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Shared Uncertainty in Measurement Error Problems With Application to Nevada Test Site Fallout Data Yehua Li1 Annamaria Guolo2 F Owen Hoffman3 and Raymond J Carroll4 1 Department of Statistics University of Georgia Athens GA 30605 U S A 2 Department of Statistics University of Padova Via Cesare Battisti 241 35121 Padova Italy 3 SENES Oak Ridge Center for Risk Analysis 102 Donner Drive Oak Ridge TN 37830 U S A 4 Department of Statistics Texas A M University 3143 TAMU Texas A M University College Station TX 77843 3143 U S A email carroll stat tamu edu Abstract 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 Thyroid Disease Study the Berkson measurement errors are correlated within strata This paper 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 MCMC and Monte Carlo EM 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 Nevada Test Site 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

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