Confidence intervals and hypothesis tests are developed for dose-response relations based on dichotomous data from animal carcinogenicity experiments. The functional form of the dose-response curve comes from the Armitage-Doll multistage carcinogenesis model and involves a polynomial in the dose-rate, with non-negative coefficients. Asymptotic distributions of the maximum likelihood estimators of these coefficients are used to construct confidence bounds on risk at a given dose and on the dose corresponding to a given risk. Likelihood ratio tests are developed for the presence of a positive dose-related effect and for the existence of a positive slope to the dose-response curve at zero dose. The latter test is of practical importance since a positive slope of the dose-response curve at zero dose rules out any "threshold-like" behavior and would often mean that any concentration low enough to insure a negligibly low cancer risk (e.g., 10(-6)) would be too low to be economically useful for applications such as food additives. Simulation experiments are performed to provide guidelines for applying the theory.