Bayesian bias adjustments of the lung cancer SMR in a cohort of German carbon black production workers

Background A German cohort study on 1,528 carbon black production workers estimated an elevated lung cancer SMR ranging from 1.8-2.2 depending on the reference population. No positive trends with carbon black exposures were noted in the analyses. A nested case control study, however, identified smoking and previous exposures to known carcinogens, such as crystalline silica, received prior to work in the carbon black industry as important risk factors. We used a Bayesian procedure to adjust the SMR, based on a prior of seven independent parameter distributions describing smoking behaviour and crystalline silica dust exposure (as indicator of a group of correlated carcinogen exposures received previously) in the cohort and population as well as the strength of the relationship of these factors with lung cancer mortality. We implemented the approach by Markov Chain Monte Carlo Methods (MCMC) programmed in R, a statistical computing system freely available on the internet, and we provide the program code. Results When putting a flat prior to the SMR a Markov chain of length 1,000,000 returned a median posterior SMR estimate (that is, the adjusted SMR) in the range between 1.32 (95% posterior interval: 0.7, 2.1) and 1.00 (0.2, 3.3) depending on the method of assessing previous exposures. Conclusions Bayesian bias adjustment is an excellent tool to effectively combine data about confounders from different sources. The usually calculated lung cancer SMR statistic in a cohort of carbon black workers overestimated effect and precision when compared with the Bayesian results. Quantitative bias adjustment should become a regular tool in occupational epidemiology to address narrative discussions of potential distortions.