Novel statistical models and estimation methods for survival and longitudinal data.

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The objective of this research project is to investigate some important issues in analyzing survival data in clinical and observational studies and to propose novel statistical models and estimation methods to tackle the issues. One such issue is survival data with a cured fraction, where some subjects are immune to the event of interest and often named as cured. Such data can often be found in cancer treatments and in other disciplines such as economics and social studies. Another issue we will deal with is clustered survival data, where the subjects in the data can form clusters based on, for example, families or hospitals/medical centers. The survival time and cure status from the same cluster tend to be correlated due to shared genetics and environment. The issues also include handling survival data with a cured fraction from a case-cohort design, causal inference in survival models, and joint analysis of longitudinal proportional or multi-item data and survival data with a cured fraction. We will tackle the issues by developing new statistical models and estimation methods to properly analyze the data arising in the settings. For example, we will develop new estimating equations for the marginal cure models. The estimates from this new method are expected to be more efficient and less reliant on parametric assumptions than existing methods. We will develop data driven methods to select an appropriate model for survival data among a number of recently proposed cure models and classic survival models. We will develop cure models that are suitable for survival data in the case-cohort design. We will investigate the performance of some existing methods for causal inference and propose new methods that will be proved to be effective. The proposed research will contribute to advances in statistical methodology that has wide applications in real world problems in clinical and observational studies and in other disciplines. It will also provide opportunities to train even more Master's and PhD students and post-doctoral fellows than I achieved in the last NSERC proposal. It allows the trainees to develop skills and knowledge required as professional statisticians to deal with survival data.