Skin painting studies on transgenic mice have recently been approved by the Food and Drug Administration (FDA) for carcinogenicity testing. Data consist of serial skin tumor counts on the backs of shaved mice in each of several dose groups. Current methods for assessing the tumorigenicity of test compounds are based on generalized estimating equations and require large samples. This paper proposes a new framework for modeling of the change over time in the papilloma burden in each mouse. A latent variable underlying the observed papilloma response is assumed to follow a generalized linear mixed-effects transition model. The model accounts for heterogeneity among animals and serial dependency in the skin tumor counts. Extensions of existing Markov chain Monte Carlo procedures for Bayesian estimation in generalized linear mixed models are proposed. The methods are applied to data from a National Toxicology Program short-term carcinogenicity study of lauric acid.