Research On Marginal Model Regression Analysis And Group Sequential Test Of Multivariate Survival Data With Staggered Entry

Multivariate survival analysis is an important research problem,and its application areas include biomedical research,financial risk modeling,reliability analysis in systems engineering,etc.Since multivariate survival data are often censored and there are correlations between different survival times,higher requirements are placed on statistical methods.The marginal model is a widely used regression model in multivariate survival analysis,which is robust and easy to implement.Because the entry time of the experimental subjects can not be determined in advance,the survival data may also have calendar time attributes.This type of data is called survival data with staggered entry.Theoretical research on the marginal method regression model under staggered entry is rare and more difficult.In some biomedical clinical trials,data monitoring of survival data is often required to end the clinical trial at its early stages.Group sequential hypothesis testing is a widely used data monitoring method.This thesis conducts a theoretical study of the marginal model regression method for multivariate survival data with staggered entry and considers the corresponding group sequential hypothesis testing problem.Marginal method models do not model the correlation of multiple survival times and are therefore suboptimal in terms of estimating efficiency.This thesis proposes to partition the calendar time by using a sequence of natural interim analysis times that come from a group sequential test,then constructs an estimation equation,and finally derives the partitioning estimation under the staggered entry,to improve estimation efficiency.Due to the consideration of calendar time,it is difficult to investigate the theoretical properties of the partitioning estimation obtained in this thesis.We use the martingale theory as well as the empirical process theory to prove the consistency and asymptotic normality of the partitioning estimates and study the large sample property of the partitioning estimation’s covariance structure.This thesis actually proves that the partitioning score process has asymptotically independent increments,limited to the straight line where the calendar time and the survival time are identical.To the best of our knowledge,the asymptotically independent increments property demonstrated in this thesis is among the first of its kind in existing researches based on related marginal regression model with staggered entry.Due to the establishment of the excellent theoretical properties of partitioning estimation,this thesis also discusses the problem of group sequential testing.The related solution is relatively simple,so it can be utilized in practice.This thesis also carries out a large number of simulation studies on partitioning estimation and group sequential hypothesis testing,the result shows that the theory and methods proposed in this thesis are effective.