In observational cohort mortality studies with prolonged periods of exposure to the agent under study, independent risk factors for death commonly determine subsequent exposure to the study agent. For example, in occupational mortality studies, date of termination of employment is both a determinant of subsequent exposure to the chemical agent under study (since terminated individuals receive no further exposure) and an independent risk factor for death (since disabled individuals tend to leave employment). When a risk factor determines subsequent exposure and is determined by previous exposure, standard analyses that estimate age-specific mortality rates as a function of cumulative exposure can underestimate the true effect of exposure on mortality, whether or not one adjusts for the risk factor in the analysis. This observation raises the question, "Which, if any, empirical population parameter can be causally interpreted as the true effect of exposure in observational mortality studies?" In answer, we offer a graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods. We reanalyze the mortality experience of a cohort of arsenic-exposed copper smelter workers using our approach and compare our results with those obtained using standard methods. We find an adverse effect of arsenic exposure on all cause and lung cancer mortality, which standard methods failed to detect. The analytic approach introduced in this paper may be necessary to control bias in any epidemiologic study in which there exists a risk factor which both determines subsequent exposure and is determined by previous exposure to the agent under study.