Statistical methods for the analysis of tumor multiplicity data.

The fit of tumor multiplicity data from 93 mouse skin, lung, and liver carcinogenicity experiments to Poisson, negative binomial, and normal distributions was studied. The data were fitted well by the negative binomial distribution. This distribution has two parameters, the mean tumor multiplicity and an exponent determined by the interanimal homogeneity of tumor response. The value of the latter parameter was related to animal strain and the target tissue studied in the carcinogenicity experiments. The null distribution of the two-sample likelihood ratio test based on the negative binomial with common exponent model for tumor multiplicity data was shown by simulation studies to be approximately chi 2 with 1 d.f. Simulation also indicated that the likelihood ratio test has sufficiently better performance when the negative binomial model is valid to make its use more attractive than the more commonly used Wilcoxon test or Student t test. Charts for estimating the number of animals per group that are required to detect specified differences in tumor multiplicities are provided for several commonly used assays.