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We aimed to estimate credibility intervals for the British occupational cancer burden to account for bias uncertainty, using a method adapted from Greenland’s Monte Carlo sensitivity analysis.The attributable fraction (AF) methodology used for our cancer burden estimates requires risk estimates and population proportions exposed for each agent/cancer pair. Sources of bias operating on AF estimator components include non-portability of risk estimates, inadequate models, inaccurate data including unknown cancer latency and employment turnover and compromises in using the available estimators. Each source of bias operates on a component of the AF estimator. Independent prior distributions were estimated for each bias, or graphical sensitivity analysis was used to identify plausible distribution ranges for the component variables, with AF recalculated following Monte Carlo repeated sampling from these distributions. The methods are illustrated using the example of lung cancer due to occupational exposure to respirable crystalline silica in men.Results are presented graphically for a hierarchy of biases contributing to an overall credibility interval for lung cancer and respirable crystalline silica exposure. An overall credibility interval of 2.0% to 16.2% was estimated for an AF of 3.9% in men. Choice of relative risk and employment turnover were shown to contribute most to overall estimate uncertainty. Bias from using an incorrect estimator makes a much lower contribution.The method illustrates the use of credibility intervals to indicate relative contributions of important sources of uncertainty and identifies important data gaps; results depend greatly on the priors chosen.