Research Risk Estimation with Epidemiologic Data When Response Attenuates at High-Exposure Levels Kyle Steenland,1 Ryan Seals,1 Mitch Klein,1 Jennifer Jinot,2 and Henry D. Kahn 2 1Rollins School of Public Health, Emory University, Atlanta, Georgia, USA; 2National Center for Environmental Assessment, U.S. Environmental Protection Agency, Washington, District of Columbia, USA Background : In occupational studies, which are commonly used for risk assessment for environmental settings, estimated exposure–response relationships often attenuate at high expo- sures. 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. Methods : 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. r sulte : Linear RR models fit the data better than do corresponding log-linear models. Among lin- ear RR models, linear (untransformed), log-transformed, square root–transformed, linear-exponen- tial, 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. c onclusi : Although a number of models may fit attenuating data well, models that assume lin- ear 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. k ye sdrow : ethylene oxide, risk assessment, statistical models. Environ Health Perspect 119:831–837 (2011). doi:10.1289/ehp.1002521 [Online 10 January 2011] A key goal of risk assessment is to develop a quantitative exposure–response model from which excess risk of disease can be estimated for any given exposure. Increasingly, human epidemiologic data are being used to construct these models that form the basis for risk esti- mates. When appropriate epidemiologic studies with good exposure–response data are available, these data are usually preferred over labora- tory animal data for risk assessment, because animal data introduce additional uncertainty due to cross-species extrapolation. Here we dis- cuss risk assessment methods using epidemio- logic data with a dichotomous disease outcome and observations across a variety of exposure levels, such that exposure–response modeling is possible, with cumulative exposure as the exposure metric of interest (as is common for chronic disease). We use a variety of relative risk (RR) models, both log-linear (log RR = β1 × exposure; no intercept term β0 is fit in Cox regression) and linear (of the form RR = 1+ β × exposure). The models can include cova- riates and different transformations of functions of exposure. Linear RR models (sometimes called excess RR models) have some advantages, that is, they are more easily interpretable than are log RR models, and they provide a straight line to the origin in the low-dose region. When using human cancer data, the U.S. Environmental Protection Agency (EPA) often calculates the estimated lifetime expo- sure concentration that results in an excess risk of disease of 1% [exposure concentra- tion (EC01)], although other smaller ECs are sometimes used (U.S. EPA 2005). Larger ECs (e.g., EC05 or EC10) are generally used for rodent studies of carcinogens; however, for human cancer studies, extra risk seldom rises to such levels in the observable range of the data, which is especially true for rare cancers, such as nasopharyngeal cancer in relation to formaldehyde. The U.S. EPA then uses the exposure concentration correspond- ing to the 95% lower bound on the EC01 (i.e., the LEC01) as a point of departure for low-dose (low-exposure) linear extrapolation to estimate the risk associated with a one-unit increase in exposure (or dose). The LEC01 is essentially the same as the benchmark dose lower limit. Linear low-dose extrapolation from the point of departure to the origin is generally used to estimate low-dose risks for carcinogens, unless a nonlinear mode of action has been established (U.S. EPA 2005). The U.S. EPA uses the following formula to calculate excess risk (or extra risk) for a given level of exposure: (Lifetime risk in exposed – lifetime risk in nonexposed) ÷ (1 – lifetime risk in nonexposed). [1] Environmental Health Perspectives • volume 119 | number 6 | June 2011 The background risk of the disease of inter- est (i.e., the lifetime risk in the nonexposed) is subtracted from 1 in the denominator to scale the excess risk to the population expected to be free of background disease, a procedure used conventionally with rodent data. Lifetime risks for the exposed and nonexposed populations are calculated using actuarial methods in which mortality from other causes is taken into account. Exposure is assumed to be constant over time, and hence cumulative exposure increases over time. Age- specific background rates for disease in the non- exposed are multiplied by rate ratios estimated from the epidemiologic exposure–response model for given cumulative exposure levels to get age-specific rates of disease in the exposed, and lifetime risks for both exposed and nonex- posed are calculated across ages. Under certain circumstances, estimates of the exposure concentration corresponding to a 1% excess risk can be highly dependent on the exposure–response model chosen to model the epidemiologic data. One such case where this occurs is when the observed exposure–response data level off or plateau (attenuate) at higher exposures, as has been observed frequently in occupational epidemiology. For example, this phenomenon has been seen for cancer in rela- tion to dioxin, silica, 1,3-butadiene, cadmium, beryllium, radon daughters, diesel fumes, nickel, arsenic, ethylene oxide (EtO), and hexavalent chromium (Stayner et al. 2003). Such attenuation also has been observed in some studies of noncancer outcomes, for example, silica and kidney disease, and silica and silicosis mortality (e.g., Steenland et al. 2001; ’t Mannetje et al. 2002). A number of reasons for such an attenu- ation effect have been advanced, including depletion of susceptible individuals in the population, saturation of biological pro- cesses, misclassification of exposure at high levels, and the healthy worker–survivor effect (Stayner et al. 2003). Typically, models that provide a good fit to the data in this situation, Address correspondence to K. Steenland, Rollins School of Public Health, 1518 Clifton Rd., Atlanta, Georgia 30322 USA. Telephone: (404) 7128277. Fax: (404) 7128277. Email: nsteenl@sph.emory.edu Supplemental Material is available online (doi:10.1289/ehp.1002521 via http://dx.doi.org/). T h i s s t u d y w a s s u p p o r t e d b y t h e U . S . Environmental Protection Agency. The authors declare they have no actual or potential competing financial interests. Received 4 June 2010; accepted 10 January 2011. 831