惩罚logistic回归与多因子降维法交互作用分析及其应用

发布时间：2018-05-04 00:31

本文选题：惩罚Logistic回归模型 + MDR　；参考：《山西医科大学》2009年硕士论文

【摘要】： 目的:应用惩罚logistic回归模型(Penalized logistic regression.,PLR)解决传统logistic回归不能分析高阶交互作用的问题,并将PLR与现阶段国外广泛用于分析基因—基因、基因—环境交互作用的多因子降维法(Multifactor dimensionality reduction, MDR)进行对比分析,阐明二者在完成交互作用分析时各自的优劣势及其适用条件,为复杂的生物医学现象交互作用解释与分析提供合理的方法学依据。方法:介绍MDR分析原理及MDR交互作用分析技术。介绍惩罚logistic回归模型与原理。针对传统Logistic回归参数估计中遇到的样本含量问题,检测低阶、高阶交互作用能力问题等进行模拟研究,全部过程在R软件中编程实现。结合实例应用,进一步对比研究PLR、MDR解决医学应用问题,阐明其适用条件以及不同方法分析交互作用的优势。结果:模拟研究与实例分析表明,不同的调整参数λ对惩罚logistic回归模型的分析结果会产生较大的影响;调整参数λ使得统计量C得分最小的模型偏差最小,得到的估计系数相对较稳定,是推荐采纳的最佳模型。经PLR与LR的对比模拟研究,认为PLR偏差更小,得到的模型更稳定。尤其在样本量低于200时,惩罚Logistic回归模型显示出了更多的优势。交互作用检测能力模拟研究显示,在低维交互作用检测中,惩罚Logistic回归表现出MDR无可比拟的优越性。在高维或高阶交互作用检测时,MDR和PLR检测交互作用的能力相近,均能灵敏地检测出交互作用。即使加入干扰项后,也不会降低其检测交互作用的能力。MDR对高阶交互作用较敏感,能够检测出各种类型的交互作用,而惩罚Logistic回归更适合于相乘模型的交互作用分析。结论:惩罚Logistic回归、MDR与其他方法相比,更能有效得检测出多因素交互作用的存在。本文经过模拟研究与实例分析得出如下结论:(1)当样本含量较小时传统Logistic回归估计结果欠稳定;样本量低于200时,惩罚Logistic回归更具优势。(2)由于MDR在检测低阶低维交互作用方面的能力不足,而惩罚Logistic回归更适合于相乘模型的交互作用分析,对存在其它类型交互作用资料的分析,可以结合广义相对危险度模型或结合其他方法分析、处理。
[Abstract]:Objective: to apply the logistic regression model (Penalized logistic regression., PLR) to solve the problem that the traditional logistic regression can not analyze the high order interaction. And PLR and the multi factor reduction method (Multifactor dimensionality reduction, MDR) which are widely used in the analysis of gene gene, gene and environment interaction abroad at present. The comparative analysis shows the advantages and disadvantages of the two and their applicable conditions for the completion of the interaction analysis, and provide a reasonable methodological basis for the interpretation and analysis of the complex interaction of biomedical phenomena.
Methods: introduce the principle of MDR analysis and the technology of MDR interaction analysis. Introduce the logistic regression model and principle. In view of the sample content problems encountered in the traditional Logistic regression parameter estimation, the low order and high order interaction ability problems are simulated, and the whole process is programmed in R software. Step by step, PLR and MDR were applied to solve the problem of medical application, and its application conditions and advantages of different methods were analyzed.
Results: the simulation and case analysis show that the different adjustment parameters will have a great influence on the analysis results of the penalty logistic regression model. The adjustment parameter lambda makes the minimum C score model with the smallest model deviation, and the estimated coefficient is relatively stable. It is the best model adopted by the PLR and LR. It is considered that the PLR error is smaller and the model is more stable. Especially when the sample size is below 200, the penalty Logistic regression model shows more advantages. The simulation of interaction detection ability shows that in the low dimensional interaction detection, the penalty Logistic regression shows the superiority of the MDR non comparable simulation. The interaction ability of MDR and PLR detection is similar, and the interaction can be detected sensitively. Even if the interference item is added, the ability to detect interaction is not reduced,.MDR is more sensitive to the higher order interaction, and can detect various types of interaction, and the penalty of Logistic regression is more suitable for the interaction of the multiplicative model. Analysis.
Conclusion: to punish Logistic regression, MDR is more effective than other methods to detect the existence of multi factor interaction. The following conclusions are obtained by simulation and example analysis: (1) when the sample content is low, the result of the traditional Logistic regression estimation is not stable; when the sample size is below 200, the penalty for Logistic regression is more advantageous. (2) because The ability of MDR to detect low order and low dimensional interaction is insufficient, and the punishment of Logistic regression is more suitable for the interaction analysis of the multiplicative model. The analysis of other types of interaction data can be combined with the generalized relative risk model or the other methods.

【学位授予单位】：山西医科大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：R311

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