In any study based on an occupational cohort, it is important to consider the variation in risk factors over time. Cumulative exposure is the most important time-related factor for exposure-response analyses, whereas other time-related factors such as age at risk, year at risk, and length of follow-up may be confounders and effect modifiers. This paper examines the family of exponential models which can be used for time-related analyses of studies based on an occupational cohort. Analyses using Poisson regression, the proportional hazards model, and the logistic model are presented, and their interrelationships explored. These models are illustrated with data from a cohort study of lung cancer mortality among asbestos textile plant workers. All three approaches yielded similar effect estimates. In particular, Poisson regression and the proportional hazards model yielded very similar findings, but Poisson regression has some conceptual and computational advantages.