Concentration–time–response modeling for acute and short-term exposures

Abstract

Risk of health effects from acute and short-term exposure depends on exposure time as well as exposure concentration. A general approach to extending a concentration–response model to include time as a variable is described using mortality of rats exposed to hydrogen sulfide (H 2S) as an example. This particular example resulted in a logit model with concentration–time ( c– t) relationship linear in time and log-concentration. It provided an improved statistical fit, based on the Akaike information criterion in the observed time range, 30m–360m, over implementing the c– t relationship of [ten Berge, W.F., Zwart, A., Appelman, L.M., 1986. Concentration–time mortality response relationship of irritant and systemically acting vapours and gases. J. Hazard. Mater. 13, 301–309] as a default in the logit model. This approach also indicated that there might be a fundamental difference in the relationship between concentration, time, and response at short exposure times, somewhere less than 30m, a hypothesis for further consideration from a biological perspective. In general, the proposed approach provides flexibility to develop a concentration–time–response model, and the associated concentration–time relationship, from the data. Interpretation and potential implications, however, need to be considered within the context of biological plausibility as well. Implementation of the proposed approach requires adequate data for separate concentration–response modeling at each of several exposure durations.