This paper discusses a method of estimating numerical characteristics of unobservable stages of carcinogenesis from data on tumor size at detection. To this end, a stochastic model of spontaneous carcinogenesis has been developed to allow for a simple pattern of tumor growth kinetics. It is assumed that a tumor becomes detectable when its size attains some threshold level, which is treated as a random variable. The model yields a parametric family of joint distributions for tumor size and age at detection. Some estimation problems associated with the proposed model appear to be tractable. This is illustrated with an application to the statistical analysis of data on primary breast cancer.