, (3) to apply the newly defined MIMIC ME model to atomic bomb survivor data to study the impact of dyslipidemia and radiation dose on the physical manifestations of dyslipidemia. As a by-product of our work, we also obtain a data-driven estimate of the variance of the classical measurement error associated with an estimate of the amount of radiation dose received by atomic bomb survivors at the time of their exposure.
doi:10.1002/sim.6243
PMCID: PMC4184955  PMID: 24962535
Atomic bomb survivor data; Berkson error; Dyslipidemia; Instrumental Variables; Latent variables; Measurement error; MIMIC models
14.  SIMEX and standard error estimation in semiparametric measurement error models 
SIMEX is a general-purpose technique for measurement error correction. There is a substantial literature on the application and theory of SIMEX for purely parametric problems, as well as for purely non-parametric regression problems, but there is neither application nor theory for semiparametric problems. Motivated by an example involving radiation dosimetry, we develop the basic theory for SIMEX in semiparametric problems using kernel-based estimation methods. This includes situations that the mismeasured variable is modeled purely parametrically, purely non-parametrically, or that the mismeasured variable has components that are modeled both parametrically and nonparametrically. Using our asymptotic expansions, easily computed standard error formulae are derived, as are the bias properties of the nonparametric estimator. The standard error method represents a new method for estimating variability of nonparametric estimators in semiparametric problems, and we show in both simulations and in our example that it improves dramatically on first order methods.
We find that for estimating the parametric part of the model, standard bandwidth choices of order O(n−1/5) are sufficient to ensure asymptotic normality, and undersmoothing is not required. SIMEX has the property that it fits misspecified models, namely ones that ignore the measurement error. Our work thus also more generally describes the behavior of kernel-based methods in misspecified semiparametric problems.
doi:10.1214/08-EJS341
PMCID: PMC2710855  PMID: 19609371
Berkson measurement errors; measurement error; misspecified models; nonparametric regression; radiation epidemiology; semiparametric models; SIMEX; simulation-extrapolation; standard error estimation; uniform expansions
15.  Bayesian adjustment for measurement error in continuous exposures in an individually matched case-control study 
Background
In epidemiological studies explanatory variables are frequently subject to measurement error. The aim of this paper is to develop a Bayesian method to correct for measurement error in multiple continuous exposures in individually matched case-control studies. This is a topic that has not been widely investigated. The new method is illustrated using data from an individually matched case-control study of the association between thyroid hormone levels during pregnancy and exposure to perfluorinated acids. The objective of the motivating study was to examine the risk of maternal hypothyroxinemia due to exposure to three perfluorinated acids measured on a continuous scale. Results from the proposed method are compared with those obtained from a naive analysis.
Methods
Using a Bayesian approach, the developed method considers a classical measurement error model for the exposures, as well as the conditional logistic regression likelihood as the disease model, together with a random-effect exposure model. Proper and diffuse prior distributions are assigned, and results from a quality control experiment are used to estimate the perfluorinated acids' measurement error variability. As a result, posterior distributions and 95% credible intervals of the odds ratios are computed. A sensitivity analysis of method's performance in this particular application with different measurement error variability was performed.
Results
The proposed Bayesian method to correct for measurement error is feasible and can be implemented using statistical software. For the study on perfluorinated acids, a comparison of the inferences which are corrected for measurement error to those which ignore it indicates that little adjustment is manifested for the level of measurement error actually exhibited in the exposures. Nevertheless, a sensitivity analysis shows that more substantial adjustments arise if larger measurement errors are assumed.
