Biomedical sciences and mathematical statistics in Japan: personal experiences and future outlook.

A successful application of statistics to medical sciences is our experience with analysis of data from the Cornell Medical Index-Health Questionnaire. (1-13). K. Fukamachi and T. Kanehisa of Kyushu University translated the Cornell Medical Index Questionnaire and tried to establish a diagnostic rule to distinguish neurotic and mentally unhealthy patients from mentally healthy patients at the department of internal medicine at Kyushu University hospital. I was approached for suggestions. After some analysis I decided to reduce the data to a bivariate form. The first component was the square root of the number of physical complaints. The reason was an intuitive one based on various scatter diagrams and also on the outcome of a preliminary statistical analysis made by Dr. Fukamachi regarding a comparison of numbers of complaints between mentally healthy patients and in healthy ones in various categories. They collected data for several years and had accumulated data on 50 solidly diagnosed psychosomatic cases and 50 nonpsychosomatic cases. I drew lines representing the linear discrimination function and added two more lines indicating what are called the "doubtful regions" in the terminology of Rao (14). Thus there are four regions. If the data fall in the first region, the patient is diagnosed suffering from psychosomatic illness; this is the region consisting of points deviating significantly from the mentally healthy patients' mean vector. The second region is one where patients are tentatively diagnosed suffering from psychosomatic illness; in this region the points do not lie a significant distance from those for "healthy" patients, but the value of the linear discriminant function indicates the patient has a psychosomatic complaint. The third and fourth regions are for patients provisionally diagnosed and de-