Distinguishing effects on tumor multiplicity and growth rate in chemoprevention experiments

In some types of cancer chemoprevention experiments and short-term carcinogenicity bioassays, the data consist of the number of observed tumors per animal and the times at which these tumors were first detected. In such studies, there is interest in distinguishing between treatment effects on the number of tumors induced by a known carcinogen and treatment effects on the tumor growth rate. Since animals may die before all induced tumors reach a detectable size, separation of these effects can be difficult. This paper describes a flexible parametric model for data of this type. Under our model, the tumor detection times are realizations of a delayed Poisson process that is characterized by the age-specific tumor induction rate and a random latency interval between tumor induction and detection. The model accommodates distinct treatment and animal-specific effects on the number of induced tumors (multiplicity) and the time to tumor detection (growth rate). A Gibbs sampler is developed for estimation of the posterior distributions of the parameters. The methods are illustrated through application to data from a breast cancer chemoprevention experiment.