Methods to Derive Uncertainty Intervals for Lifetime Risks for Lung Cancer Related to Occupational Radon Exposure

Lifetime risks are a useful tool in quantifying health risks related to radiation exposure and play an important role in the radiation detriment and, in the case of radon, for radon dose conversion. This study considers the lifetime risk of dying from lung cancer related to occupational radon exposure. For this purpose, in addition to other risk measures, the lifetime excess absolute risk (LEAR) is mainly examined. Uncertainty intervals for such lifetime risk estimates and corresponding statistical methods are rarely presented in the radon literature. Based on previous work on LEAR estimates, the objective of this article is to introduce and discuss novel methods to derive uncertainty intervals for lifetime risk estimates for lung cancer related to occupational radon exposure. Uncertainties of two main components of lifetime risk calculations are modeled: uncertainties of risk model parameter estimates describing the excess relative risk for lung cancer and of baseline mortality rates. Approximate normality assumption (ANA) methods derived from likelihood theory and Bayesian techniques are employed to quantify uncertainty in risk model parameters. The derived methods are applied to risk models from the German "Wismut" uranium miners cohort study (full Wismut cohort with follow-up up to 2018 and sub-cohort with miners first hired in 1960 or later, designated as "1960+ sub-cohort"). Mortality rate uncertainty is assessed based on information from the WHO mortality database. All uncertainty assessment methods are realized with Monte Carlo simulations. Resulting uncertainty intervals for different lifetime risk measures are compared. Uncertainty from risk model parameters imposes the largest uncertainty on lifetime risks but baseline lung cancer mortality rate uncertainty is also substantial. Using the ANA method accounting for uncertainty in risk model parameter estimates, the LEAR in % for the 1960+ sub-cohort risk model was 6.70 with a 95% uncertainty interval of [3.26; 12.28] for the exposure scenario of 2 Working Level Months from age 18-64 years, compared to the full cohort risk model with a LEAR in % of 3.43 and narrower 95% uncertainty interval [2.06; 4.84]. ANA methods and Bayesian techniques with a non-informative prior yield similar results, whenever comparable. There are only minor differences across different lifetime risk measures. Based on the present results, risk model parameter uncertainty accounts for a substantial share of lifetime risk uncertainty for radon protection. ANA methods are the most practicable and should be employed in the majority of cases. The explicit choice of lifetime risk measures is negligible. The derived uncertainty intervals are comparable to the range of lifetime risk estimates from uranium miners studies in the literature. These findings should be accounted for when developing radiation protection policies, which are based on lifetime risks.