• Low toxic effects;
  • Regression approach;
  • Hypothesis testing


The use of no-observed-effect levels (NOLs) and lowest-observed-effect levels (LOELs) assummary statistics for low toxic effects has been criticized recently. In this paper, we explore the regression-based approach for estimating low toxic effects. Key questions with this approach include: (1) is the approach practical with typical toxicity data sets, (2) can low toxic effects be estimated with confidence, (3) what models are appropriate for typical data sets and endpoints, and (4) how do point estimates of low toxic effects (e.g., EC10) compare with their corresponding LOELs and NOELs? Analyses of 198 toxicity data sets (all but 13 unpublished) revealed that: (1) even with a range of models to choose from (three models in the logistic family, probit model, Weibull model), >80% of the data sets did not produce a single adequate model fit; (2) estimates of low toxic effects were often model dependent when an extrapolation beyond the toxicity data was required; (3) confidence intervals can be quite large at 5% effect and lower; (4) of the five models, the three-parameter logistic equation with a steep slope parameter had the best model fit in the majority of the data sets; and (5) 76.9% of the NOELs and 100% of the LOELs were higher than their corresponding 10% effect point estimates from the best-fit model equations, suggesting that NOELs and LOELs are poor indicators of low toxic effects. We believe that the regression-based approach is a better tool than hypothesis testing for estimating low toxic effects. The approach, however, does not produce adequate model fits unless there is an obvious concentration–response relationship and several treatments with partial effects.