条件确切推断完全排列算法研究及医学应用

发布时间：2018-05-10 15:23

本文选题：列联表 + 确切推断　；参考：《山西医科大学》2005年博士论文

【摘要】：本次研究在对确切推断有关文献、算法的全面收集、整理和分析基础上,指出了目前确切推断理论与算法方面存在的主要问题,其一是确切检验方法体系及相关软件尚不完整,主要表现在大多数专业统计软件中提供的确切检验方法基本局限于列联表资料的假设检验;其二是算法和程序实现手段单一,主要表现在算法选择问题上,大多数专业统计软件单纯选择网络算法。由此,对应用于其它数据资料和模型的确切检验方法以及效率更高、更具特色的算法进行研究,具有重大的意义。本次研究即在这一背景下,结合医学领域数据特点,对列联表条件确切检验、Hardy-Weinberg平衡条件确切检验和列联表对数线性模型拟合优度确切检验的有关假设检验方法进行了较为全面的分析,并系统地提出了相应的基于递归技术和数据库技术的完全排列算法。在列联表条件确切检验方面,分别对2×2、2×c、r×c列联表资料,及s ( 2×2)、s ( 2×c)、s ( r×c)分层列联表资料的数据结构特点、适用检验方法、参照系及排列表确切概率等内容进行了系统的分析与讨论。对于2×2列联表,不同的资料收集方式,即完全随机设计和配对设计,对应了两类不同的检验方法,由于其确切检验参照系不同,对应的完全排列算法也不相同;对于2×c列联表,尽管列分类变量可为有序或无序变量,相应的假设检验方法也比较多,但其确切检验参照系是相同的,从而仅需设计一种完全排列算法,通过构造不同的检验统计量,即可实现不同的确切检验; r×c列联表的情形与2 ×c列联表类似,不同的资料收集方式和不同的分类变量属性,可分别对应不同的假设检验方法,但其确切检验参照系是相同的,从而通过构造不同的检验统计量,使用共同的完全排列算法,即可实现不同的确切检验;对于各种分层列联表资料,一般来说,首先应进行各层之间的齐性检验,如满足齐性要求,可进一步就行列分类变量之间关联关系进行相应的假设检验,此两类检验分别对应了两种不同的完全排列算法,齐性检验对应于三维列联表对数线性模型齐性关联模型的拟合优度确切检验,而关联关系检验对应于三维列联表对数线性模型条件独立模型的拟合优度确切检验。在算法的构造与实现方面,本研究从一维列联表
[Abstract]:Based on the comprehensive collection, arrangement and analysis of the relevant documents and algorithms, this study points out the main problems existing in the theory and algorithm of exact inference at present. One is that the exact testing method system and related software are not complete. This is mainly manifested in the fact that the exact testing methods provided by most professional statistical software are basically limited to the hypothesis testing of the data in the column tables. The second is the single method of algorithm and program implementation, which is mainly manifested in the problem of algorithm selection. Most professional statistical software simply select network algorithm. Therefore, it is of great significance to study the exact test methods and more efficient and characteristic algorithms applied to other data and models. In this context, this study combines the characteristics of medical data, In this paper, the hypothesis testing methods of Hardy-Weinberg equilibrium condition and fitting goodness test of logarithmic linear model are analyzed. The corresponding complete arrangement algorithm based on recursive technology and database technology is proposed systematically. In terms of the exact test of the condition of the column table, the data structure characteristics of 2 脳 2 脳 2 脳 cr 脳 c column data and s (2 脳 2 / 2) (2 脳 2 / s (r 脳 c) stratified table data are respectively applied to the data structure of the data of the 2 脳 2 脳 2 脳 cr 脳 c column, and the method of testing is applied to the data structure of the data. The exact probability of reference frame and permutation table are systematically analyzed and discussed. For the 2 脳 2 column table, different data collection methods, that is, complete random design and pairing design, correspond to two different kinds of inspection methods, and the corresponding complete arrangement algorithms are different because of the difference of the exact test reference frame, and for the 2 脳 c column coupling table, Although column classification variables can be ordered or disordered variables, and the corresponding hypothesis testing methods are more numerous, the exact test reference frame is the same, so it is only necessary to design a complete arrangement algorithm and construct different test statistics. The case of r 脳 c column coupling table is similar to that of 2 脳 c column coupling table. Different data collection methods and different attributes of classification variables can correspond to different hypothesis testing methods, but the exact test frame is the same. Therefore, by constructing different test statistics and using common complete arrangement algorithm, different exact tests can be realized. If the homogeneity requirement is satisfied, we can further test the correlation relationship between column and column classification variables. The two kinds of tests correspond to two different complete permutation algorithms, respectively. The homogeneity test corresponds to the exact test of the goodness of fit of the homogeneous correlation model of the three dimensional list logarithmic linear model, while the correlation relation test corresponds to the exact test of the fit degree of the conditional independent model of the three dimensional list logarithmic linear model. In the construction and implementation of the algorithm, this study starts with the one dimensional list.
【学位授予单位】：山西医科大学
【学位级别】：博士
【学位授予年份】：2005
【分类号】：R181.3

【参考文献】