Uncertainty in internal doses: using Bayes to transfer information from one worker to another

Uncertainty in estimates of internal doses to can arise for a variety of reasons, which include a lack of knowledge about assumed model parameters, uncertainty in exposure conditions, paucity of measurement data, and variability between individuals. In some cases, for example, causation or epidemiological studies, it is essential to be able to quantify this uncertainty for each individual in the study. It is often the case that some individuals within a cohort will have been subject to extensive measurements, enabling precise estimates of organ doses to be derived, while for others, the measurement data are sparse. The question is how can one make use of the measurement data on the former individuals to improve dose estimates for the latter? It will be seen that Bayesian inference provides the mechanism for doing this, since the essence of the Bayesian approach is to start with knowledge before the measurement data are known (prior knowledge), and then use the measurement data to revise it (posterior knowledge). This paper illustrates the Bayesian method by taking two such cases, who were both exposed by accidental inhalation of the same form of americium compound. Essentially, the comprehensive bioassay data available for the first worker is used to derive posterior probability distributions of absorption parameters for the americium material, which are used as prior information to improve the dose assessment for the second worker. Direct assessment of the uncertainty in the second worker’s dose, both with and without the additional information from the first worker, quantifies the improvement in dose assessment obtained.