The statistical analysis of cancer inhibition/promotion experiments

The purpose of this paper is to address the very important problem of accurate statistical analysis of certain types of cancer inhibition/promotion (IP) experiments. These experiments are routinely used by the National Cancer Institute to test the effects of potential chemopreventative agents. The statistical analysis is difficult since there is Type I censoring. In the IP experiments under investigation, laboratory animals (rats) are injected with a single dose of either a direct or indirect acting carcinogen. In the mammary tumor system, animals in the control group generally develop 5-7 tumors and typical experiments are usually terminated after 4-6 months. Animals are sacrificed at the end of the experiment and all observed tumors are confirmed. The two most common response variables are the number of observed tumors per animal and the rate of tumor development. The difficulty in analyzing these experiments occurs because experiments are terminated before all induced tumors have been observed. Fewer observed tumors in one group compared to another could be the result of a decreased number of induced tumors, a decrease in growth rate, or a combination of both. It is essential for the experimenter to distinguish between these two different biological actions. Present statistical techniques do not account for this confounding and since they rely primarily on nonparametric procedures, do not present an accurate description of potential IP agents. In this paper we introduce a parametric procedure that explicitly acknowledges the confounding present in experiments of this nature. The analysis is based on the comparison of the mean number of tumors per group (lambda) and the mean time to tumor appearance (mu). A longer mean time to development is believed to indicate a slower tumor growth rate. Hypothesis tests are developed to determine if there is an overall experiment effect, to isolate which groups are contributing to an observed experiment effect, and to isolate factors (tumor number and/or growth rate) contributing to an observed group difference. Confidence regions for (lambda, mu) are also generated. This analysis leads to a better understanding of how potential IP agents function.