Recommendations on statistical approaches to account for dose uncertainties in radiation epidemiologic risk models.

PURPOSE: Epidemiological studies of stochastic radiation health effects such as cancer, meant to estimate risks of the adverse effects as a function of radiation dose, depend largely on estimates of the radiation doses received by the exposed group under study. Those estimates are based on dosimetry that always has uncertainty, which often can be quite substantial. Studies that do not incorporate statistical methods to correct for dosimetric uncertainty may produce biased estimates of risk and incorrect confidence bounds on those estimates. This paper reviews commonly used statistical methods to correct radiation risk regressions for dosimetric uncertainty, with emphasis on some newer methods. We begin by describing the types of dose uncertainty that may occur, including those in which an uncertain value is shared by part or all of a cohort, and then demonstrate how these sources of uncertainty arise in radiation dosimetry. We briefly describe the effects of different types of dosimetric uncertainty on risk estimates, followed by a description of each method of adjusting for the uncertainty. CONCLUSIONS: Each of the method has strengths and weaknesses, and some methods have limited applicability. We describe the types of uncertainty to which each method can be applied and its pros and cons. Finally, we provide summary recommendations and touch briefly on suggestions for further research.

Adjusting for Berkson error in exposure in ordinary and conditional logistic regression and in Poisson regression.

BACKGROUND: INTEROCC is a seven-country cohort study of occupational exposures and brain cancer risk, including occupational exposure to electromagnetic fields (EMF). In the absence of data on individual exposures, a Job Exposure Matrix (JEM) may be used to construct likely exposure scenarios in occupational settings. This tool was constructed using statistical summaries of exposure to EMF for various occupational categories for a comparable group of workers. METHODS: In this study, we use the Canadian data from INTEROCC to determine the best EMF exposure surrogate/estimate from three appropriately chosen surrogates from the JEM, along with a fourth surrogate based on Berkson error adjustments obtained via numerical approximation of the likelihood function. In this article, we examine the case in which exposures are gamma-distributed for each occupation in the JEM, as an alternative to the log-normal exposure distribution considered in a previous study conducted by our research team. We also study using those surrogates and the Berkson error adjustment in Poisson regression and conditional logistic regression. RESULTS: Simulations show that the introduced methods of Berkson error adjustment for non-stratified analyses provide accurate estimates of the risk of developing tumors in case of gamma exposure model. Alternatively, and under some technical assumptions, the arithmetic mean is the best surrogate when a gamma-distribution is used as an exposure model. Simulations also show that none of the present methods could provide an accurate estimate of the risk in case of stratified analyses. CONCLUSION: While our previous study found the geometric mean to be the best exposure surrogate, the present study suggests that the best surrogate is dependent on the exposure model; the arithmetic means in case of gamma-exposure model and the geometric means in case of log-normal exposure model. However, we could present a better method of Berkson error adjustment for each of the two exposure models. Our results provide useful guidance on the application of JEMs for occupational exposure assessments, with adjustment for Berkson error.

Issues in Implementing Regression Calibration Analyses.

Regression calibration is a popular approach for correcting biases in estimated regression parameters when exposure variables are measured with error. This approach involves building a calibration equation to estimate the value of the unknown true exposure given the error-prone measurement and other covariates. The estimated, or calibrated, exposure is then substituted for the unknown true exposure in the health outcome regression model. When used properly, regression calibration can greatly reduce the bias induced by exposure measurement error. Here, we first provide an overview of the statistical framework for regression calibration, specifically discussing how a special type of error, called Berkson error, arises in the estimated exposure. We then present practical issues to consider when applying regression calibration, including: 1) how to develop the calibration equation and which covariates to include; 2) valid ways to calculate standard errors of estimated regression coefficients; and 3) problems arising if one of the covariates in the calibration model is a mediator of the relationship between the exposure and outcome. Throughout, we provide illustrative examples using data from the Hispanic Community Health Study/Study of Latinos (United States, 2008-2011) and simulations. We conclude with recommendations for how to perform regression calibration.

The perils of using predicted values in place of observed covariates: an example of predicted values of body composition and mortality risk.

