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Evaluation of measurement error.

Symanski-E; Chan-W; Smith-MA
Atlanta, GA: U.S. Department of Health and Human Services, Public Health Service, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health, Grant Number R03-OH-007834, 2007 Dec; :1-47
In a simple linear regression model with a latent independent random variable, the slope coefficient is smaller than it should be when a surrogate (i.e., error-prone) measure is used instead. The ratio of the slope coefficients from the regression models using the surrogate or latent variables reflects the attenuation bias. This bias can also be expressed as the ratio of the variance of the latent variable to the sum of the variances of the latent and surrogate variables. The traditional approach for estimating the attenuation bias uses this ratio and its estimated variances. Recognizing that the slope ratio cannot be estimated because the latent variable is unobservable, we developed a Bayesian-type estimator using the observations from the surrogate and outcome variables. One objective of this study was to examine the distributional behavior of the traditional and proposed estimators of attenuation bias. In the empirical study, we found that if the focus is on estimating attenuation bias, then it is preferable to use the traditional method; if the focus is on estimating the latent slope and the error variance of the simple linear regression is relatively large as compared to the variance of the latent variable, then it is preferable to use the proposed method; and if the focus is on estimating the latent slope and the error variance of the simple linear regression is relatively small as compared to the variance of the latent variable, then the traditional method may be preferable because it has a higher probability of producing estimates that are closer to the latent slope even though it has a larger mean bias. Finally, the traditional method was more likely to encounter numerical difficulties and thus produced a higher proportion of estimates that could not be obtained. In this case, the proposed method would provide a valid alternative for estimating the latent slope or the attenuation bias. For a given set of outcome and independent surrogate measurements in a simple linear Regression, we expressed the proposed latent slope and attenuation bias in an almost explicit form that can be used for approximation. These forms provide us with an alternative computational method for finding the estimates, other than the simulation method that was also presented. In addition, we found that the conditional distribution of the latent slope given the observed outcome and surrogate variables that were used for the proposed estimator, is proportional to the ratio of a noncentral chi-squared variate to a normal variate. Due to non-dependence of the numerator and the denominator of the latent slope, the proposed estimators of the latent slope and the attenuation bias are complicated. This leads to difficulty in comparing the distribution of the attenuation bias derived from the proposed method with the traditional method known as an F or approximated F distribution depending upon whether the surrogate measurements are balanced or unbalanced. For the latent slope, the estimator using the traditional method is complicated and its distribution is not yet identified. Further, we examined attenuation bias using a large database of multiple exposure measures collected on workers in a variety of different workplaces. Our findings indicate that there was more measurement error (attenuation bias) in biomarkers with shorter rather than longer half-lives and in exposure measurements collected via personal rather than biological sampling, although both types of monitoring data provided examples of exposure measures fraught with error. Our results also indicate substantial imprecision in the estimates of exposure measurement error, suggesting that greater attention needs to be given in the future to studies that collect sufficient data to allow for a better characterization of the attenuating effects of an error-prone exposure measure.
Risk-factors; Risk-analysis; Exposure-levels; Exposure-assessment; Biological-effects; Biomarkers; Mathematical-models
Elaine Symanski, PhD, Division of Epidemiology and Disease Control, University of Texas School of Public Health at Houston, 1200 Herman Pressler Drive, RAS 643, Houston, TX 77030
Publication Date
Document Type
Final Grant Report
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NIOSH Division
Priority Area
Research Tools and Approaches: Exposure Assessment Methods
Source Name
National Institute for Occupational Safety and Health
Performing Organization
University of Texas, Health Science Center, Houston