Conclusions
In individually matched case-control studies, the use of conditional logistic regression likelihood as a disease model in the presence of measurement error in multiple continuous exposures can be justified by having a random-effect exposure model. The proposed method can be successfully implemented in WinBUGS to correct individually matched case-control studies for several mismeasured continuous exposures under a classical measurement error model.
doi:10.1186/1471-2288-11-67
PMCID: PMC3120807  PMID: 21569573
16.  Identification and Estimation of Nonlinear Models Using Two Samples with Nonclassical Measurement Errors 
This paper considers identification and estimation of a general nonlinear Errors-in-Variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values; and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest — the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates — is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterized, we propose sieve Quasi Maximum Likelihood Estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.
doi:10.1080/10485250902874688
PMCID: PMC2873792  PMID: 20495685
Data combination; Measurement error; Misspecified parametric latent model; Nonclassical measurement error; Nonlinear errors-in-variables model; Nonparametric identification; Sieve quasi likelihood
17.  Structured measurement error in nutritional epidemiology: applications in the Pregnancy, Infection, and Nutrition (PIN) Study 
Preterm birth, defined as delivery before 37 completed weeks’ gestation, is a leading cause of infant morbidity and mortality. Identifying factors related to preterm delivery is an important goal of public health professionals who wish to identify etiologic pathways to target for prevention. Validation studies are often conducted in nutritional epidemiology in order to study measurement error in instruments that are generally less invasive or less expensive than ”gold standard” instruments. Data from such studies are then used in adjusting estimates based on the full study sample. However, measurement error in nutritional epidemiology has recently been shown to be complicated by correlated error structures in the study-wide and validation instruments. Investigators of a study of preterm birth and dietary intake designed a validation study to assess measurement error in a food frequency questionnaire (FFQ) administered during pregnancy and with the secondary goal of assessing whether a single administration of the FFQ could be used to describe intake over the relatively short pregnancy period, in which energy intake typically increases. Here, we describe a likelihood-based method via Markov Chain Monte Carlo to estimate the regression coefficients in a generalized linear model relating preterm birth to covariates, where one of the covariates is measured with error and the multivariate measurement error model has correlated errors among contemporaneous instruments (i.e. FFQs, 24-hour recalls, and/or biomarkers). Because of constraints on the covariance parameters in our likelihood, identifiability for all the variance and covariance parameters is not guaranteed and, therefore, we derive the necessary and suficient conditions to identify the variance and covariance parameters under our measurement error model and assumptions. We investigate the sensitivity of our likelihood-based model to distributional assumptions placed on the true folate intake by employing semi-parametric Bayesian methods through the mixture of Dirichlet process priors framework. We exemplify our methods in a recent prospective cohort study of risk factors for preterm birth. We use long-term folate as our error-prone predictor of interest, the food-frequency questionnaire (FFQ) and 24-hour recall as two biased instruments, and serum folate biomarker as the unbiased instrument. We found that folate intake, as measured by the FFQ, led to a conservative estimate of the estimated odds ratio of preterm birth (0.76) when compared to the odds ratio estimate from our likelihood-based approach, which adjusts for the measurement error (0.63). We found that our parametric model led to similar conclusions to the semi-parametric Bayesian model.
PMCID: PMC2440718  PMID: 18584067
Adaptive-Rejection Sampling; Dirichlet process prior; MCMC; Semiparametric Bayes
18.  I-131 Dose Response for Incident Thyroid Cancers in Ukraine Related to the Chornobyl Accident 
Environmental Health Perspectives  2011;119(7):933-939.
Background: Current knowledge about Chornobyl-related thyroid cancer risks comes from ecological studies based on grouped doses, case–control studies, and studies of prevalent cancers.
Objective: To address this limitation, we evaluated the dose–response relationship for incident thyroid cancers using measurement-based individual iodine-131 (I-131) thyroid dose estimates in a prospective analytic cohort study.
Methods: The cohort consists of individuals < 18 years of age on 26 April 1986 who resided in three contaminated oblasts (states) of Ukraine and underwent up to four thyroid screening examinations between 1998 and 2007 (n = 12,514). Thyroid doses of I-131 were estimated based on individual radioactivity measurements taken within 2 months after the accident, environmental transport models, and interview data. Excess radiation risks were estimated using Poisson regression models.