BACKGROUND: Several studies have assessed the relation of body composition to health outcomes by using values of fat and lean mass that were not measured but instead were predicted from anthropometric variables such as weight and height. Little research has been done on how substituting predicted values for measured covariates might affect analytic results. OBJECTIVES: We aimed to explore statistical issues causing bias in analytical studies that use predicted rather than measured values of body composition. METHODS: We used data from 8014 adults ≥40 y old included in the 1999-2006 US NHANES. We evaluated the relations of predicted total body fat (TF) and predicted total body lean mass (TLM) with all-cause mortality. We then repeated the evaluation using measured body composition variables from DXA. Quintiles and restricted cubic splines allowed flexible modeling of the HRs in unadjusted and multivariable-adjusted Cox regression models. RESULTS: The patterns of associations between body composition and all-cause mortality depended on whether body composition was defined using predicted values or DXA measurements. The largest differences were observed in multivariable-adjusted models which mutually adjusted for both TF and TLM. For instance, compared with analyses based on DXA measurements, analyses using predicted values for males overestimated the HRs for TF in splines and in quintiles [HRs (95% CIs) for fourth and fifth quintiles compared with first quintile, DXA: 1.22 (0.88, 1.70) and 1.46 (0.99, 2.14); predicted: 1.86 (1.29, 2.67) and 3.24 (2.02, 5.21)]. CONCLUSIONS: It is important for researchers to be aware of the potential pitfalls and limitations inherent in the substitution of predicted values for measured covariates in order to draw proper conclusions from such studies.

Thyroid doses in Ukraine due to 131I intake after the Chornobyl accident. Report I: revision of direct thyroid measurements.

The increased risk of thyroid cancer among individuals exposed during childhood and adolescence to Iodine-131 (131I) is the main statistically significant long-term effect of the Chornobyl accident. Several radiation epidemiological studies have been carried out or are currently in progress in Ukraine, to assess the risk of radiation-related health effects in exposed populations. About 150,000 measurements of 131I thyroid activity, so-called 'direct thyroid measurements', performed in May-June 1986 in the Ukrainian population served as the main sources of data used to estimate thyroid doses to the individuals of these studies. However, limitations in the direct thyroid measurements have been recently recognized including improper measurement geometry and unknown true values of calibration coefficients for unchecked thyroid detectors. In the present study, a comparative analysis of 131I thyroid activity measured by calibrated and unchecked devices in residents of the same neighboring settlements was conducted to evaluate the correct measurement geometry and calibration coefficients for measuring devices. As a result, revised values of 131I thyroid activity were obtained. On average, in Vinnytsia, Kyiv, Lviv and Chernihiv Oblasts and in the city of Kyiv, the revised values of the 131I thyroid activities were found to be 10-25% higher than previously reported, while in Zhytomyr Oblast, the values of the revised activities were found to be lower by about 50%. New sources of shared and unshared errors associated with estimates of 131I thyroid activity were identified. The revised estimates of thyroid activity are recommended to be used to develop an updated Thyroid Dosimetry system (TD20) for the entire population of Ukraine as well as to revise the thyroid doses for the individuals included in post-Chornobyl radiation epidemiological studies: the Ukrainian-American cohort of individuals exposed during childhood and adolescence, the Ukrainian in utero cohort and the Chornobyl Tissue Bank.

Bias due to Berkson error: issues when using predicted values in place of observed covariates.

Studies often want to test for the association between an unmeasured covariate and an outcome. In the absence of a measurement, the study may substitute values generated from a prediction model. Justification for such methods can be found by noting that, with standard assumptions, this is equivalent to fitting a regression model for an outcome variable when at least one covariate is measured with Berkson error. Under this setting, it is known that consistent or nearly consistent inference can be obtained under many linear and nonlinear outcome models. In this article, we focus on the linear regression outcome model and show that this consistency property does not hold when there is unmeasured confounding in the outcome model, in which case the marginal inference based on a covariate measured with Berkson error differs from the same inference based on observed covariates. Since unmeasured confounding is ubiquitous in applications, this severely limits the practical use of such measurements, and, in particular, the substitution of predicted values for observed covariates. These issues are illustrated using data from the National Health and Nutrition Examination Survey to study the joint association of total percent body fat and body mass index with HbA1c. It is shown that using predicted total percent body fat in place of observed percent body fat yields inferences which often differ significantly, in some cases suggesting opposite relationships among covariates.

STRATOS guidance document on measurement error and misclassification of variables in observational epidemiology: Part 1-Basic theory and simple methods of adjustment.

Measurement error and misclassification of variables frequently occur in epidemiology and involve variables important to public health. Their presence can impact strongly on results of statistical analyses involving such variables. However, investigators commonly fail to pay attention to biases resulting from such mismeasurement. We provide, in two parts, an overview of the types of error that occur, their impacts on analytic results, and statistical methods to mitigate the biases that they cause. In this first part, we review different types of measurement error and misclassification, emphasizing the classical, linear, and Berkson models, and on the concepts of nondifferential and differential error. We describe the impacts of these types of error in covariates and in outcome variables on various analyses, including estimation and testing in regression models and estimating distributions. We outline types of ancillary studies required to provide information about such errors and discuss the implications of covariate measurement error for study design. Methods for ascertaining sample size requirements are outlined, both for ancillary studies designed to provide information about measurement error and for main studies where the exposure of interest is measured with error. We describe two of the simpler methods, regression calibration and simulation extrapolation (SIMEX), that adjust for bias in regression coefficients caused by measurement error in continuous covariates, and illustrate their use through examples drawn from the Observing Protein and Energy (OPEN) dietary validation study. Finally, we review software available for implementing these methods. The second part of the article deals with more advanced topics.

