Assessment and indirect adjustment for confounding by smoking in cohort studies using relative hazards models

Workers' smoking histories are not measured in many occupational cohort studies. Here we discuss the use of negative control outcomes to detect and adjust for confounding in analyses that lack information on smoking. We clarify the assumptions necessary to detect confounding by smoking and the additional assumptions necessary to indirectly adjust for such bias. We illustrate these methods using data from 2 studies of radiation and lung cancer: the Colorado Plateau cohort study (1950-2005) of underground uranium miners (in which smoking was measured) and a French cohort study (1950-2004) of nuclear industry workers (in which smoking was unmeasured). A cause-specific relative hazards model is proposed for estimation of indirectly adjusted associations. Among the miners, the proposed method suggests no confounding by smoking of the association between radon and lung cancer--a conclusion supported by adjustment for measured smoking. Among the nuclear workers, the proposed method suggests substantial confounding by smoking of the association between radiation and lung cancer. Indirect adjustment for confounding by smoking resulted in an 18% decrease in the adjusted estimated hazard ratio, yet this cannot be verified because smoking was unmeasured. Assumptions underlying this method are described, and a cause-specific proportional hazards model that allows easy implementation using standard software is presented.