Results: Sixty-five incident thyroid cancers were diagnosed during the second through fourth screenings and 73,004 person-years (PY) of observation. The dose–response relationship was consistent with linearity on relative and absolute scales, although the excess relative risk (ERR) model described data better than did the excess absolute risk (EAR) model. The ERR per gray was 1.91 [95% confidence interval (CI), 0.43–6.34], and the EAR per 104 PY/Gy was 2.21 (95% CI, 0.04–5.78). The ERR per gray varied significantly by oblast of residence but not by time since exposure, use of iodine prophylaxis, iodine status, sex, age, or tumor size.
Conclusions: I-131–related thyroid cancer risks persisted for two decades after exposure, with no evidence of decrease during the observation period. The radiation risks, although smaller, are compatible with those of retrospective and ecological post-Chornobyl studies.
doi:10.1289/ehp.1002674
PMCID: PMC3222994  PMID: 21406336
Chernobyl nuclear accident; Chornobyl, Ukraine, 1986; dose–response relationship; incidence, thyroid neoplasms/epidemiology; iodine; radioactive; radiation
19.  A STUDY OF THE PHYSIOLOGICAL ACTIVITY OF ADENOMATA OF THE THYROID GLAND, IN RELATION TO THEIR IODINE CONTENT, AS EVIDENCED BY FEEDING EXPERIMENTS ON TADPOLES 
It seems evident from the foregoing experiments that the so called tumors (adenomata) of the thyroid possess the property of taking up iodine and metabolizing it into the active combination in the same way that the non-tumorous thyroid tissue does, although not so readily nor to the same degree, and the action on tadpoles of feeding desiccated tumorous thyroid tissue does not differ qualitatively from feeding desiccated non-tumorous thyroid tissue. The action in either case depends upon the iodine (active iodine) content, and in the case of the adenomata bears no constant relation to the state of their growth or differentiation. Examination of Tables II and III shows that in the main this is true. There are, however, certain discrepancies as to time of death, appearance of first forelegs, degree of emaciation, and rate of growth in certain dishes of the series, the action being not quite parallel to the iodine content. Some of these discrepancies may be explained in part by accidents of feeding, slight differences in size, age) and susceptibility of the different tadpoles receiving the same thyroid, and also by the variations in the amount of thyroid consumed by the different individuals in the same dish. Lenhart has shown that the action of the same thyroid varies with the quantity fed. Another important factor which has to be considered is the condition of the iodine itself. It was suspected at the time of these experiments that the iodine might be present in an active and an inactive form, but no satisfactory proof of this assumption, at the beginning of these experiments, was at hand. Support of this point has been afforded by the work of Kendall on the isolation of the active principle of thyroid and the separation of the iodine into two fractions. Since the completion of our experiments Marine has demonstrated by means of perfusion experiments in vivo and in vitro that iodine is rapidly taken up by the thyroid cells, and though the iodine increase in the perfused lobe may be 1,000 per cent in 2 hours as compared with the control lobe, yet the action on tadpoles is no greater. It then becomes an important question to determine the time required by the thyroid to take up inorganic iodine and manufacture it into the active thyroid principle. It is known that iodine is rapidly taken up by the thyroid, and in man the iodine content of the thyroid is subject to greater variations than in animals on account of the prevalent therapeutic use of iodine and the iodides in goiter and other conditions; even the iodine used in preparing patients for operations would increase the iodine content of the thyroid in a short time, so that one might expect such variations in the action of a given thyroid preparation fed to tadpoles as appear in these experiments. In this connection it is interesting to note (Table II) that Thyroid 20 with 4.31 mg. of iodine was only slightly more active than No. 5 with 1.31 mg. of iodine. Two possibilities have to be considered here. First, No. 20 may have active iodine slightly greater than 1.31 mg. and the balance present as inactive iodine. Second, No. 5 with 1.31 mg. of iodine might represent the maximum possible effect under the conditions of the experiment and a larger quantity of active thyroid iodine could produce no greater effect. Of course with the lower iodine contents the variations in effects might well come within the limits of errors of observation. Also the percentage error would be greater in the iodine determinations, accidents of feeding, etc. Our conclusions as to the effect of feeding desiccated thyroid to tadpoles agree in general with those of Lenhart. The action of the thyroid depends not upon a specific stimulus to differentiation