A Bayesian hierarchical approach to account for left-censored and missing radiation doses prone to classical measurement error when analyzing lung cancer mortality due to γ-ray exposure in the French cohort of uranium miners.

Epidemiological data on cohorts of occupationally exposed uranium miners are currently used to assess health risks associated with chronic exposure to low doses of ionizing radiation. Nevertheless, exposure uncertainty is ubiquitous and questions the validity of statistical inference in these cohorts. This paper highlights the flexibility and relevance of the Bayesian hierarchical approach to account for both missing and left-censored (i.e. only known to be lower than a fixed detection limit) radiation doses that are prone to measurement error, when estimating radiation-related risks. Up to the authors' knowledge, this is the first time these three sources of uncertainty are dealt with simultaneously in radiation epidemiology. To illustrate the issue, this paper focuses on the specific problem of accounting for these three sources of uncertainty when estimating the association between occupational exposure to low levels of γ-radiation and lung cancer mortality in the post-55 sub-cohort of French uranium miners. The impact of these three sources of dose uncertainty is of marginal importance when estimating the risk of death by lung cancer among French uranium miners. The corrected excess hazard ratio (EHR) is 0.81 per 100 mSv (95% credible interval: [0.28; 1.75]). Interestingly, even if the 95% credible interval of the corrected EHR is wider than the uncorrected one, a statistically significant positive association remains between γ-ray exposure and the risk of death by lung cancer, after accounting for dose uncertainty. Sensitivity analyses show that the results obtained are robust to different assumptions. Because of its flexible and modular nature, the Bayesian hierarchical models proposed in this work could be easily extended to account for high proportions of missing and left-censored dose values or exposure data, prone to more complex patterns of measurement error.