The role of the mathematical model is to express the biological theory in the form of a set of numerical predictions which can be reconciled with data. We have fitted the model implicit in current theory, and the predictions from that do not fit the observed facts. Either the theory or the observed facts (or both) are wrong. If the facts are right, then our final model (Model II) points to the changes in the theoretical concept which are necessary. Increasing conversion from carcinoma in situ to invasive carcinoma with age must be accepted and explained. The fall in prevalence of dysplasia and carcinoma in situ before the major onset of invasive cancer must be fully appreciated and explained. The regression of carcinoma in situ to dysplasia or normal in large numbers must be accepted and explained either biologically or by error in categorization, or both.