title: Risk estimation with epidemiologic data when response attenuates at high-exposure levels.
abstract: BACKGROUND
  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.
  
  
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Rollins School of Public Health, Emory University, Atlanta, Georgia 30322, USA. nsteenl@sph.emory.edu
authors.forename: Kyle
authors.initials: K
authors.lastname: Steenland
authors.forename: Ryan
authors.initials: R
authors.lastname: Seals
authors.forename: Mitch
authors.initials: M
authors.lastname: Klein
authors.forename: Jennifer
authors.initials: J
authors.lastname: Jinot
authors.forename: Henry D
authors.initials: HD
authors.lastname: Kahn
mesh_terms: D001943:Breast Neoplasms / Q000139:chemically induced* / Q000453:epidemiology*; D002273:Carcinogens / Q000633:toxicity*; D015331:Cohort Studies; D004202:Disinfectants / Q000633:toxicity*; D005027:Ethylene Oxide / Q000633:toxicity*; D005260:Female; D006801:Humans; D016014:Linear Models; D016273:Occupational Exposure; D012306:Risk; D014481:United States / Q000453:epidemiology
chemical_list: D002273:Carcinogens; D004202:Disinfectants; D005027:Ethylene Oxide