纵向数据与生存数据联合模型的统计推断

In cancer clinical trials, patient’s longitudinal proportional measurements and survival time are important endpoints. The classical analysis of longitudinal proportional data in clinical trials ignores the constraint and may lead to misleading conclusion. Moreover, some patients may drop out of study due to recurrence, which cause informative dropout and censored survival time. In this project, we develop the joint models of longitudinal proportional measurements and survival time to accommodate the association between them, and employ the simplex distribution to consider the constraint of longitudinal proportional measurements. The existing joint modeling did not explore the inference for the joint model based on the simplex distribution, a non-exponential distribution. We employ Laplace approximation, penalized joint likelihood, QEM approach to improve the efficiency of parameter estimation, and establish the statistical inference for the simplex joint model, the spline joint model and the joint model with a cure fraction. This project would enrich the statistical inference framework for joint modeling of longitudinal proportional measurements and survival time. The results could be applied to assess the treatment efficacy and optimize the treatment regimens in clinical trials.

在临床试验等领域，纵向比例观测值往往伴随着生存时间数据。以往纵向比例数据的分析忽略了变量的有界性，从而造成分析结果的偏差。另外，由于一些病人的中途退出导致纵向比例观测值的缺失与生存数据的删失。本项目致力于给出纵向比例观测值与生存数据联合模型的统计推断，基于单纯形分布考量联合模型中纵向比例观测值的有界性，在补偿数据信息损失的同时，刻画纵向观测值与生存时间的相关性。已有联合模型并没有给出非指数族单纯形联合模型的统计推断。本项目分别考虑单纯形联合模型、样条联合模型和联合治愈模型，探讨利用拉普拉斯近似、惩罚联合似然和QEM算法来建立联合模型的统计推断过程，改进参数估计的有效性。此项目的研究可以丰富基于联合模型框架下纵向比例观测值与生存数据的分析方法并提供相关理论依据。所得结果可以用于临床试验中综合疗效评估、治疗方案优化等领域，解决实际问题。

本项目致力于纵向变量与生存时间的联合统计推断，针对复杂数据中的有界性、信息缺失、可治愈个体以及时依动态变化，研究了单纯形联合分析、联合治愈模型、样条联合模型近似。我们通过单纯形分布的小散度渐近正态性、广义治愈模型的风险成比例结构，采用拉普拉斯近似，建立了惩罚部分似然近似函数的统计推断；基于Smooth cubic B-splines的光滑性，近似联合治愈模型中部分线性混合效应函数和基准风险函数，实现样条联合模型的EM算法估计。对提出的推断方法进行了数值试验，充分验证估计的有效性和稳健性，并对临床试验中纵向生活质量观测与生存时间的复杂数据结构进行了实例分析，刻画纵向轨迹曲线的时间变化趋势，估计协变量对纵向生活质量和生存时间的影响效果，并将相关科研成果整理成3篇学术论文和1部书章。