Effects of time-variant exposure on toxic substance response

Sources of time-variant exposure to toxic substances are identified and examined for their effects on the estimation of response. It is shown that only time-averaged target tissue concentrations are required to obtain rigorous risk estimates from the one-hit and multihit models. In contrast, detailed concentration histories need to be retained throughout analyses involving two-event models with intermediate-stage clonal growth advantage (clonal two-stage) and multistage models. Cumulative incidence ratios, based on the exact to time-averaged treatment of concentration time dependencies, are evaluated for substances whose toxic responses exhibit moderate (arsenic) and strong (ethylene dibromide) dependence on time of actual exposure. These ratios reveal that time-averaged dose approximations may lead to several orders of magnitude error in both the multistage and clonal two-stage models if exposure periods are short, and that 3.4-fold (arsenic) and 8-fold (ethylene dibromide) errors still exist even when an actual two-thirds lifetime exposure is averaged over a full lifetime. Finally, the effects of time-variant exposure on risk estimation due to migration and birth-death in an epidemiological setting are examined. A residence time distribution calculation shows that, if these effects are ignored for a population orally exposed to arsenic and characterized by an out-migration rate in excess of 5%/yr, response errors will exceed an order of magnitude.