Analysis of Stomach Cancer Incidence by Histologic Subtypes Based on a Mathematical Model of Multistage Cancer Induction and Exponential Growth

A mathematical model incorporating the processes of both cancer induction and subsequent tumor growth has been developed. The model was applied to incidence data of stomach cancer classified into histologic subtypes: papillary adenocarcinoma (PAP), well and moderately differentiated tubular adenocarcinomas (WEL and MOD), poorly differentiated adenocarcinoma (POR), mucinous adenocarcinoma (MUC) and signet‐ring cell carcinoma (SIG). The multistage theory was assumed for cancer induction as in the Armitage‐Doll model. For the period of growth, exponential growth was assumed and clinical surfacing was formulated as a stochastic process related to tumor diameter. The number of stages in cancer induction and the tumor growth rate were simultaneously estimated for each histologic subtype using the maximum likelihood procedure. The present model showed better fits than the Armitage‐Doll model in most histologic subtypes except WEL. PAP, WEL and MOD, which are characterized as differentiated subtypes with less mucous production, showed different features from POR, MUC and SIG: 1) the number of stages was estimated to be larger, 2) the differences in incidence rates between males and females were more marked, and 3) males tended to have larger growth rates in PAP and MOD, while in POR, MUC and SIG, females had larger values. The present study showed that an analysis by histologic subtypes is of importance in stomach cancer and that the period of tumor growth should not be ignored when formulating a model of the natural history of stomach cancer.