Semiparametric Empirical Likelihood Estimation for Two-stage Outcome-dependent Sampling under the Frame of Generalized Linear Models

Epidemiologic studies use outcome-dependent sampling （ODS） schemes where, in addition to a simple random sample, there are also a number of supplement samples that are collected based on outcome variable. ODS scheme is a cost-effective way to improve study efficiency. We develop a maximum semiparametric empirical likelihood estimation （MSELE） for data from a two-stage ODS scheme under the assumption that given covariate, the outcome follows a general linear model. The information of both validation samples and nonvalidation samples are used. What is more, we prove the asymptotic properties of the proposed MSELE.