Research On Sensitivity Of Frailty Distribution In Shared Frailty Model

As a classic model in the field of survival analysis,Cox proportional hazard model has been widely studied and applied.For clustered survival data,the shared frailty model is commonly used instead of the classic Cox model for characterizing the correlation be-tween individuals in each cluster,which assumes independence conditional on a scalar non-negative random variable.Although the shared frailty model has been widely used in practice,its properties are still being studied continuously.An important question that we concerned is that how sensitive is the parameter estimate of the frailty distribution to the misspecified shared frailty model? Since the true frailty distribution is unobservable and unknown,which is commonly replaced by a specified distribution in practice,it is worth to explore the impact of the frailty model on the parameter estimates.In this thesis,we considered the semiparametric estimation of the Gamma frailty as the specified frailty distribution due to its wide application,and studied the sensitivity of the parameter estimates to the misspecified Gamma shared frailty model under three dif-ferent frailty distributions by a class of simulation works.The simulation results show that when the true frailty distribution is one of log-normal,mixed log-normal,and Gamma dis-tribution,the estimate of regression coefficients can guarantee approach bias,but the mean square error of the variance estimate of the frailty is more sensitive to the use of Gamma frailty distribution,which could lead to frailty estimation with low efficiency.In order to avoid misspecifying the frailty distribution,we propose to use a semi--nonparametric model for frailty and apply the EM algorithm for maximum likelihood estimation of pa-rameters.In the implementation of the EM algorithm,since the E step includes complex integration calculations,we recommend using the MCEM algorithm to approximate the integration,where the construction of the Markov chain is based on the Metropolis–Hast-ing algorithm.