Modeling Tumor Onset and Multiplicity Using Transition Models with Latent Variables

Summary. We describe a method for modeling carcinogenicity from animal studies where the data consist of counts of the number of tumors present over time. The research is motivated by applications to transgenic rodent studies, which have emerged as an alternative to chronic bioassays for screening possible carcinogens. In transgenic mouse studies, the endpoint of interest is frequently skin papilloma, with weekly examinations determining how many papillomas each animal has at a particular point in time. It is assumed that each animal has two unobservable latent variables at each time point. The first indicates whether or not the tumors are in a multiplying state and the second is the potential number of additional tumors if the tumors are in a multiplying state. The product of these variables follows a zero‐inflated Poisson distribution, and the EM algorithm can be used to maximize the observed‐data pseudo‐likelihood, based on the latent variables. A generalized estimating equations robust variance estimator adjusts for dependency among outcomes within individual animals. The method is applied to testing for a dose‐related trend in both tumor incidence and multiplicity in carcinogenicity studies.