On The Special Designs In Survival Analysis

Survival analysis, also called duration analysis, is an important hot topic in recent thirty years. It was originally raised in medical research, but has been widely used in other areas such as quality control, socio-economics, finance, etc. Methodologies are required for various applications in all these areas. More recently, in socio-economics, management, finance, medical science, etc, there are more and more data from special-ly designed studies, for instance, data from two-stage sampling, doubly truncated data, case-cohort data and nested case-control data, etc. It is important and difficult to anal-ysis these survival data. Unlike the usual cohort study, these specially designed studies deal with dependent censoring, limited sampling frame, low incidence and other com-plex cases. Due to the complexity of the data, the classical approaches are no longer appropriate and specially designed methods are required for corresponding situation.Based on the literatures, this thesis works on the statistical inference for data from specially designed studies and is mainly divided into four parts.First, for data from two-stage sampling, based on the semi-Markov model, the nonparametric maximum likelihood estimator is proposed and is shown to be asymp-totic normal and asymptotic efficient. In addition, a uniform consistent estimator for the covariance function of the proposed estimator is provided. This approach is more efficient than the existing one and makes it possible for inference.Second, for doubly truncated data, the accelerated failure time model is studied and an estimator is proposed for the regression coefficient. The proposed estimator is shown to be consistent asymptotic normal. Besides, the random weighting based procedure is proposed for inference. The corresponding perturbed estimator is shown to be conditionally asymptotic normal given the observed data.Third, for the case cohort data, an estimation procedure is proposed for the quantile regression model. The corresponding estimator is shown to be consistent and asymp-totic normal. To conduct the inference, a new specific random weighting procedure is proposed and is justified via joint asymptotic normality. It is the first time that the quantile regression is studied under case cohort design.Finally, for the nested case-control data, an estimation procedure is proposed for the quantile regression model and similar results are obtained as for the case cohort data. Also, it is the first time that the quantile regression is studied under nested case-control design.