Hypothesis Testing In Outcome-dependent Sampling Design Under Generalized Linear Models

In many large cohort studies,observations of primary covariates can be expensive or time-consuming,resulting in a sharp increase in the budget and cost of the study.In the case of limited research resources,researchers have a tendency to use some cost-effectiveness sampling strategy to improve research efficiency.Outcome-dependent sampling(ODS)design is a retrospective biased sampling scheme where one assembles the primary covariates with a probability that depends on the observed outcome values.Thus,researchers attempt to select more subjects from the resources where there is the greatest amount of information to reduce the cost and increase the efficiency.The generalized linear models(GLMs)are flexibly fitted data and widely used in many fields as an extension of the classical linear model.Under the frame of GLMs,the distribution of outcome is assumed to be generated from a specific distribution in the exponential family,and the outcome is connected to the linear predictor by a link function.However,there are few work about hypothesis testing procedures of the GLMS under the ODS design.In this paper,we study how to test hypotheses on the parameters of the GLMs under the ODS design.Based on a profile-likelihood function obtained by a semiparametric empirical likelihood approach,we construct likelihood-ratio,Wald and score test statistics.Asymptotic properties of the proposed tests are established and the null limiting distributions are derived.The finite-sample behavior of the proposed methods is evaluated through simulation studies,and an application to a Wilms tumor data is illustrated to demonstrate the application value in practice.This paper is organized as follows:In chapter 1,we introduce the backgrounds of this paper,review the current development situations of the research direction,summarize the previous results and present the main content and the innovation of this paper.In chapter 2,we review a semiparametric empirical likelihood inference method for the regression parameter of the GLMs under the ODS design.In chapter 3,we propose the hypothesis testing procedures and establish the asymptotic properties of the proposed test statistics.In chapter 4,we conduct a series of simulation studies to assess the finite-sample performance of the proposed tests.In chapter 5,We illustrate the proposed method by analyzing a data set from a Wilms tumor study to demonstrate the application value in practice.In Chapter 6,we summarize the main work of this paper and further prospects for future research work.