Statistical Inference Methods And Applications Of Outcome-Dependent Sampling Designs Under Generalized Linear Models

In many large cohort studies,the measurement cost of primary exposure variables is always expensive.With a limited budget,the researchers need to find a cost-effective sampling design to address this problem.The outcome-dependent sampling(ODS)design is a retrospective sampling scheme where one assembles the important expo-sure variables with a probability that depends on the observed outcome values.While obtaining overall information about the population,the ODS design concentrates re-sources where there is the greatest amount of information about the exposure-response relationship.Thus,this biased-sampling method can improve the efficiency and reduce the cost of studies effectively.As an extension of the classical linear models,the gener-alized linear models(GLMs),enjoying the great flexibility,have been applied in many research fields.By assuming that the distribution of response variable is a member of the exponential family and introducing a link function to establish the connection between the conditional expectation of response variable and the linear predictor,the GLMs receive wider attention and application in numerous fields than classical linear models.However,there are few developments having been done with the GLMs for data from the ODS designs.In this paper,we study how to fit the GLMs to data obtained by the original ODS design and the two-phase ODS design respectively,establish corresponding statistical inference methods and discuss the asymptotic theory of the proposed estimators.We conduct a series of simulations to assess the finite-sample performance of the proposed estimators and apply the proposed methods to real data analysis to demonstrate the application value in practice.This thesis consists of six parts as follows:In chapter 1,we introduce the backgrounds of this thesis,review the current devel-opment situations of the research direction,summarize the previous results and present the main work and the innovation,of this thesis.In chapter 2,we propose a semiparametric empirical likelihood inference method for the regression parameter of GLMs using data from the original ODS design,and establish the asymptotic theory of the proposed estimation method.In chapter 3,we propose the maximum semiparametric empirical likelihood esti-mator and its asymptotic properties for the regression parameter of GLMs using data from the two-phase ODS design.In chapter 4,we conduct a series of simulations to assess the finite-sample perfor-mance of the above two ODS designs.In chapter 5,we analyze two real data—the Wilms tumor data and an air quality data,to assess the applications of our proposed methods in practice.In chapter 6,we summary the main work of this thesis and further prospects for future research work.