Modeling the effect of dose on the lifetime tumor rate from an animal carcinogenicity experiment

The proportion of tumor-bearing animals in a chronic bioassay is often used as a basis for assessing risk at human exposure levels that are below the experimental range. However, such a crude experimental tumor rate can be biased by dose-related differences in the nontumor mortality. To adjust tumor rates for competing mortality, Kodell, Gaylor, and Chen (1986, Biometrics 42, 867-873) propose a standardized tumor rate, calculated separately in each dose group from dose-specific estimates of the tumor prevalence and mortality functions. This paper extends the approach of Kodell et al, by developing a method of modeling the standardized rate as a function of dose. An advantage of this approach is that it leads to estimates that are monotone in dose. In addition, by modeling the lifetime risk as a function of dose directly, it is possible to obtain estimates for the risk at dose levels outside the experimental range, such as for low-dose extrapolation, and estimation of the "tumorigenic dose 50" (TD50). A semiparametric model is developed, as well as the nonparametric alternative of isotonic regression. Simulations are provided to show the relative bias and precision of the two approaches to that of Kodell et al.