Exploratory study for structure of the multidimensional data and its application to the clinical data.

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The unbalanced development of facial skeleton makes one's feature abnormal. The dental treatment is often carried out to such patients. In this study, we examine relationship between therapeutic effects and the growth of mandibular bone. The growth pattern of facial skeleton has a great individual variety. We realized the clinical problem as the following statistical problem : The classification of the unbalanced growth data considering random effects. We developed the statistical methods and the softwares to carry out data analysis effectively.The achievements of our study were summarized as follows.(1) The data base for the analysis was constructed. The items were longitudinal measurements of the length of various sites of the mandibular bone (by using x-ray photographs), the age at each examination and therapeutic effects.(2) The graphical software was developed to visualize the process of development of facial bone.(3) The Gompertz curve was fitted to an individual growth, and the estimated Gompertz parameters were classified with the k-means method to explore the outliers or unknown backgrounds that was supposed to give effect to the response variables.(4) The growth curve model with random effects were proposed. Individual response profiles were fitted by the polynomial regression model, and the fitted regression coefficients were classified based on the normal mixture model.(5) The software named "NKMeans" was developed to estimate normal mixture model. It is effective on data including missing values or outliers.