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

面部骨骼发育不平衡，使人容貌异常。牙科治疗通常是对这样的患者进行的。在这项研究中，我们研究了治疗效果与下颌骨生长的关系。面部骨骼的生长模式具有很大的个体多样性。我们将临床问题归结为以下统计学问题：考虑随机效应的不平衡增长数据的分类。为了有效地进行数据分析，我们开发了统计方法和软件。我们的研究成果总结如下：(1)建立了数据分析的数据库。通过对下颌骨各部位长度的纵向测量(使用X光片)、每次检查时的年龄和治疗效果。(2)开发图形软件来可视化面部骨骼的发育过程。(3)将Gompertz曲线与个体生长进行拟合，并用k-均值方法对估计的Gompertz参数进行分类，以探索应该影响响应变量的异常值或未知背景。(4)提出了考虑随机效应的生长曲线模型。用多项式回归模型对个体反应曲线进行拟合，并根据正态混合模型对拟合出的回归系数进行分类。(5)开发了正态混合模型估计软件NKMeans。它对包括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.