title: Estimation of a partially linear additive model for data from an outcome-dependent sampling design with a continuous outcome.
abstract: Outcome-dependent sampling (ODS) designs have been well recognized as a cost-effective way to enhance study efficiency in both statistical literature and biomedical and epidemiologic studies. A partially linear additive model (PLAM) is widely applied in real problems because it allows for a flexible specification of the dependence of the response on some covariates in a linear fashion and other covariates in a nonlinear non-parametric fashion. Motivated by an epidemiological study investigating the effect of prenatal polychlorinated biphenyls exposure on children's intelligence quotient (IQ) at age 7 years, we propose a PLAM in this article to investigate a more flexible non-parametric inference on the relationships among the response and covariates under the ODS scheme. We propose the estimation method and establish the asymptotic properties of the proposed estimator. Simulation studies are conducted to show the improved efficiency of the proposed ODS estimator for PLAM compared with that from a traditional simple random sampling design with the same sample size. The data of the above-mentioned study is analyzed to illustrate the proposed method.
authors.affiliation: Department of Biostatistics, School of Public Health and Key Laboratory of Public Health Safety, Fudan University, Shanghai 200032, China.
authors.forename: Ziwen
authors.initials: Z
authors.lastname: Tan
authors.affiliation: Department of Biostatistics, School of Public Health and Key Laboratory of Public Health Safety, Fudan University, Shanghai 200032, China gyqin@fudan.edu.cn.
authors.forename: Guoyou
authors.initials: G
authors.lastname: Qin
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
authors.forename: Haibo
authors.initials: H
authors.lastname: Zhou
mesh_terms: D002648:Child; D002657:Child Development / Q000502:physiology; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D007360:Intelligence / Q000502:physiology; D008962:Models, Theoretical; D011247:Pregnancy; D011297:Prenatal Exposure Delayed Effects / Q000139:chemically induced; D012107:Research Design / Q000592:standards*
keywords: Design-based sampling; Empirical likelihood; Polychlorinated biphenyls; Semi-parametric model