Statistical analysis of the age-adjusted incidence rates of human neoplasias: changes in time and space from early 1960's to mid 1980's with special reference to the steroid criminal hypothesis of carcinogenesis.

Our earlier reports indicated that the changes of age-adjusted incidence rates (AAIRs) of any 2 tumors in time and space, as investigated by the sequential regression analysis, showed a good fitness to the equilibrium model under the control of the law of mass action. The purpose of this study is to investigate the problem of whether or not the changes of AAIRs of individual tumors in time and space show a similar fitness to the equilibrium model of the law of mass action. The cancer risk data set of: a) 20 neoplasias in scope; b) 6 cancer registration areas in space; and c) 5 sequential investigations from early 1960's to mid 1980's in time, were subjected to the sequential regression analysis - a modification of the least square method. Results obtained are as follows: a) out of 20 tumors tested, all tumors other than 5 tumor types showed a good fitness (P<0.05) to the equilibrium model of the law of mass action in their risk changes in space. The 5 tumor types that failed to fit to the equilibrium model were male gall-bladder cancer, male breast cancer, male thyroid cancer, female liver cancer and female laryngeal cancer. They were all classified as the members of low-risk gender in the cancer family with sex discrimination of cancer risk. b) All tumors other than male thyroid cancer of Birmingham-England showed a good fitness to the equilibrium model of the law of mass action in their risk changes in time. c) It is argued that the good fitness to the equilibrium model of the law of mass action and the poor fitness to the equilibrium model can be taken each as indication of the predominant expression of oncogene activation and the emergence of intervention of tumor suppressor gene inactivation to the full expression of oncogene activation in the mathematical structure of the cancer risk data set. The significance of the above findings as the supporting evidence of the steroid criminal hypothesis of carcinogenesis as well as the pertinence of the least square method to the mathematical analysis of cancer risk are discussed in the light of historical development of science from early 19th century to late 20th century.