摘要
人工神经网络是一门新兴的边缘学科，与传统医学统计方法相比，人工神经网络不需要精确的数学模型，没有任何对变量的假设(如正态性、独立性等)要求，因此可以弥补传统统计方法的不足，解决一些用传统统计方法不能解决的问题。
人工神经网络的应用已经逐渐进入医学领域。对医学工作者而言，如何构建网络模型，使之具有较好的推广能力，解决实际问题是他们所关心的重点。本文针对在医学领域应用最广的BP神经网络展开研究，介绍了BP网络的基本原理，并从统计学的角度对学习过程进行描述。结合数据模拟通过对BP网络的构建、训练、优化和评价进行讨论，提出一些简易可行的网络优化方法，如如何确定隐单元数、通过修剪对网络进行简化以提高网络性能、提前终止训练等，并探讨它们的统计学应用和联系。
我们通过构造无隐含层的单层BP网络，对网络构建的一般原则、训练过程、评价指标进行总结，这些原则对多层BP网络也同样适用，对实际工作者具有指导意义。由于单层BP网络在医学危险因素筛选方面具有特殊的意义，我们对单层网络训练的样本大小要求进行模拟研究，而在此以前，国外只针对多层网络的训练样本提出过要求。模拟结果显示，训练样本大小与连接权数的比为10：1时，即可获得具有一定推广能力的网络模型。
我们对多层BP网络中隐单元的功能进行描述，并引入信息论的观点，提出一种应用信息熵估计隐单元数的方法。通过数据模拟与现有几种隐单元数确定方法的效果进行比较，熵法构造的模型的判别效果优于其它隐单元数模型。
探讨修剪算法对网络结构优化的作用以及它的实际意义。我们将修剪算法引入医学多因素资料的分析；首次探讨了单层网络中的修剪算法在变量筛选方面的作用，提出修剪后的单层BP网络模型的连接权与回归系数具有相同的含义，为
医学研究中危险因素的筛选提供了一个新的途径。
将前面提出的网络构建和优化的原理，包括隐单元数目的估计，修剪算法、
提前终止训练等进一步应用于预后资料的实例分析中，并与传统医学统计方法
比较。
本研究创新之处在于:
l)将信息论中的嫡引入网络模型构建，提出一种新的隐单元计算方法:根
据信息嫡估计隐单元数，在数据模拟和实际应用中取得较好的效果。
2)首次将网络修剪算法应用到医学多元资料的分析中，并对修剪算法与传
统统计学的联系进行探讨，实现了在网络训练中进行变量筛选。
3)通过模拟，对单层神经网络训练所需的样本含量进行初步探讨，提出最
低样本含量的要求。
由于时间和搜集的资料的限制，实例应用中对生存资料的分析仅限于单一
时间点模型，未对其他模型进行深入探讨，对删失数据在神经网络中的处理也
没有进一步研究。此外，对信息嫡估计隐单元数的方法还要进行更大规模的模
拟，以进一步证实。
Artificial neural network (ANN) is a rising borderline science. Compared to the mathematical statistics, it doesn't need exact mathematical model and dose not have any consumption (such as distribution and independence) demanding the variables to meet. It can make up the deficiency of mathematical statistical methods and solve some problems that traditional statistical methods failed to resolve.
In medical study fields, the application of ANN is more and more popular. Particularly attention had been given to how to build a suitable ANN model to resolve the actual problems. This study focuses on the back propagation network (BP network) which is the most popular model used in medical filed. The fundamental of BP network was introduced and the description from the statistical point of view was given. Several simulative BP network architectures had been set up to discuss the designing, learning, optimizing and evaluation of the BP networks. The details of some simple optimizing methods, such as how to design the number of hidden units, prune the network to improve its generalization, and stop learning properly were studied. The performance and relation to statistics of these methods had also been discussed.
There were three parts of the main study.
The BP model without hidden layer (also can be taken as single layer model) was constructed and its principles of architecture designing and learning process and the methods of evaluation were summarized, which also can be used in multi-layer BP model and can be used as a conduct in application. Residual analysis and AUC of
ROC were introduced as methods of evaluation. For the particular meaning of single layer BP model using in risk factor screening in medicine, a simulating study to derive the approximation bounds of its learning sample was conducted. Only the multi-layer BP model' bound had been studied before by other scholars. The outcome of simulation indicated that a stable model with proper ability of generalization had been derived when the relationship between sample size and links number is 10:1.
For multi-layer BP model, we focused on the study of hidden layer. Description of the function of hidden layer was given. Information theory was inducted into the study of the number of hidden units. A novel method using entropy to estimate the number of hidden units was proposed. The simulation outcome showed that the effect of BP model with the number of hidden units generated by entropy performed better than other model.
To simplifying the structure, the effect of pruning algorithms application in BP network model and its relationship with medical statistics were studied. In our study, one of the pruning algorithms - optimal brain damage method was applied in multi-variable data analysis. It is the first time that the application in variable selection with this method was discussed. We found that pruning in single layer BP network model can act as variable selection, and the weight of BP network model after pruning had the same meaning as regression coefficient. Thus a new method for the hazard factor screening in medical study has been proposed.
Those principles of BP network designing and optimization were also applied on actual medical prognosis data and survival data. The result of that was also compared with the performance of logistic regression to test and verify.
The innovation of this study lied in the following:
Inducting the entropy in information theory into the BP network architecture constructing and bring a novel method of hidden units number designing using entropy.
The pruning algorithm being used in medical data as a method of variable selection for the first time.
The approximation bounds of single layer BP model being studied by
simulated data.
For the limit of time and data collection, the study on actual survival data was only conducted by one architecture model. The further study should be conducted on the analysis of other models and the censored data treatment should be considered. The entropy method of
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