| Right censoring data is common in biomedical studies.A lot of models are used to analyze these data in survival analysis.The semiparametric regression models are usually modeled for the conditional hazard function.Many researchers studied these models and presented a lot of methods to estimate parameters and nonparametric func-tion.In particular,the proportional hazards model,additive hazards model and additive-multiplicative hazards model are three mainly types of the condition risk models.The famous partial likelihood method,instead of the full likelihood approach,is used to estimate the coefficients for the proportional hazards model.But the elegant martin-gale methods,similar as the score equations of the partial likelihood method,are useful to estimate the regression parameters for the additive hazards model and the additive-multiplicative hazards model.For the baseline cumulative hazard function,Breslow proposed the classical Breslow estimator.However,researchers often find that there is an important time for treating or con-trolling some diseases.We are interest in how to extract the auxiliary information for parametric estimation in the proportional hazards model,the additive hazards model and the additive-multiplicative hazards model.Thus,we pick up the auxiliary informa-tion in the important time via subgroup analysis,and subsequently employ the method of generalized moment to combine the auxiliary survival information in the above three models.The consistency and asymptotic normality of the proposed methods are estab-lished.At the same time,the weak convergence of Breslow estimator is also investigat-ed.Our approach could automatically unite the vitally auxiliary subgroup information.From the asymptotic covariances,we show that the method of generalized moment is more efficient than partial likelihood approach or the martingale methods in these three models.This thesis is organized as follows:Chapter 1 and Chapter 2 aim to outline the background and basic concepts of survival analysis,the method of generalized moment,and introduce the main results of the thesis.Chapter 3 is to propose the extracting method for the useful survival information in important time point and employ the generalized moment method to estimate coef-ficients in the three models.In order to show the important of combining the auxiliary information,the generalized moment method without subgroup information is also pre-sented.The consistency and asymptotic normality of the proposed estimates are shown.Simultaneously,the explicit estimators for the asymptotic covariances are also suggest-ed.We establish that the generalized moment method with auxiliary information is the most efficient of all from the large sample properties.However,the efficiency of the generalized moment method without auxiliary information is the same as the par-tial likelihood approach or the martingale method.In particular,when the number of subgroup is one,the efficiency of the three methods are similar in the three models.In Chapter 4,we demonstrate some simulations to show the finite-sample perfor-mance of our proposed method in the three models.A series of simulations results show that the generalized moment method with auxiliary information is more efficient than partial likelihood approach or the martingale methods,and the estimator of asymptotic covariance is accurate in the three models.In addition,the simulation outcomes also establish that the method of subgroup analysis is useful in parametric estimation.In Chapter 5,we mainly apply the method of generalized moment to a real data.The parametric estimation results also indicate that the generalized moment method with auxiliary survival information is more efficient.In the final Chapter 6,we summarize our works and describe the future studies. |
