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

面部骨骼发育的不平衡，使人的五官畸形。牙科治疗通常是对这些患者进行的。在本研究中，我们探讨治疗效果与下颌骨生长的关系。面部骨骼的生长方式有很大的个体差异。我们将临床问题归结为以下统计问题：考虑随机效应的不平衡生长数据的分类。我们开发了统计方法和软件来有效地进行数据分析。(1)建立了分析的数据库。项目包括下颌骨各部位长度的纵向测量（使用X线照片）、每次检查的年龄和治疗效果。(2)开发了面骨发育过程可视化软件。(3)将Gompertz曲线拟合到个体生长，并使用k均值方法对估计的Gompertz参数进行分类，以探索应该对响应变量产生影响的离群值或未知背景。(4)建立了具有随机效应的生长曲线模型。通过多项式回归模型拟合个体响应曲线，并基于正态混合模型对拟合的回归系数进行分类。(5)开发了"NKMeans"软件对正态混合模型进行估计。它对包含缺失值或离群值的数据有效。

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.