Genetics applications in multivariate survival analysis

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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.