Genetics applications in multivariate survival analysis

在以家庭为基础的设计中，当医学研究为每个个体产生多个相关的生存结果时，分级生存数据就会出现。这种设置涉及个体之间和个体内部的依赖关系。对个体之间和个体内部的依赖关系进行建模、估计和理解是许多从业者最感兴趣的事情。在本项目的第一部分，我们将提出并比较基于Copula的方法来对这些依赖项进行建模。我们将表达风险预测函数，该函数评估经历未来的几率，即使在给定这些依赖结构方面的某个点的可用信息的情况下也是如此。我们将提供指导方针，帮助用户选择哪种策略更适合他们的数据。我们将推导推理程序，在存在选择偏差的情况下，使用标准的右审查观测来估计和测试从这些模型得出的兴趣量。在这个项目的第二部分，我们将推导程序来测试一组包含常见和罕见变异的遗传协变量与存在家族依赖的多个生存结果之间的关联。我们将调查几种策略来评估派生测试的重要性。在项目的最后部分，我们将推广关联检验来评估协变量对生存结果之间相关性的影响。

Hierarchical survival data arise when medical studies yield multiple correlated survival outcomes per individual in family-based design. This setting involves between- and within-individuals dependencies. Modelling, estimating and understanding the between- and within-individuals dependencies is of prime interest to many practitioners. In the first part of this project, we will propose, and compare copula-based approaches to model these dependencies. We will express risk prediction functions that assess the odds of experiencing a future even given the information available at some point in terms of these dependence structures. We will provide a guideline to help the users choose which strategy is more appropriate for their data. We will derive inference procedures to estimate and test the quantities of interest derived from these models using standard right-censored observations in the presence of a selection bias. In the second part of this project, we will derive procedures to test the association between a set of genetic covariates containing common and rare variants and multiple survival outcomes in the presence of familial dependencies. We will investigate several strategies to assess the significance of the derived tests. In the last part of the project, we will generalize association test to assess the effect of covariates on the correlation between survival outcomes.