Simulation Extrapolation Method for Cox Regression Model with a Mixture of Berkson and Classical Errors in the Covariates using Calibration Data.

Many biomedical or epidemiological studies often aim to assess the association between the time to an event of interest and some covariates under the Cox proportional hazards model. However, a problem is that the covariate data routinely involve measurement error, which may be of classical type, Berkson type or a combination of both types. The issue of Cox regression with error-prone covariates has been well-discussed in the statistical literature, which has focused mainly on classical error so far. This paper considers Cox regression analysis when some covariates are possibly contaminated with a mixture of Berkson and classical errors. We propose a simulation extrapolation-based method to address this problem when two replicates of the mismeasured covariates are available along with calibration data for some subjects in a subsample only. The proposed method places no assumption on the mixture percentage. Its finite-sample performance is assessed through a simulation study. It is applied to the analysis of data from an AIDS clinical trial study.

Reverse attenuation in interaction terms due to covariate measurement error.

Covariate measurement error may cause biases in parameters of regression coefficients in generalized linear models. The influence of measurement error on interaction parameters has, however, only rarely been investigated in depth, and if so, attenuation effects were reported. In this paper, we show that also reverse attenuation of interaction effects may emerge, namely when heteroscedastic measurement error or sampling variances of a mismeasured covariate are present, which are not unrealistic scenarios in practice. Theoretical findings are illustrated with simulations. A Bayesian approach employing integrated nested Laplace approximations is suggested to model the heteroscedastic measurement error and covariate variances, and an application shows that the method is able to reveal approximately correct parameter estimates.

Multiple indicators, multiple causes measurement error models.

Multiple indicators, multiple causes (MIMIC) models 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 as follows: (i) 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; (ii) to develop likelihood-based estimation methods for the MIMIC ME model; and (iii) 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.

A pseudo-penalized quasi-likelihood approach to the spatial misalignment problem with non-normal data.

Spatially referenced datasets arising from multiple sources are routinely combined to assess relationships among various outcomes and covariates. The geographical units associated with the data, such as the geographical coordinates or areal-level administrative units, are often spatially misaligned, that is, observed at different locations or aggregated over different geographical units. As a result, the covariate is often predicted at the locations where the response is observed. The method used to align disparate datasets must be accounted for when subsequently modeling the aligned data. Here we consider the case where kriging is used to align datasets in point-to-point and point-to-areal misalignment problems when the response variable is non-normally distributed. If the relationship is modeled using generalized linear models, the additional uncertainty induced from using the kriging mean as a covariate introduces a Berkson error structure. In this article, we develop a pseudo-penalized quasi-likelihood algorithm to account for the additional uncertainty when estimating regression parameters and associated measures of uncertainty. The method is applied to a point-to-point example assessing the relationship between low-birth weights and PM2.5 levels after the onset of the largest wildfire in Florida history, the Bugaboo scrub fire. A point-to-areal misalignment problem is presented where the relationship between asthma events in Florida's counties and PM2.5 levels after the onset of the fire is assessed. Finally, the method is evaluated using a simulation study. Our results indicate the method performs well in terms of coverage for 95% confidence intervals and naive methods that ignore the additional uncertainty tend to underestimate the variability associated with parameter estimates. The underestimation is most profound in Poisson regression models.

Expected estimating equation using calibration data for generalized linear models with a mixture of Berkson and classical errors in covariates.

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. We investigated its finite-sample performance numerically. Our method is illustrated by an application to real data from an HIV vaccine study.

Berkson errors in radiation dose assessments and their impact on radiation risk estimates.

OBJECTIVE: To estimate the influence of Berkson errors in exposure doses on the results of risk analysis within example of radiation epidemiological studies of the thyroid cancer prevalence. MATERIALS AND METHODS: The impact of Berkson errors of the thyroid doses in a dose-response analysis is studied by the method of stochastic simulation. RESULTS: Presence of errors in doses results in bias of the naive estimations of baseline morbidity and absolute risk excess in the linear logistic regression model. With the increase of dose errors the bias of the naive estimate increases almost linearly. The use of the full maximum likelihood method developed by authors improves essentially the estimates of parameters in the excess absolute risk model. CONCLUSION: Ignoring of the significant Berkson errors in dose assessment leads to the bias in estimates of background morbidity (overestimated) and of the excess absolute risk (underestimated). At that the bias is essentially less than the one for the case of classical error.