but upon a stimulation of metabolism in general in proportion to the active iodine and the quantity consumed. High iodine contents produce rapid emaciation, at the same time resulting in differentiation even in tadpoles dying in 8 to 12 days. Low iodine contents result in differentiation at an earlier period than the controls. Tadpoles fed on thyroid with practically no iodine grow better than the controls, in this instance the thyroid acting simply as a food. Finally, the interest that the results of these experiments may have in connection with the question of function in tumor tissue should be pointed out. To those who hold that tumor lacks the capacity for physiological function, the adenomata of the thyroid could not be consistently regarded as tumors. To those who hold physiological function as a possible property of tumor tissue, the adenomata might be regarded as tumors. Future studies might warrant a recognition of different grades or degrees of tumor. On this basis the fetal adenoma (very little differentiation) might represent a higher degree of tumor than the diffuse colloid or simple adenomatous thyroid in which the adenomatous nodules are present to a great extent throughout the whole gland and are well differentiated. It is certain that there are all grades and degrees of growth and differentiation in the life history of fetal adenomata of the thyroid, from the pure fetal, undifferentiated adenoma with little or no iodine to the simple or colloid adenoma, well differentiated and with varying amounts of iodine approaching that of normal thyroid.
PMCID: PMC2125468  PMID: 19868046
20.  A toolkit for measurement error correction, with a focus on nutritional epidemiology 
Statistics in Medicine  2014;33(12):2137-2155.
Exposure measurement error is a problem in many epidemiological studies, including those using biomarkers and measures of dietary intake. Measurement error typically results in biased estimates of exposure-disease associations, the severity and nature of the bias depending on the form of the error. To correct for the effects of measurement error, information additional to the main study data is required. Ideally, this is a validation sample in which the true exposure is observed. However, in many situations, it is not feasible to observe the true exposure, but there may be available one or more repeated exposure measurements, for example, blood pressure or dietary intake recorded at two time points. The aim of this paper is to provide a toolkit for measurement error correction using repeated measurements. We bring together methods covering classical measurement error and several departures from classical error: systematic, heteroscedastic and differential error. The correction methods considered are regression calibration, which is already widely used in the classical error setting, and moment reconstruction and multiple imputation, which are newer approaches with the ability to handle differential error. We emphasize practical application of the methods in nutritional epidemiology and other fields. We primarily consider continuous exposures in the exposure-outcome model, but we also outline methods for use when continuous exposures are categorized. The methods are illustrated using the data from a study of the association between fibre intake and colorectal cancer, where fibre intake is measured using a diet diary and repeated measures are available for a subset. © 2014 The Authors.
doi:10.1002/sim.6095
PMCID: PMC4285313  PMID: 24497385
measurement error; regression calibration; moment reconstruction; multiple imputation; diet diary; food frequency questionnaire; nutritional epidemiology
21.  Model Calibration in the Continual Reassessment Method 
Background
The continual reassessment method (CRM) is an adaptive model-based design used to estimate the maximum tolerated dose in dose finding clinical trials. A way to evaluate the sensitivity of a given CRM model including the functional form of the dose-toxicity curve, the prior distribution on the model parameter, and the initial guesses of toxicity probability at each dose is using indifference intervals. While the indifference interval technique provides a succinct summary of model sensitivity, there are infinitely many possible ways to specify the initial guesses of toxicity probability. In practice, these are generally specified by trial and error through extensive simulations.
Methods
By using indifference intervals, the initial guesses used in the CRM can be selected by specifying a range of acceptable toxicity probabilities in addition to the target probability of toxicity. An algorithm is proposed for obtaining the indifference interval that maximizes the average percentage of correct selection across a set of scenarios of true probabilities of toxicity and providing a systematic approach for selecting initial guesses in a much less time consuming manner than the trial and error method. The methods are compared in the context of two real CRM trials.
