The present study is an extension of our recent study in which we attempted statistical analysis of the data assembly of age-adjusted incidence rates (AAIRs) of a tumor without topological data manipulation for each of 20 individual tumors in scope, for each of 6 cancer registration areas in space, and for a period of early 1960's to mid 1980's in time. This time, a data assembly of log AAIR changes in time and space first passed through the process of topological data manipulation, and then underwent the sequential regression analysis so that we could assess the fitness of log AAIR changes either in space or in time to the equilibrium model of the law of mass action from the viewpoint of the interaction between oncogene activation and tumor suppressor gene inactivation. For the sake of comparison, the fitness of the cancer risk data to the equilibrium model was assessed in the framework of 3 sets of coordinates: a) the original (x org, y org) coordinates in which most of the log AAIR data assemblies in their data variations were classified as the oncogene activation type in the field of centripetal force (r seq=-1.000). b) The rect (X rect, Y rect) coordinates in which the log AAIR data assemblies were very often classified as the tumor suppressor gene inactivation type in the field of centrifugal force (r seq=+1.000). c) The para (X para, Y para) coordinates in which the log AAIR data assemblies were mostly classified as the intermediate type as regards the fitness to the equilibrium model. The rect-coordinates and the para-coordinates, 2 variants of angular rotation of the original coordinates, were so designed as to allow their X-axes to run each at a right angle and parallel to the regression line of the original pair data block. The results obtained were as follows: a) poor fitness of the log AAIR changes in space to the equilibrium model in the rect-coordinates was found in male breast cancer, male thyroid cancer, female esophageal cancer, female laryngeal cancer and female lung cancer. The summation of the present study and the last study from our laboratory led to the conclusion that the members of low-risk gender in the tumor family with sex discrimination of cancer risk were inclined to show either failed expression of oncogene activation or failed expression of tumor suppressor gene inactivation or both. b) There was a subtle difference of the fitness of log AAIR data to the equilibrium model between the log AAIR changes in time and those in space in that the log AAIR changes in time within the framework of the rect-coordinates, which usually represented the field of centrifugal force or site of tumor suppressor gene inactivation expression, showed an increase in the number of oncogene activation type data sets as compared with the log AAIR changes in space. c) Upon further insight into the AAIR changes in time, consistent association of prominent cancer risk increase in time with the transition of tumor suppressor gene inactivation expression (r seq=+1.000) from the rect-coordinates to the para-coordinates was detected in skin cancer of both sexes, testicular tumor, liver cancer of both sexes and thyroid cancer of both sexes, all of which were related to the prevalence of environmental hormones as regards the recent boost of their cancer risks in the Western countries. In summary, the log AAIR, a cancer risk parameter, in its changes in time and space was found to provide useful information in assessing the interaction between the oncogene-tumor suppressor gene complex and the hormonal milieu of the host in the genesis of both environmental hormone-dependent and -independent human neoplasias. The significance of our statistical maneuver (the sequential regression analysis) is discussed in the light of the development of mathematics in early 19th century.

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