With a binary response Y, the dose-response model under consideration is logistic in flavor with pr(Y=1 | D) = R (1+R)−1, R = λ0 + EAR D, where λ0 is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as
Dimes=fiQimes/Mimes. Here,
Qimes is the measured content of radioiodine in the thyroid gland of person i at time tmes,
Mimes is the estimate of the thyroid mass, and fi is the normalizing multiplier. The Qi and Mi are measured with multiplicative errors
ViQ and
ViM, so that
Qimes=QitrViQ (this is classical measurement error model) and
Mitr=MimesViM (this is Berkson measurement error model). Here,
Qitr is the true content of radioactivity in the thyroid gland, and
Mitr is the true value of the thyroid mass. The error in fi is much smaller than the errors in (
Qimes,
Mimes) and ignored in the analysis.
By means of Parametric Full Maximum Likelihood and Regression Calibration (under the assumption that the data set of true doses has lognormal distribution), Nonparametric Full Maximum Likelihood, Nonparametric Regression Calibration, and by properly tuned SIMEX method we study the influence of measurement errors in thyroid dose on the estimates of λ0 and EAR. The simulation study is presented based on a real sample from the epidemiological studies. The doses were reconstructed in the framework of the Ukrainian-American project on the investigation of Post-Chernobyl thyroid cancers in Ukraine, and the underlying subpolulation was artificially enlarged in order to increase the statistical power. The true risk parameters were given by the values to earlier epidemiological studies, and then the binary response was simulated according to the dose-response model.