Results
For both trials, the initial guesses selected by the proposed algorithm had similar operating characteristics as measured by percentage of correct selection, average absolute difference between the true probability of the dose selected and the target probability of toxicity, percentage treated at each dose and overall percentage of toxicity compared to the initial guesses used during the conduct of the trials which were obtained by trial and error through a time consuming calibration process. The average percentage of correct selection for the scenarios considered were 61.5% and 62.0% in the lymphoma trial, and 62.9% and 64.0% in the stroke trial for the trial and error method versus the proposed approach.
Limitations
We only present detailed results for the empiric dose toxicity curve, although the proposed methods are applicable for other dose toxicity models such as the logistic.
Conclusions
The proposed method provides a fast and systematic approach for selecting initial guesses of probabilities of toxicity used in the CRM that are competitive to those obtained by trial and error through a time consuming process, thus, simplifying the model calibration process for the CRM.
doi:10.1177/1740774509105076
PMCID: PMC2884971  PMID: 19528132
22.  The effect of measurement error on the dose-response curve. 
In epidemiological studies for an environmental risk assessment, doses are often observed with errors. However, they have received little attention in data analysis. This paper studies the effect of measurement errors on the observed dose-response curve. Under the assumptions of the monotone likelihood ratio on errors and a monotone increasing dose-response curve, it is verified that the slope of the observed dose-response curve is likely to be gentler than the true one. The observed variance of responses are not so homogeneous as to be expected under models without errors. The estimation of parameters in a hockey-stick type dose-response curve with a threshold is considered on line of the maximum likelihood method for a functional relationship model. Numerical examples adaptable to the data in a 1986 study of the effect of air pollution that was conducted in Japan are also presented. The proposed model is proved to be suitable to the data in the example cited in this paper.
PMCID: PMC1567852  PMID: 2269223
23.  Exposure measurement error in time-series studies of air pollution: concepts and consequences. 
Environmental Health Perspectives  2000;108(5):419-426.
Misclassification of exposure is a well-recognized inherent limitation of epidemiologic studies of disease and the environment. For many agents of interest, exposures take place over time and in multiple locations; accurately estimating the relevant exposures for an individual participant in epidemiologic studies is often daunting, particularly within the limits set by feasibility, participant burden, and cost. Researchers have taken steps to deal with the consequences of measurement error by limiting the degree of error through a study's design, estimating the degree of error using a nested validation study, and by adjusting for measurement error in statistical analyses. In this paper, we address measurement error in observational studies of air pollution and health. Because measurement error may have substantial implications for interpreting epidemiologic studies on air pollution, particularly the time-series analyses, we developed a systematic conceptual formulation of the problem of measurement error in epidemiologic studies of air pollution and then considered the consequences within this formulation. When possible, we used available relevant data to make simple estimates of measurement error effects. This paper provides an overview of measurement errors in linear regression, distinguishing two extremes of a continuum-Berkson from classical type errors, and the univariate from the multivariate predictor case. We then propose one conceptual framework for the evaluation of measurement errors in the log-linear regression used for time-series studies of particulate air pollution and mortality and identify three main components of error. We present new simple analyses of data on exposures of particulate matter < 10 microm in aerodynamic diameter from the Particle Total Exposure Assessment Methodology Study. Finally, we summarize open questions regarding measurement error and suggest the kind of additional data necessary to address them.
Images
PMCID: PMC1638034  PMID: 10811568
24.  Neonatal Thyroid Function in Seveso 25 Years after Maternal Exposure to Dioxin 
PLoS Medicine  2008;5(7):e161.
Background
Neonatal hypothyroidism has been associated in animal models with maternal exposure to several environmental contaminants; however, evidence for such an association in humans is inconsistent. We evaluated whether maternal exposure to 2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD), a persistent and widespread toxic environmental contaminant, is associated with modified neonatal thyroid function in a large, highly exposed population in Seveso, Italy.
