Abstract
The functional regression model is a model that can put non-traditional types of variables in and make further estimations. In survival data, Kong et al. (2014) proposed a Functional Linear Cox Regression Model (FLCRM). They combine both Functional Principal Component Analysis (FPCA) and Cox proportional hazards model to analyze relations between brain images and Alzheimer’s disease. In this thesis, more method is presented to deal with this type of survival data; furthermore, the Cox proportional hazards model in FLCRM is replaced with a more general semiparametric transformation model, which makes finding relations between functional or image types of data and patients’ survival time more convenient. Thus, a functional semiparametric transformation model is proposed, which can be further subdivided into four methods, and in the end comparisons will be made between these four methods through numerical simulation, then validate these methods outcome by applying actual Alzheimer’s disease neuroimaging initiative data through above model.