Risk estimation with epidemiologic data when response attenuates at high-exposure levels

In occupational studies, which are commonly used for risk assessment for environmental settings, estimated exposure-response relationships often attenuate at high exposures. Relative risk (RR) models with transformed (e.g., log- or square root-transformed) exposures can provide a good fit to such data, but resulting exposure-response curves that are supralinear in the low-dose region may overestimate low-dose risks. Conversely, a model of untransformed (linear) exposure may underestimate risks attributable to exposures in the low-dose region.

We examined several models, seeking simple parametric models that fit attenuating exposure-response data well. We have illustrated the use of both log-linear and linear RR models using cohort study data on breast cancer and exposure to ethylene oxide.

Linear RR models fit the data better than do corresponding log-linear models. Among linear RR models, linear (untransformed), log-transformed, square root-transformed, linear-exponential, and two-piece linear exposure models all fit the data reasonably well. However, the slopes of the predicted exposure-response relations were very different in the low-exposure range, which resulted in different estimates of the exposure concentration associated with a 1% lifetime excess risk (0.0400, 0.00005, 0.0016, 0.0113, and 0.0100 ppm, respectively). The linear (in exposure) model underestimated the categorical exposure-response in the low-dose region, whereas log-transformed and square root-transformed exposure models overestimated it.

Although a number of models may fit attenuating data well, models that assume linear or nearly linear exposure-response relations in the low-dose region of interest may be preferred by risk assessors, because they do not depend on the choice of a point of departure for linear low-dose extrapolation and are relatively easy to interpret.