Methods and Findings
Between 1994 and 2005, in individuals exposed to TCDD after the 1976 Seveso accident we conducted: (i) a residence-based population study on 1,014 children born to the 1,772 women of reproductive age in the most contaminated zones (A, very high contamination; B, high contamination), and 1,772 age-matched women from the surrounding noncontaminated area (reference); (ii) a biomarker study on 51 mother–child pairs for whom recent maternal plasma dioxin measurements were available. Neonatal blood thyroid-stimulating hormone (b-TSH) was measured on all children. We performed crude and multivariate analyses adjusting for gender, birth weight, birth order, maternal age, hospital, and type of delivery. Mean neonatal b-TSH was 0.98 μU/ml (95% confidence interval [CI] 0.90–1.08) in the reference area (n = 533), 1.35 μU/ml (95% CI 1.22–1.49) in zone B (n = 425), and 1.66 μU/ml (95% CI 1.19–2.31) in zone A (n = 56) (p < 0.001). The proportion of children with b-TSH > 5 μU/ml was 2.8% in the reference area, 4.9% in zone B, and 16.1% in zone A (p < 0.001). Neonatal b-TSH was correlated with current maternal plasma TCDD (n = 51, β = 0.47, p < 0.001) and plasma toxic equivalents of coplanar dioxin-like compounds (n = 51, β = 0.45, p = 0.005).
Conclusions
Our data indicate that environmental contaminants such as dioxins have a long-lasting capability to modify neonatal thyroid function after the initial exposure.
Andrea Baccarelli and colleagues show that maternal exposure to a dioxin following the industrial accident in Seveso, Italy in 1976 is associated with modified neonatal thyroid function even many years later.
Editors' Summary
Background.
The thyroid, a butterfly-shaped gland in the neck, controls the speed at which the human body converts food into the energy and chemicals needed for life. In healthy people, the thyroid makes and releases two hormones (chemical messengers that travel around the body and regulate the activity of specific cells) called thyroxine (T4) and triiodothyronine (T3). The release of T4 and T3 is controlled by thyroid secreting hormone (TSH), which is made by the pituitary gland in response to electrical messages from the brain. If the thyroid stops making enough T4 and T3, a condition called hypothyroidism (an underactive thyroid) develops. Adults with hypothyroidism put on weight, feel the cold, and are often tired; children with hypothyroidism may also have poor growth and mental development. Because even a small reduction in thyroid hormone levels increases TSH production by the pituitary, hypothyroidism is often diagnosed by measuring the amount of TSH in the blood; it is treated with daily doses of the synthetic thyroid hormone levothyroxine.
Why Was This Study Done?
Although hypothyroidism is most common in ageing women, newborn babies sometimes have hypothyroidism. If untreated, “neonatal” hyperthyroidism can cause severe mental and physical retardation so, in many countries, blood TSH levels are measured soon after birth. That way, levothyroxine treatment can be started before thyroid hormone deficiency permanently damages the baby's developing body and brain. But what causes neonatal hypothyroidism? Animal experiments (and some but not all studies in people) suggest that maternal exposure to toxic chemicals called dioxins may be one cause. Dioxins are byproducts of waste incineration that persist in the environment and that accumulate in people. In this study, the researchers investigate whether exposure to dioxin (this name refers to the most toxic of the dioxins—2,3,7,8-Tetrachlorodibenzo-p-dioxin) affects neonatal thyroid function by studying children born near Seveso, Italy between 1994 and 2005. An accident at a chemical factory in 1976 heavily contaminated the region around this town with dioxin and, even now, the local people have high amounts of dioxin in their bodies.
What Did the Researchers Do and Find?
The researchers identified 1,772 women of child-bearing age who were living very near the Seveso factory (the most highly contaminated area, zone A) or slightly further away where the contamination was less but still high (zone B) at the time of the accident or soon after. As controls, they selected 1,772 women living in the surrounding, noncontaminated (reference) area. Altogether, these women had 1,014 babies between 1994 and 2005. The babies born to the mothers living in the reference area had lower neonatal blood TSH levels on average than the babies born to mothers living in zone A; zone B babies had intermediate TSH levels. Zone A babies were 6.6. times more likely to have a TSH level of more than 5 μU/ml than the reference area babies (the threshold TSH level for further investigations is 10 μU/ml; the average TSH level among the reference area babies was 0.98 μU/ml). The researchers also examined the relationship between neonatal TSH measurements and maternal dioxin measurements at delivery (extrapolated from measurements made between 1992 and 1998) in 51 mother–baby pairs. Neonatal TSH levels were highest in the babies whose mothers had the highest blood dioxin levels.
