Statistical procedures to test for linearity and estimate threshold doses for tumor induction with nonlinear dose-response relationships in bioassays for carcinogenicity.

Sublinear shapes of the dose-response curve in the low-dose range of toxicity testing are often postulated to be indicative of a no-effect threshold. We present statistical procedures to test sublinear dose responses in bioassays for carcinogenicity against the hypothesis of linearity and estimate a lower confidence limit for the dose at the postulated breakpoint. First, a control tumor incidence of 0 is assumed. Tumor incidence at dose 1 is allowed to range from 0 to 4 tumor-bearing animals (TBAs) in groups of 50 animals, dose 2 is assumed to result in a tumor incidence of 5-25 TBAs. The null hypothesis of a linear dose response is tested by (i) the likelihood ratio (LR) test and (ii) the minimum chi(2) (MC) method. Validation by simulation showed the MC method to be more conservative than the LR test. At the 5% level with MC, the following observed numbers of TBAs for the dose sequence 0-1-2 resulted in rejection of the hypothesis of linearity: 0-0-6, 0-1-10, 0-2-13, 0-3-16, 0-4-18. Second, the analysis was adapted to allow for a control tumor incidence of 0-4 TBAs/50 and a tumor incidence of 0-10 TBAs/50 at dose 1, and the minimum number of TBAs at dose 2 to reject linearity at the 5% level was calculated. Third, a program is made available to analyze data derived from protocols that include nonstandard dose span and group size. Internet access to the respective statistics software and source file is provided. Examples for nasal tumor induction by formaldehyde and for the induction of renal adenocarcinoma by ochratoxin A are shown. The proposed analysis may be useful to test sublinear sections of the dose response for the possibility of a threshold for carcinogens and to define dose levels that could be used as a starting point for setting exposure standards.