Statistical Analysis Of Survival Data With Time-dependent Covariates

There are two common types of covariates in survival analysis:(a)baseline variables,which do not change over time,and(b)longitudinal data,which change over time and need to be measured repeatly.Joint models offers an attractive method for the longitudnial survival data analysis,with the Cox proportional risk(Cox PH)framework often being modeled as the classical framework for survival analysis.To address the limitation of the assumption of PH model,The accelerated failure model(AFT)model can be an alternative to the Cox PH model.Different from the most joint models use a linear mixed model for the longitudinal component,a multiplicative effects joint AFT model is proposed in this thesis,in which the longitudinal data is treated as a discrete implementation of a continuous process and be fitted by B-spline method,is proposed in this paper.The Hamiltonian Monte Carlo method is applied for parameters estimation and statistical estimation.The propsed method is explained in the primary biliary cirrhosis(PBC)data,to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients,the results show that the proposed method has good fitting goodness.