Objectives: Residual confounding can be present in epidemiological studies because information on confounding factors was not collected. A Bayesian framework, which has the advantage over frequentist methods that the uncertainty in the association between the confounding factor and exposure and disease can be reflected in the credible intervals of the risk parameter, is proposed to assess the magnitude and direction of this bias.
Methods: To illustrate this method, bias from smoking as an unmeasured confounder in a cohort study of lung cancer risk in the European asphalt industry was assessed. A Poisson disease model was specified to assess lung cancer risk associated with career average, cumulative and lagged bitumen fume exposure. Prior distributions for the exposure strata, as well as for other covariates, were specified as uninformative normal distributions. The priors on smoking habits were specified as Dirichlet distributions based on smoking prevalence estimates available for a sub-cohort and assumptions about precision of these estimates.
Results: Median bias in this example was estimated at 13%, and suggested an attenuating effect on the original exposure–disease associations. Nonetheless, the results still implied an increased lung cancer risk, especially for average exposure.
Conclusions: This Bayesian framework provides a method to assess the bias from an unmeasured confounding factor taking into account the uncertainty surrounding the estimate and from random sampling error. Specifically for this example, the bias arising from unmeasured smoking history in this asphalt workers’ cohort is unlikely to explain the increased lung cancer risk associated with average bitumen fume exposure found in the original study.
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Funding: The Asphalt Workers’ cohort study was sponsored by the European Commission (grant number: BMH4-CT95-1100), EAPA, Eurobitume and CONCAWE. The project described in this manuscript was conducted within a training fellowship grant from the European Union Sixth Framework Programme Network of Excellence on Environmental Cancer Risk, Nutrition and Individual Susceptibility (ECNIS) (grant number: FOOD-CT-2005-513 943).
Competing interests: None.
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