结合图像分析的非参数随机效应模型及其在临床医学数据中的应用研究

Large amount of valuable clinical trial and treatment datasets about endocrine diseases has been accumulated in Peking Union Medical College Hospital, which includes many images and high-dimensional data. From the data we found that due to the diversity of the individual patients, the distribution law of the treatment effects are quite complex . This project intends to build some mathematical models from the datasets by combining the image processing techniques and the nonparametric random effects models together. We propose to design efficient and stable algorithms for statistical inference and investigate the variation of the endocrine and metabolic functions for patients with different treatments. The research in this project will provide some scientific evidence for the clinical treatments and lay the theoretical foundation to improve the domestic level of treatment for the menopausal syndrome. In this project, we use variational and statistical image processing methods to extract key features needed in the following statistical analysis. Then, by combining the empirical likelihood and the EM algorithm, we will transform the nonparametric likelihood into profile likelihood under some constraint. And then，the Monte Carlo simulation method from the Bayesian statistics can be used in our models and this will avoid the numerical computation of high-dimensional integrals and asymptotic variance.

协和医院妇科内分泌医疗数据包含大量影像资料以及高维复杂数据。同时，由于患者个体差异很大，治疗效果呈现不同的分布规律。本项目拟采用图像处理技术和非参数随机效应模型相结合的方法对协和医院妇科内分泌医疗数据建立数学模型。通过新模型设计高效, 稳定的统计和计算方法，研究国内妇科内分泌疾病患者治疗前后全身内分泌代谢功能等各项指标的变化规律，为临床治疗提供确切的基础研究依据，为进一步提高我国更年期综合征的治疗水平打下理论基础。在研究中，首先采用变分方法进行图像分析提取图像特征。然后利用经验似然和EM算法, 将结合图像信息的非参数随机效应模型产生的复杂似然函数在一定约束条件下转化为剖面似然。最后结合贝叶斯统计学和Monte Carlo模拟方法, 研究非参数、半参数模型中关心参数的统计推断，从而避免了高维积分和渐近方差估计等计算难题。

本项目研究内容包含统计方法研究，统计应用研究，图像处理研究，和医学研究四方面。研究了非参数贝叶斯方法在矩约束条件下的统计推断。与协和医院妇产科合作，利用随机效应模型研究不同治疗方案下病人各类激素数据的变化规律，分析了各类激素数据在不同的治疗方案下的异同点，为分析各类药物的疗效提供依据。对于妇女更年期综合症数据，不孕不育症医疗机构相关数据进行了统计分析。研究了运动物体的动态追踪问题，提出了基于主动轮廓模型优化迭代求解方法。对相位恢复算法开展了研究，分析了成像模型、算法与测量方法和次数对相位信息恢复的影响。对量化光声层析成像算法开展了研究，改进了已有的成像算法，提高了成像精度和计算速度。