  Most conventional risk analysis methods rely on a single best estimate of
exposure per person which does not allow for adjustment for exposure-related
uncertainty. Here, we propose a Bayesian model averaging method to properly
quantify the relationship between radiation dose and disease outcomes by
accounting for shared and unshared uncertainty in estimated dose. Our Bayesian
risk analysis method utilizes multiple realizations of sets (vectors) of doses
generated by a two-dimensional Monte Carlo simulation method that properly
separates shared and unshared errors in dose estimation. The exposure model
used in this work is taken from a study of the risk of thyroid nodules among a
cohort of 2,376 subjects following exposure to fallout resulting from nuclear
testing in Kazakhstan. We assessed the performance of our method through an
extensive series of simulation tests and comparisons against conventional
regression risk analysis methods. We conclude that when estimated doses contain
relatively small amounts of uncertainty, the Bayesian method using multiple
realizations of possibly true dose vectors gave similar results to the
conventional regression-based methods of dose-response analysis. However, when
large and complex mixtures of shared and unshared uncertainties are present,
the Bayesian method using multiple dose vectors had significantly lower
relative bias than conventional regression-based risk analysis methods as well
as a markedly increased capability to include the pre-established 'true' risk
coefficient within the credible interval of the Bayesian-based risk estimate.
An evaluation of the dose-response using our method is presented for an
epidemiological study of thyroid disease following radiation exposure.