What Do These Findings Mean?
These findings suggest that maternal dioxin exposure has a long-lasting, deleterious effect on neonatal thyroid function. Because the long-term progress of the children in this study was not examined, it is not known whether the increases in neonatal TSH measurements associated with dioxin exposure caused any developmental problems. However, in regions where there is a mild iodine deficiency (the only environmental exposure consistently associated with reduced human neonatal thyroid function), TSH levels are increased to a similar extent and there is evidence of reduced intellectual and physical development. Future investigations on the progress of this group of children should show whether the long-term legacy of the Seveso accident (and of the high environmental levels of dioxin elsewhere) includes any effects on children's growth and development.
Additional Information.
Please access these Web sites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.0050161.
The MedlinePlus encyclopedia provides information about hypothyroidism and neonatal hypothyroidism; MedlinePlus provides links to additional information on thyroid diseases (in English and Spanish)
The UK National Health Service Direct health encyclopedia provides information on hypothyroidism
The Nemours Foundation's KidsHealth site has information written for children about thyroid disorders
Toxtown, an interactive site from the US National Library of Science, provides information on environmental health concerns including exposure to dioxins (in English and Spanish)
More information about dioxins is provided by the US Environmental Protection Agency and by the US Food and Drug Administration
Wikipedia has a page on the Seveso disaster (note: Wikipedia is a free online encyclopedia that anyone can edit; available in several languages)
doi:10.1371/journal.pmed.0050161
PMCID: PMC2488197  PMID: 18666825
25.  Thyroid nodules, polymorphic variants in DNA repair and RET-related genes, and interaction with ionizing radiation exposure from nuclear tests in Kazakhstan 
Radiation research  2009;171(1):77-88.
Risk factors for thyroid cancer remain largely unknown except for ionizing radiation exposure during childhood and a history of benign thyroid nodules. Because thyroid nodules are more common than thyroid cancers and are associated with thyroid cancer risk, we evaluated several polymorphisms potentially relevant to thyroid tumors and assessed interaction with ionizing radiation exposure to the thyroid gland. Thyroid nodules were detected in 1998 by ultrasound screening of 2997 persons who lived near the Semipalatinsk nuclear test site in Kazakhstan when they were children (1949-62). Cases with thyroid nodules (n=907) were frequency matched (1:1) to those without nodules by ethnicity (Kazakh or Russian), gender, and age at screening. Thyroid gland radiation doses were estimated from fallout deposition patterns, residence history, and diet. We analyzed 23 polymorphisms in 13 genes and assessed interaction with ionizing radiation exposure using likelihood ratio tests (LRT). Elevated thyroid nodule risks were associated with the minor alleles of RET S836S (rs1800862, p = 0.03) and GFRA1 -193C>G (rs not assigned, p = 0.05) and decreased risk with XRCC1 R194W (rs1799782, p-trend = 0.03) and TGFB1 T263I (rs1800472, p = 0.009). Similar patterns of association were observed for a small number of papillary thyroid cancers (n=25). Ionizing radiation exposure to the thyroid gland was associated with significantly increased risk of thyroid nodules (age and gender adjusted excess odds ratio/Gy = 0.30, 95% confidence interval 0.05-0.56), with evidence for interaction by genotype found for XRCC1 R194W (LRT p value = 0.02). Polymorphisms in RET signaling, DNA repair, and proliferation genes may be related to risk of thyroid nodules, consistent with some previous reports on thyroid cancer. Borderline support for gene-radiation interaction was found for a variant in XRCC1, a key base excision repair protein. Other pathways, such as genes in double strand break repair, apoptosis, and genes related to proliferation should also be pursued.
doi:10.1667/RR1327.1
PMCID: PMC2875679  PMID: 19138047
Thyroid nodules; single nucleotide polymorphisms; epidemiology; thyroid cancer; ionizing radiation; interaction

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