Hypothesis Testing In Linear Regression Model Under Outcome-Dependent Sampling Design

A cost-effective sampling design is desirable in large cohort studies due to the cost of measurement on expensive covariates.An outcome-dependent sampling(ODS)design is such a biased-sampling scheme which can improve efficiency by allowing researchers to oversample in the regions of most information.The ODS design is a retrospective sampling scheme where one assembles the important exposure variables with a prob-ability that depends on the observed outcome values.The advantage of such ODS design is that,while providing overall information about the population,it allows the researchers to concentrate resources on the region that of the greatest amount of infor-mation about the exposure-response relationship.The linear regression model is one of the most widely used models for studying the relationship between covariates and outcome variables.However,there are few developments having been done with the hypothesis testing problems for the linear regression model under an ODS design.We study hypothesis testing under the linear regression model for data from the ODS design.We propose a likelihood ratio statistic and a Wald statistic for testing the significance of the model,and a U statistic for testing the significance of regression parameter by applying a semiparametric empirical profile-likelihood method.We es-tablish the asymptotic theory for the proposed test statistics.We conduct simulation studies to assess the finite-sample performance of the proposed tests.We illustrate the application of the proposed methods with a real data example.This thesis consists of five parts as follows:In Chapter 1,we introduce the backgrounds of this thesis,review the current development situations of the research direction,summarize the previous results and present the main work and the innovation of this thesis.In Chapter 2,we first introduce a semiparametric empirical likelihood estimator of regression parameter.We then propose test statistics for the hypothesis testing problems under the linear regression model.We establish the asymptotic theory for the proposed test statistics.In Chapter 3,we conduct a series of simulation studies to assess the finite-sample performance of the proposed testing methods.In Chapter 4,we analyze a real data to assess the applications of our proposed methods in practice.In Chapter 5,we summary the main work of this thesis and further prospects for future research work.