Simple Parametric Analysis of Animal Tumorigenicity Data

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Abstract
The usual onset/death model for tumorigenicity data can be characterized by the tumor incidence rate and the conditional death rates for tumor-free and tumor-bearing animals. If the tumor is unobservable in live animals, however, these rates are difficult to estimate without cause-of-death data or numerous sacrifices. This article proposes simple but flexible parametric models for another set of functions that can be estimated directly from survival/sacrifice data. These estimates can be transformed to obtain estimates of and suggest parametric models for other functions of interest, such as the tumor incidence rate, the conditional death rates, and the relative risk. No cause-of-death data are needed and, due to its parametric nature, the analysis requires few sacrifice times. This approach makes no assumptions about the degree of tumor lethality, nor is the tumor assumed to operate independently of other diseases. The huge ED 01 study provides an excellent basis for assessing the proposed parametric approach. This unique experiment involved approximately 24,000 mice and incorporated 8 interim sacrifices at times ranging from 9 to 24 months. A known carcinogen, 2-acetylaminofluorene, was administered at various doses. The chemical affected survival only at the highest dose and had no effect on four of the six tumors investigated: uterine polyps, lung tumors, reticulum cell sarcomas, and lymphomas. A large subset of the EDm data was formed by pooling the mice from all but the highest-dose group. This collection of nearly 20,000 mice is used to demonstrate the appropriateness of the assumed parametric models; the parametric estimates of overall survival, tumor prevalence, and tumor incidence are consistent with the nonparametric estimates. Because the mice were housed in six rooms, the various room/dose combinations constitute natural subsets of the ED 01 data. An examination of 15 of these smaller subsets having similar sacrificing schedules suggests that in general the variability, bias, and mean squared error of the parametric estimates are at least as small as (and often much smaller than) those of the nonparametric estimates. Finally, the data from the smallest of these room/dose combinations illustrate the fit of the parametric and nonparametric estimates in a typical-sized study.

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