基于复杂纵向数据的混合联合模型研究

It often happens in longitudinal studies that repeated measurements of markers are observed with various data features of multilevel structure, heterogeneity, non-normality, missingness and mismeasured covariates. However, relatively few studies have been conducted on simultaneously accounting for the biases induced by these data features and it is not clear how they may interact and simultaneously influence inferential procedures. Statistical inference and analysis complicate dramatically when these features arise. Based on our previous research, this proposal explores a finite mixture of hierarchical joint models of longitudinal measures with an attempt to alleviate departures from homogeneous characteristics, adjust departures from normality, tailor missing observations and mediate accuracy from measurement error in covariate. The Bayesian joint modeling is employed to not only estimate all parameters in mixture of joint models, but also evaluate probabilities of class membership. The proposed modeling procedure is applied to analyze real data and simulation studies are conducted to assess the performance of the proposed models and method. In the meantime, associated statistical package will be developed..Finally we provide a platform by establishing a pre-diabetes cohort for application and promotion of proposed method which may complement and implement the analysis methodological system of longitudinal data, and provide a methodological reference for disease risk assessment, individual treatment and the data analysis of large scale longitudinal survey and cohort study.

纵向数据中的多水平结构、异质性、非正态分布、数据缺失、协变量测量误差等特征较常见，但鲜有研究探讨这些特征同时存在时产生的偏倚，对统计推断的联合影响也尚不明确。当这些特征同时存在时统计推断和数据分析将会极其复杂。前期研究对上述部分特征通过引入偏态分布、应变量缺失机制及单个协变量测量误差构建了有限混合模型，拟合效果良好。本课题在前期研究基础上，拟以有限混合模型为框架，构建含高水平随机效应、偏斜分布、应变量和/或协变量缺失机制、多维时协变量测量误差的混合联合模型；采用Bayesian方法进行统计推断，同步获得模型的参数估计及个体归属于每一轨迹类别的概率，开发统计实现软件包。用实际数据和Monte Carlo模拟对模型和方法进行诊断，通过糖尿病前期队列作实践验证。以期进一步补充或完善纵向数据分析的方法学体系，为疾病风险评估与个体化治疗、大型纵向调查及队列研究的数据分析等提供方法学支持。

本项目主要对复杂纵向数据进行深入而系统的创新性研究，用有限混合模型与多维时变协变量测量误差模型组建混合联合模型，发展了新的建模理论和推断方法。其主要研究内容：（1）评估高水平随机效应及其对混合联合模型的影响；（2）混合成分的确定及个数的选择；（3）应变量非正态分布时，模型的随机效应和误差的分布的设定；（4）应变量与协变量均存在缺失情形的模型构建；（5）多维时协变量测量误差的联合分布及协变量间的交互效应；（6）混合联合模型的识别性及算法的收敛性。用实际数据和Monte Carlo模拟对模型和方法进行诊断，通过糖尿病前期队列作实践验证。将构建的混合联合模型应用于医学纵向数据的影响因素分析，为解决实际问题提供了有效的统计方法和可靠的理论支持。本项目内容是当今统计学研究的热点，具有重大的理论意义和实际应用价值。